THE UNIVERSITY OF M I C H I GA N COLLEGE OF ENGINEERING Department of Nuclear Engineering Technical Report SCINTILLATION ANISOTROPY IN CRYSTALLINE ANTHRACENE Donald Bruce Oliver Glenn F. Knoll ORA Project 07357 supported by: NATIONAL SCIENCE FOUNDATION GRANT NO. GK-433 WASHINGTON, D. C. 20550 administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR June 1969

This report was also a dissertation submitted by the first author in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan, 1969. ii

TABLE OF CONTENTS Page LIST OF TABLES v LIST OF FIGURES vi CHAPTER 1. INTRODUCTION 1 1.1. Background 1 1.1.1. Properties of crystalline anthracene 2 1.1.2. Previous scintillation experiments 2 1.2. The Present Investigation 8 2. CHARGED PARTICLE INTERACTIONS IN CRYSTALLINE ANTHRACENE 11 2.1. Introduction 11 2.2. Primary Processes 11 2.3. Secondary Processes 16 3. ANALYSIS OF THE SCINTILLATION PROCESS IN CRYSTALLINE ANTHRACENE 19 3.1. Introduction 19 5.2. Static Quenching Model 20 352.1. Partition of the specific energy loss 21 3.2.2. Extension of the model to anisotropic media 23 3.3. Dynamic Quenching Models 29 3.3.1. General equations 30 5.5.2. Biexcitonic quenching model 40 3.3.3. Linear quenching model 49 4. THE SCINTILLATION RESPONSE TO PROTONS AND CARBON IONS 58 4.1. Introduction 58 4.2. Experimental Arrangement 63 4.2.1. Scattering system 63 4.2.2. Detection and analysis systems 64 4.3. Experimental Technique 66 4.3.1. Practical considerations 66 4.3.2. Timing and discrimination 71 4.3.3. Measurements 76 4.4. Experimental Results 80 4.4.1. Directional response scans 83 4.4.2. Energy response 90 iii

TABLE OF CONTENTS (Concluded) CHAPTER Page 4.5. Discussion of Results 92 4.5.1. Static quenching 92 4.5-2. Dynamic quenching 94 5. RADIATION DAMAGE EFFECTS ON THE DIRECTIONAL RESPONSE 98 5.1. Introduction 98 5.2. Experimental Arrangement 99 5.2.1. Reflecting chamber 99 5.2.2. Detection and analysis system 101 5.3. Experimental Technique 103 5.3.1. Electronic system parameters 103 5.3.2. Empirical investigation of perturbations 104 5.3.3. Measurements 107 5.4. Experimental Results 111 5.4.1. Response scans with no damage 112 5.4.2. Response after radiation damage 114 5.5. Discussion of Results 117 5.5.1. Prompt component 117 5.5.2. Delayed component 117 6. CONCLUSIONS 119 6.1. This Study 119 6.2. Suggested Experiments 120 REFERENCES 122 iv

LIST OF TABLES Table Page 1. Diffusion and Interaction Constants 32 2. Significant Interactions in Scintillator I 72 3. Response Anisotropy Ratios I 83 4. Response Anisotropy Ratios II 112 v

LIST OF FIGURES Figure Page 1. Positions of the anthracene molecules in the unit cell. 5 2. Scintillation response of anthracene crystals-I. 4 3. Channeling effects in anthracene. 7 4. Characteristic times of selected processes. 12 5. Energy level diagram for crystalline anthracene. 15 6. Partition of specific energy loss. 24 7. Weighted difference in specific light yield as a function of specific energy loss-I. 28 8. Computer solutions of the diffusion-kinetics equation. 42 9. Scintillation response of anthracene crystals-II. 44 10. Scattering arrangement. 59 11. Pictorial view of experimental apparatus. 60 12. Electronic system-I. 62 13. Relationship between ion recoil direction and crystallographic axes. 67 14. Scintillation pulse height spectra in scintillator II-I. 77 15. Scintillation pulse height spectra in scintillator II-II. 78 16. Recoil carbon ion scintillation pulse height spectrum in anthracene crystal. 81 17. Recoil proton scintillation pulse height spectrum in anthracene crystal. 82 18. Directional response of anthracene crystal to 0.92 MeV protons. 84 vi

LIST OF FIGURES Figure Page 1. Positions of the anthracene molecules in the unit cell. 5 2. Scintillation response of anthracene crystals-I. 4 5. Channeling effects in anthracene. 7 4. Characteristic times of selected processes. 12 5. Energy level diagram for crystalline anthracene. 13 6. Partition of specific energy loss. 24 7. Weighted difference in specific light yield as a function of specific energy loss-I. 28 8. Computer solutions of the diffusion-kinetics equation. 42 9. Scintillation response of anthracene crystals-II. 44 10. Scattering arrangement. 59 11. Pictorial view of experimental apparatus. 60 12. Electronic system-I. 62 13. Relationship between ion recoil direction and crystallographic axes. 67 14. Scintillation pulse height spectra in scintillator II-I. 77 15. Scintillation pulse height spectra in scintillator II-II. 78 16. Recoil carbon ion scintillation pulse height spectrum in anthracene crystal. 81 17. Recoil proton scintillation pulse height spectrum in anthracene crystal. 82 18. Directional response of anthracene crystal to 0.92 MeV protons. 84 vii

LIST OF FIGURES (Concluded) Figure Page 19. Directional response of anthracene crystal to 1.88 MeV protons. 20. Directional response of anthracene crystal to 3 MeV carbon ions* 21. Directional response of anthracene crystal to 4.8 and 7.3 Mel protons. 22. Directional response of anthracene crystal to 0.92 and 7.3 MeV protons and 3 MeV carbon ions. 25. Directional response of anthracene crystal as a function of energy. 24. Weighted difference in specific light yield as a function of specific energy loss-II. 25. Scintillation response of anthracene crystals-Ill. 26. Reflecting chamber. 27. Electronic system-II. 28. Two-dimensional prompt and delayed scintillation component pulse height spectrum for gamma ray and alpha particle excitation. 29. Prompt scintillation component pulse height spectrum. 30. Delayed scintillation component pulse height spectrum. 31. Prompt and delayed directional scintillation response of anthracene crystal to 5.3 MeV alpha particles. 32. Effects of radiation damage on the prompt directional scintillation response. 33. Variation of prompt and delayed scintillation response with Co-60 gamma ray dose. 85 86 V 87 89 91 93 95 100 102 106 lo09 109 115 viii

CHAPTER 1 INTRODUCTION The subject of this dissertation is the directional dependence in the scintillation light yield of crystalline anthracene. Original experimental results are presented which show the influence of the specific energy loss of excitation particles and the effects of permanent radiation damage. Interpretation of the results is based on three models of the scintillation process. In each model the directional variations in the light yield are assumed to result from different fundamental excitation or energy transfer mechanisms. Anisotropic exciton diffusion is concluded to be the most plausible source of the directional effects. 1.o 1 BACKGROUND In 1958 Coon first noted that the total scintillation light yield (response) of anthracene, stilbene, and p-terphenyl crystals depends on the direction of incidence of monoenergetic fast neutrons relative to the crystallographic axes of the scintillators. Measurements indicated a maximum variation in light yield of 15,0 for 14 MeV incident neutrons. Subsequently there have been numerous investigations of the phenomenon. eKeinzle iand Flammersfeld examined twelve crystalline organic compounds and found the scintillation response to 8.75 MeV alpha particles to be directionally dependent in all cases. There is no experimental evidence of anisotropic response to electrons. 1

2 Crystalline anthracene was selected for the investigation reported here because large crystals of adequate purity are easily obtained and many of the solid state phenomena in anthracene are reasonably well understood. 1.1.1. Properties of Crystalline Anthracene Anthracene molecules (C14H1o) in the condensed phase form monoclinic crystals belonging to the space group P2 /. There are two molecules per unit cell as illustrated in Figure 1. The angle defined by the a and c axes is 1247~0. Shown in the figure with the true crystal axes (a,b, and c) is the artificial axis (c') which is normal to the ab plane. It is defined for future convenience. Dimensions of the unit cell are: a = 8.56 A, b = 6.04 A, and c = 11.16 A. The ab plane is the only prominent cleavage plane. Large anthracene crystals are grown from the melt by the Bridgman method. As a result the crystals are in the form of long cylinders with the ab cleavage plane perpendicular to the axis of the cylinder. Right circular cylindrical crystals of a desired length, such as those used in the present study, are obtained by cleaving the long crystal. Small crystals have often been used in response anisotropy measurements involving alpha particles. Such crystals are grown from solution or by vacuum deposition and have the form of lamella with the flat surfaces parallel to the ab crystal plane. 1.1.2. Previous Scintillation Experiments Figure 2 illustrates the results of several room temperature scintillation experiments involving anthracene crystals. Specific scintillation light yield (dL/dx) is plotted as a function of specific energy loss (dE/dx)

3 a 1 2 3 4 5 6 7 8 9 10 o I,, I I I I I I A FIGURE 1 Positions of the anthracene molecules in the unit cell.

4 0.5 E P,c' U P a I& Pc' Deuteron Energy (MeV) / '0.1 i,,1 0..03 0.12 1.0 1 4.0 =-a SpecAlpha Particle Energy ( MeV ) cm.05are curves fitting the alpha particle and deutern results f chtt.b 5 2 1 0.5 0.20.1 -- isProton Energy (MeV) 30 20 10 Maximum dE/dx for Protons Deuteron Energy (MeV) Maximum dE/dx for Alpha Particles 01form of Birk formula is dL/dx = (dE/dx)I(l + KBdE/dx) 1 where.03 0.1 1.0 4.0 Specific Energy Loss= 5.28 x 103 cm MeV cm-1 ) C urv e labels (P, D, and by) and (a, b, an d c') indicate respectively the type of exciting particle (protons, deuterons, and alpha particles) and from direwhich crystal axis (a, b, ther c) is p arallel to the direction of incidence tween are curves fitting the alpha particle and deuteron results of Schottimilar is a curve generated by Birks' formula4 which describes Brook's compilation of anthracene response data to 1956.7 In most cases the data was obtained for particles incident parallel to the c' axis. The normalized form of Birk's formula is dL/dx = (dE/dx)(1 + KBdE/dx)-l where KB = 5.28 x l1-3 cm MeV-1 for agreement with Brook's results. are curves generated by Birk's formula with KB adjusted to fit the results of Tsukada et al.6 The relation between proton energy and dE/dx was obtained from direct measurements8 and by the calculational method of Whaling.9 The relation between alpha particle energy and dE/dx is that given by Brooks.7 The similar relation for deuterons is that given by Sch'ott.5 FIGURE 2 Scintillation response of anthracene crystals-I.

5 and the direction of the exciting particle relative to the set of orthogonal crystal axes (a,b, and c'). The light yield is normalized to that produced in the same crystal by a 1 MeV electron. It is clear that dL/dx for heavy charged particles varies nonlinearly with dE/dx and is directionally dependent for dE/dx values greater than about 40 MeV cm-1. The nonlinearity in specific light yield is commonly attributed to a process called "ionization quenching." The specific response to alpha particles begins to limit (saturate) at approximately 500 MeV cm-, and the response to protons and deuterons appears to approach saturation in a similar manner. Consequently, the ratio of the specific light yield for particles incident in one direction to the yield for particles incident in another direction (the specific response anisotropy ratio) tends toward a limiting valueo The limiting value is apparently about the same for both alpha particle and proton excitation. There is some uncertainty about the behavior of dL/dx for different types of heavy charged particles which are incident in the same direction. Birks assumes that dL/dx is the same for protons and alpha particles with the same dE/dx; whereas Schott's deuteron and alpha particle experiments imply a difference. Schott's alpha particle results also show a decrease in dL/dx as dE/dx becomes greater than about 500 MeV cm1. Voltz et al. have performed relevant experiments with thin films of Ne 102 plastic scintillator. dL/dx and dE/dx were measured directly. The results indicate that the maximum value of dL/dx differs for alpha particle and proton excitation, and dL/dx decreases as dE/dx increases beyond the value corresponding to the maximum dL/dx.

6 During measurements of the directional response of a thin (70 micron) anthracene crystal to alpha particles, Wick and Flammersfeld observed an effect which they attribute to "channeling." A plot of the response for directions of incidence parallel to the ac plane is illustrated in Figure 5. It is noted that small decreases in the response for narrowly resolved directions are superimposed upon the slowly varying portion of the directional light yield. Alpha particles incident in the directions corresponding to the small decreases in the yield are assumed to have easily penetrated the very thin crystals along channels. As a result, the total light yield was less than for other directions of incidence. The stopping power measurements of 12 Brandt et al. corroborate the existence of such channeling in anthracene. Since dL/dx and dE/dx were measured directly in the case of the anisotropic response to deuterons shown in Figure 2, it seems clear that the slowly varying response is not a result of channeling. The time behavior of the scintillation light emission can be described in terms of several distinct components. Most of the light appears as a prompt emission component which decays exponentially. The time constant varies between 10 and 30 nanoseconds depending on the purity of the crystal and 4 reabsorption effects. Recently, evidence of a small short lived component with an exponential decay constant of about 6 nanoseconds has been noted. 3' Some of the light is emitted nonexponentially over a much longer period on the order of microseconds. The relative fraction of the total yield which is contained in this delayed component increases with increasing dE/dx. 5 Apparently, the light in all the emission components arises from similar

7 a) 4-).70 C: 6c 5 Cl) L CI I I I I It I tI I I I I I I I 600 400 200 00 e 200 400 600 Scintillation yield of a 70 micron thick anthracene crystal as a function of direction for 6.75 MeV alpha particles incident in the ac crystallographic plane.1-1 The angle in the ac of incidence is 0. plane between the c' crystal axis and the direction FIGURE 35 Channeling effects in anthracene.

8 electronic transitions since the emission spectrum is not a function of time. It has been shown 178 that the response anisotropy is much greater for the prompt component than the delayed. Since most of the light is emitted as the prompt component, the total response anisotropy is essentially the same as that of the prompt component; therefore, no distinction is made in Figure 2 between the prompt and the total emission. 1.2. THE PRESENT INVESTIGATION Although luminescence phenomena in organic crystals have been intensively investigated, the origin of ionization quenching and the directional anisotropy in the scintillation response remain unclear. A prominent feature of both effects is the strong dependence on the specific energy loss of the incident particles. The purpose of the experimental study reported here was a better understanding of the nature of the response anisotropy. Two separate investigations comprised the study. In the first investigation the response anisotropy in large anthracene crystals was measured with exciting particles having a significantly wider range of average specific energy loss than any employed in previous experiments. A novel method based onHofstadter'sCompton spectrometer technique19 was used for the measurements. Recoil protons and carbon ions with a continuous spectrum of energies were produced in the crystal of interest by fast neutron scattering. A two detector coincidence system allowed analysis of selected scintillation events corresponding to monoenergetic particles recoil

9 ing in a unique direction. Recoil directions in the ac plane near the c' axis and inclined toward the a axis resulted in maximum scintillation yields for both proton and carbon ion excitation. Minimum yields were noted. for recoils parallel to the b crystal axis. The directional response was measured for protons with energies ranging from 0.92 to 7.3 MeV. For 7.3 MeV protons the maximum directional variation in the response was 20%. As the energy was decreased to 0.92 MeV, the variation increased to 35%. Response measurements were made for recoil carbon ions with energies between 2 and 3.5 MeV. The results provide the first accurate values for the magnitude and the anisotropy of the response of anthracene to carbon ions in this energy range. For recoil directions giving maximum response the light yield per MeV was 1.9% of that produced by a 1 MeV electron. Over the energy range considered, the maximum directional variation of the yield for carariation ions remained constant at 40l0. It is significant that the maximum variation in the directional light yield for 0.92 MeV protons and 2 to 53.5 MeV carbon ions differs by only 10%, whereas the average specific energy loss differs by a factor of 10. The object of the second investigation was the determination of the effects of permanent radiation damage on the anisotropy of both the prompt and the delayed emission components. Excitation was provided by 5.5 MeV alpha particles. The response was measured for various directions of incidence parallel to the ab crystal plane. With no radiation damage the maximum variation in the prompt component was 26.5%. The percentage variation remained essentially unchanged as the crystal was subjected to 1000 kilorad of co-60

10 gamma radiation. However, the maximum percentage variation in the delayed scintillation yield gradually increased from 5.60 for the case of no damage to 14.5% when the cumulative gamma ray dose reached 500 kilorad. Interpretation of the experimental results is necessarily based on a detailed description of the scintillation process since the directional dependence of the scintillation yield is a consequence of one or more of the many processes which follow in the wake of an energetic heavy charged particle. In Chapters 2 and 3 of this dissertation three models are formulated each emphasizing different processes. Four possibilities are examined: (1) anisotropic initial yield of the excited states which lead to fluorescence, (2) anisotropic quenching of the initial excited states by transient quenchers, (3) anisotropic exciton diffusion resulting in a directionally dependent rate of biexcitonic annihilation (quenching) of excitons, (4) anisotropic exciton diffusion out of the original excitation column where quenching results from damaged molecules. The features of model (3) are concluded to be the most consistent with published results and the experimental results of the present studies.

CHAPTER 2 CHARGED PARTICLE INTERACTIONS IN CRYSTALLINE ANTHRACENE 2.1. INTRODUCTION In this chapter a basis is established for subsequent formulations of the scintillation process in anthracene crystals. A qualitative description is given of the sequence of events which occur on a microscopic scale in a crystal along the track of an energetic charged particle. Pertinent terminology is also clarified. The description is founded on several dis7,20,21,22 cussions 7' '' of charged particle interactions in condensed media. Anthracene, in particular, is considered where appropriate. The two following figures serve as a prelude to the discussion. Figure 4 summarizes the order of magnitude estimates by Hart and Platzman21 for the duration of relevant processes or events in liquids or solids. For convenience these and other processes will be categorized as primary and secondary processes. In general the primary processes are involved in the initial deposition of energy by an incident particle; whereas the secondary processes are involved in the evolution of the initial excitation and ionization. Figure 5 shows an energy level diagram for various states in crystal25,24 line anthracene. 2.2. PRIMARY PROCESSES When an energetic charged particle traverses a solid it loses energy predominantly in direct molecular excitation and ionization events. These 11

12 1C 1C 1C )-17 --16 -15 - Moderation of a. "non-subexcitation" electron (time per eV lost) - Excitation or ionization by a charged particle - Period of electronic oscillation - Period of molecular vibration - Internal conversion in polyatomic molecule or ion - Dissociation of polyatomic molecule or ion - Absorption of a 5 MeV alpha particle -14 10 - -13 10 -12 10 C1) 0L) -p 4-).-p C1);41 co -11, -10 10 - Moderation of a subexcitation electron (time per eV lost) - Lifetime of lowest excited singlet states -8 10 10-7 lO3~ -2 10 10-1 10 - Lifetime of lowest triplet states FIGURE 4 Characteristic times of selected processes.

15 (U) U) 5 4-, o 0 (U 0 s^ pq 6 5.65 5 4.1 4 _ 3.7 5.15 3 - 2 1.8 1 //////// // Ionization energy of molecule in crystal '///// //// Conduction threshold (upper band) Conduction threshold (lower band) Si T1 0 SO Singlet and triplet exciton bands are labeled by Si and Ti respectively. The subscript identifies the band level. FIGURE 5 Energy level diagram for crystalline anthracene.

14 are called "primary events," and they necessarily occur near the path of the particle. Ensuing events are termed "secondary events." Electrons ejected during ionization have a spectrum of energies which is peaked at the low energy end. These electrons produce further electronic excitation and ionization when energetically allowed. Once the energy of an ejected electron is below that necessary for electronic excitation, the electron is termed a "subexcitation electron" and loses energy more slowly by exciting only vibrational states. Since the elastic scattering probability for ejected electrons is roughly proportional to the inverse square of electron energy, 5 the majority of the electrons are reduced to subexcitation electrons in the vicinity of the initial ionization. However, a few ejected electrons have enough energy (more than 75 to 100 eV) to travel relatively large distances while losing energy much as the original particle. These higher energy electrons are called "delta rays" and in the case of electron, proton, and alpha particle excitation they produce approximately half the total ionization and excitation. Electron-hole pairs produced directly by the original particle or resultant delta rays are referred to as "clusters." A cluster also includes any excitation or ionization produced in the vicinity by the moderation of the ejected electron. Energy loss due to elastic nuclear scattering is a second order effect considering the particles and energies of interest here. Yet, such collisions do result in atomic displacements which contribute to cumulative radia26 tion damage. According to Snyder and Neufeld, the energy dissipated in elastic nuclear collisions by an energetic carbon ion (our most extreme case)

15 does not become equal to that resulting from inelastic electron collisions until the energy of the ion is less than 95 keV. Conservative calculations based on the results of Linhard and Thomsen 7'28 indicate that, at most, 15% of the energy of a 2 MeV carbon ion is expended in elastic nuclear scattering. Other primary events involving energy loss are: direct multiple excitation and ionization of a single molecule, charge pickup and loss by the exciting particle, excitation of pure molecular vibrations, and in the case of fast electrons, bremsstrahlung. These mechanisms are at least an order of magnitude less significant than nuclear scattering in the cases considered here.2129 Thus, the tracks of the incident particle and the delta rays consist essentially of random linear distributions of directly excited molecules and clusters of excited and ionized molecules. In an organic crystal such as anthracene, excited it-orbital singlet states are among those produced directly or during electron moderation. However, it is doubtful whether many I-electron triplet states are formed in this manner since optical transitions from ground it-electron singlet states to excited it-electron triplet states are forbidden. The initially excited Tt-singlet states are considered the origin of the prompt scintillation emission; whereas the delayed emission is thought to arise indirectly from the triplet states produced predominantly by electronhole recombination. The primary processes are considered terminated once the ejected electrons have become subexcitation electrons. Since ejected electrons lose energy in a solid by electronic excitation and ionization at a typical rate of 1017 eV per second, 21 the primary processes usually end less than 10 13 seconds

16 after the primary events. 2.3. SECONDARY PROCESSES As the primary processes subside new (secondary) processes become important. Molecular excitation is dissipated by "internal quenching."* In this way directly formed highly excited. t-electron singlet states decay quickly (10-13 to 10-11 seconds) to the lowest excited states. Excited t-triplet states may decay a bit more slowly. Possibly, some excited it-states result from the deexcitation of a and K- electron states. Electron-hole recombinations yield additional highly excited. singlet and triplet states with subsequent internal quenching. Statistically, it has been calculated3 that as many as 75o of the recombinations result in triplet states. Subexcitation electrons also contribute to the vibrational energy of the system as they are thermalized at a rate of 101l to 1013 eV per second. Temporary and permanent molecular dissociation occurs. Direct dissociation occurs in approximately one-half a molecular vibrational period (about 10 13 seconds), and it probably results from excitation and ionization of 4 a-electrons. Indirect dissociation results from certain statistical concentrations of the vibrational energy of the system. Eventually, the spatial distribution of excitation and ionization begins to change significantly because of energy and charge migration through the *Internal quenching consists of "internal conversion" which is the conversion of electronic excitation to molecular vibrational energy and "internal degredation" which is the transfer of molecular vibrational energy to adjacent molecules of the crystal lattice.

17 crystal lattice. The theory which properly describes the migration of the excited rt-electron energy is included in an area of scientific endeavor recently termed "excitonics." While there is disagreement about which of the various exciton models is most appropriate, it suffices here to consider excitons as wave packets which describe the migration of A-electron singlet and triplet state excitation. Excitation and charge migration result in a variety of interactions. Even though the concept of simple isotropic diffusion is limited, a convenient phenomenological description of the migration and interactions is provided by the following set of coupled equations. Cn. 1 ni = D.V2n. -EK. n. +K..n.- Z K7. n.n.+ Z K nn (2.1) 1 i j ij i jj ji j jkl ijkl i j jkl j k i where: n. = n.(r.,t), the space and time dependent concentration (number 1 i 1 cm 3) of excitons or charges in crystal quantum states of level or type i. (E.g., concentration of singlet or triplet excitons in the lowest excited level.) D. = isotropic diffusion coefficient (cm2sec-1) for members of concentration i. K.. = rate constant (sec-1) for the transition of a member of concentration i to concentration j (first order loss process for the concentration i). K.. = rate constant (sec-1) for the transition of a member of concentration j to concentration i (first order process which increases concentration i).

18 K. = rate constant (cm3sec-1) for the annihilation interaction beikl tween a member of concentration i and a member of concentration j yielding a new member in both concentrations k and 1 (second order process which decreases the concentration i). Kjkli = rate constant (cm3sec-1) for the annihilation interaction between a member of concentration j and a member of concentration k yielding a new member in both concentrations 1 and i (second order process which increases the concentration i). Examples of experimentally established first order processes relevant to the case of anthracene are: (1) Radiative decay of excitons in the lowest excited At-states to ground states, (2) Internal conversion from a higher excited state to a lower one of the same multiplicity, (3) Intersystem crossing between singlet and triplet states, (4) Capture of an exciton by an impurity, damaged molecule, or lattice discontinuity. Examples of second order processes relevant to the case of anthracene are: (1) Biexcitonic annihilation of two singlet excitons producing a ground state singlet and an electron-hole pair, (2) Biexcitonic annihilation of two triplet excitons producing a ground state singlet and an excited singlet or triplet exciton, (3) Electron-hole recombination producing a highly excited singlet or triplet exciton. Recent evidence indicates that additional processes of significance occur!' in crystalline anthracene. One such process is the annihilation of triplet excitons by free electrons. Another process is the conjectured intermediate role of charge-transfer excitons during the conversion of a recombined elec52 tron-hole pair to a singlet or triplet exciton. Because the knowledge about these processes is incomplete, they are not included in the formulations which follow.

CHAPTER 3 ANALYSIS OF THE SCINTILLATION PROCESS IN CRYSTALLINE ANTHRACENE 3.1. INTRODUCTION Considering the primary and secondary processes enumerated in the previous chapter, a variety of mechanisms may be conceived as the source of scintillation response anisotropy and ionization quenching in crystalline anthracene. Since more than one mechanism may be involved, it is an idealization to formulate them separately. However, because of the complexity of the problem, analysis is possible only if one mechanism predominates; and the others produce second order effects. Three models which emphasize different mechanisms are analyzed in this chapter. Numerical estimates are presented, when possible, which allow an evaluation of the models and the corresponding formulations. In the first model (Static Quenching Model) quenching is assumed to take place before any significant migration of excitons. Two alternate mechanisms are proposed in order to explain the observed anisotropy of the prompt scintillation emission. One mechanism is a directionally dependent initial yield of excited it-electron states; whereas the other is directionally dependent quenching. In the second and third models (Dynamic Quenching Models) the quenching is assumed to arise from the migration of excitons. Anisotropic migration is demonstrated to result in directionally dependent quenching and hence anisotropic scintillation response. The predominant process in the second model 19

20 is presumed to be the biexcitonic annihilation of singlet and triplet excitons. In the third model, quenching of diffusing excitons by temporarily damaged molecules is considered to predominate. 3.2. STATIC QUENCHING MODEL The basis for this model is the assumption that the prompt response anisotropy and ionization quenching result from mechanisms which act before the migration of excitons becomes a significant process. Along the tracks of an incident particle and the associated delta rays,,the nonradiative de-excitation of highly excited zt-electron states to ground states is presumed to be enhanced by temporarily disturbed molecules or the high local electric fields resulting from ionization. By the time the t-electron excitation energy begins to migrate, all quenching has subsided; and the excitons diffuse and decay just as if they had been formed by the absorbtion of optical photons. 10 Voltz et al. have formulated a description of the luminescence phenomena in organic materials utilizing the static quenching model. Subsequent analysis of this model is based on their description. The expression they obtained for the prompt specific scintillation component produced by a heavy charged particle is given below. dL/dx = T{s (F /ws)(dE/dx)exp[-BFTdE/dx] + (F /ws)dE/dx (531) where: dL/dx and dE/dx have been previously defined. T = quantum efficiency of fluorescence.* *The probability a transition from the lowest excited jT-singlet state to the ground state will result in a photon escaping the crystal.

21 F = the fraction of dE/dx appearing as delta ray energy. F = the fraction of dE/dx deposited in the track of the incident particle (FT = 1-F ). w = the average energy dissipated by the incident particle per excited singlet state after internal conversion of higher states to the lowest excited level. B = a quenching parameter related to the effectiveness of the quenching centers. 3.2.1. Partition of the Specific Energy Loss A singificant feature of the formulation of Voltz et al. is the separation of the excitation and ionization produced by delta rays from that produced directly in the track of the incident particle. They suggest the following method of estimating the partition of the specific energy loss by use of the Rutherford scattering law and Bethe's stopping power formula.25 The energy transferred in the production of a delta ray is assumed to be large compared to the binding energy of the ejected electron. This assumption allows the scattering collision to be treated as an elastic collision between the incident particle and an initially stationary free electron. The specific energy loss of a heavy charged particle due to elastic collision with free electrons in which at least a minimum amount of energy (T ) is imparted to the electron is T max 2ite 4z2 dT (dE/dx Zc/137 ~V~c (5.2) T e T - o o e where:

22 m = the rest mass of an electron. e e = the charge of an electron. z = the charge of the incident particle. V = the velocity of the incident particle. n = the density of the free electrons. e T = the energy transferred to the electron. T = the maximum energy that can be imparted to an electron. (T = 4m E/M where E and M are the energy and mass of the incident particle respectively.) T = the minimum initial energy of a delta ray assumed hence to be o 100 eV. c = the velocity of light. Z = the charge number of the atoms actually comprising the medium. According to Bethe the specific energy loss of a heavy charged particle due to electronic interactions is 42 4me dE/dx = 2 n Zc/137 << V << c (3.3) e where I for a particular medium can be deduced from experimental results. Voltz et al. used the method of Sternheimer33 to calculate I for NE 102. Similar calculations give a value of I for anthracene of 64.5 eV. The partition F is now given by the ratio (dE/dx) /(dE/dx) or - o /4m E\ \n' e1 F 2 - m; E > MT/4me; Zc/137 << V << c (4) ln MI

25 The validity of Equations (3.2), (3.3), and (3.4) becomes questionable outside the velocity range indicated. The lower limit is of concern here. When the velocity of the incident particle decreases to about that of the orbital electrons of the atoms in the medium (Zc/137), the charge of the particle begins to fluctuate due to charge pick-up and loss. Also, the faster orbital electrons in the medium (K-shell) cease participation in the energy loss process. Thus, there is a decrease in both the effective charge of the incident particle and the effective electron density of the medium. However, if the form of the Equations (3.2) and (3.3) remain valid with appropriately compensated values for z and n, then F5 is affected only through a change in I due to the lack of participation by the inner electrons. Since the logarithm of I is involved, the velocity effect should. be much less pronounced in Equation (3.4) than in either Equation (5.2) or (3.3) considered alone. The partition FE has been calculated by use of Equation (3.4) for the cases of energetic alpha particles, protons, and carbon ions slowing down in an anthracene crystal. It was assumed that I remained constant even though the velocity requirements were not met for all energies considered. Figure 6 shows the results as a plot of F5 versus specific energy loss. Also the value of dE/dx for which the velocity of the particle (V) equals (6c/137) is shown to indicate the more reliable values of F5. 35.2.2. Extension of the Model to Anisotropic Media The exponential quenching factor in Equation (3.1) arises from considering a one dimensional Poisson distribution of quenching centers along the

24.5 Protons Alpha Particles Carbonon Ions.4 v =6c/137.3 36 24 12.2 2.5-3.5 Carbon Ion _____________ Energy (MeV) 25 10 5 1 0.5.1 _ Alpha Particle Energy (MeV) 5 2 1 0.5 02 0.1 Proton Energy (MeV).0 I I I I I I I I I I I I I I 0.1 0.5 1.0 5.0 10.0 dE/dx (x103 MeV cm-1) FE is the fraction of dE/dx appearing as delta ray energy. Alpha particle and proton dE/dx versus energy relation is the same as in Figure 2. Carbon ion dE/dx versus energy relation was obtained from the data of Northcliff28 for the stopping power of carbon for energetic carbon ions. The stopping power of anthracene was deduced from that of carbon by use of the Bragg-Kleeman Rule. 4 FIGURE 6 Partition of specific energy loss.

25 path of the incident particle. All excited. t-electron states which are formed within a critical distance from these centers are assumed to be quenched. The absence of a corresponding quenching factor in the delta ray term is a simplification by Voltz et al.; therefore, an unspecified quenching factor (Q ) will be included subsequently. Voltz et al. imply that their model, qualitatively at least, describes the type of response variation with dE/dx that both they and Schott5 observed for NE 102 and crystalline anthracene respectively. However, for this model to adequately encompass the crystalline organic scintillators it must predict a directional dependence. Two alternate modifications are proposed below in cases (1) and (2). (1) In this case it is proposed that the efficiency of producing excited it-singlet states directly is different for heavy charged particles and low energy electrons than for delta rays. Likewise, the efficiency for direct excitation in anisotropic media is assumed to be anisotropic as well. These effects could result in different directionally dependent values for w in both terms of Equation (3.1). However, because of the multiple scattering of the delta ray electrons, it is assumed that the yield of excited it-singlet states resulting from delta rays is isotropic. (2) As an alternative it is proposed that only the quenching parameter B is dependent on the orientation of the track of the incident particle relative to the crystal axes. Hence the scintillation light yield resulting from excited it-electrons in the track is directionally dependent. In contrast to the quenching in the track, Q6 is presumed to be isotropic because of delta ray scattering. If Q, and w6 are isotropic, the appropriate form of Equation (3.1) for both cases is dLi/dx = rs(dE/dx) (FTwsi.)exp[-BiFTdE/dx] + (F/w)Q}. (5.5)

26 The subscript (i) indicates that either w or B and therefore dL/dx are funcs tions of the direction of incidence of the exciting particle relative to the crystal axes. Both w and B are assumed to be independent of dE/dx. s It is possible to quantitatively test Equation (3.5) for the case of anisotropic response. For example, the difference in the specific light yield for monoenergetic particles incident parallel to..thec' and b crystallographic axes can now be expressed as e dE _ dE k s dE =( exp -B,E )exp -B F d-E x d FT dx- w exp cT dx b T dx (3.6) where the subscript i in Equation (3.5) has been replaced by c' and b for the two directions of incidence, and w equals the average energy expended e per lowest excited j-singlet state by the recoil electrons used for normalization of the light yield. For case (1) B, = Bb and Equation (3.6) can be rewritten as W dL~, d\ d B d w w / _c___ dE' F dE _ e e ( - - - -) (F -) exB F - = - = const. (7) x dxdx dx/ T Td ' T d w x7 scLc sb It is clear that (dL,/dx - dLb/dx)(FT dE/dx)-1 must vary with dE/dx as the inverse of the exponential term for this expression to be valid. In case (2) it is assumed that w sc and w sb = w. Then Equation (3.6) can be written as

27 C dLEbT dE dEx dx b dELB F - exp B F d3p8b l dxdT x = Tdexp C (bF8) The absolute value of the difference of two exponential terms such as ax -bx | e - e, (a and b are constants) increases with increasing values of x to a maximum and then decreases. Eventually the value approaches the absolute value of the most slowly decaying term. Considering Equation (3.8) it is noted that (dL,/dx - dL/dx) (FT dE/dx)-1 should vary with dE/dx in a similar manner. Both cases may be evaluated by referring to Figure 7. In this figure (w /r )(dL,/dx - dL/dx)(FT dE/dx)-1 is plotted as a function of dE/dx. The difference in specific light yield. was obtained from the alpha particle re5 6 sults of Schott and the proton results of Tsukada et al. Corresponding values for FT were obtained from Figure 6. Neither of the curves in Figure 7 has the linear appearance of a logarithmic plot of a single exponential function or the proper curvature of a logarithmic plot of the difference of two exponential functions. The curve corresponding to Schott's data varies by at least 2to from a judicious linear fit of the curve over the dE/dx range of 200 to 1500 MeV cm 1. A similar variation is noted in the curve calculated from the results of Tsukada et al.; however, this curve extends over a much smaller dE/dx range. Allowance for the calculated variation of F with dE/dx in the exponents appearing in Equations (3.7) and (35.8) does not improve the agreement. Likewise, it is doubtful that the approximate nature of the calculated values for FT is the reason for the non-exponential form of the

28 5.0 x -o U-x 1.0 10 x -0 >0. 5 u a) 0.L 0. (1 i clclae ()is c alculated (1) 1) I I I I I I A4. 6. 8 1.0 1.2 1.4 1.6 dE/ex (Xlo3 rMeV cm I) the proton results of Tsukada et al1.6 the elpha particle results of SchbOtt.5 f rom from FIGURE 7 Weighted difference in specific light yield as a function of specific energy loss~-1.

29 experiment-related curves in Figure 7. The assumption that w, w b and B are independent of dE/dx is certainly an approximation; however, it would be surprising if any variation of these quantities with dE/dx is great enough to linearize or reverse the curvature of the relevant curves. In conclusion, it appears there is difficulty in interpreting the phenomenon of directional scintillation response anisotropy by use of the formulation of Voltz et al. 5.53. DYNAMIC QUENCHING MODELS Quenching and. response anisotropy may be consequences of the secondary processes. Since the prompt scintillation decay constant is apparently unaffected by the mechanisms, the processes responsible would be significant during the time interval between 10-13 to 10-9 seconds after the passage of the exciting particle. Equations from the set (2.1) are used in this section for the analysis of the secondary processes in anthracene. Unfortunately, most of the experimentally determined rate constants correspond to the lowest singlet and triplet exciton states. Nevertheless, a description of these states is a good first order approximation. They are the longest lived of those of their respective multiplicities; thus they are probably the most affected if quenching and anisotropy arise from migration. Due to the complexity of the equations describing these states, general solutions are not available. However, with adequate approximations solutions have been obtained. Discussed in order below are: the general equations, initial simplifications, simplified geometry, initial yields, and solutions

30 corresponding to special cases. 53.51. General Equations Once internal conversion from higher levels becomes negligible, the appropriate equations for the exciton concentrations in the lowest excited singlet (s) and triplet (t) levels are: t- = D V2n -(K +K +K +K +K )n -K n 2+K n2 + K n at s s sf sic sq sq st s s s st ant _ t -= Dv2n - (K +K +KK +K )n - K n2 + K n ct t t tp tic tq tq ts t tt t st s (3.9) (3-5.10) where: K,K = fluorescent or phosphorescent decay to the ground. state resf sp. spectively..,K. = decay to the ground state by internal conversion. K siC U~C KDKB sq' tq t t K,K sq tq Kst Kts K,K ss tt = quenching due to permanent radiation damage. = quenching due to transient quenching centers. = intersystem crossing, singlet to triplet or triplet to singlet states respectively. = biexcitonic annihilation. K = biexcitonic annihilation of two triplet excitons leading directly to a singlet exciton (Ktts < 1/2 Ktt). Simple expressions for several of the constants have been used recently by various authors34'35'36'37 in their discussions of exciton migration in organic crystals. The pertinent expressions arise from considering the band

31 model (weak scattering) or the hopping model (strong scattering) of exciton migration. Neither model has been demonstrated experimentally to be precisely correct and the actual case probably lies somewhere between the two. The following expressions are valid in form for both singlet and triplet excitons even though the singlet subscripts are used. Band Model Hopping Model D = - v D = -N d2 s 3 s s 6 h 1 1 ah K = -a v K = - ss 2 ss ss 2 N m c N N K = a vN K = qhq sq sq q sq N where: x = mean free path between exciton-phonon scattering events. s v = exciton velocity. a = cross section (cm2) for exciton-exciton annihilation interaction. ss A simple expression is a = tr2 where r is the effective radius ss m m of an anthracene molecule. a = cross section (cm2) of a quenching site for exciton capture and subsequent quenching (similar form for both transient and permanent damage quenches). N = concentration (number cm 3) of quenching sites (transient or perq manent damage quenchers). N = number of randomly directed hops a hopping exciton makes per sech ond. d2 = mean square displacement of a hopping exciton per hop. E = efficiency of annihilation process. a

32 N = number of anthracene molecules per cm3 (4.2 x 1021 at room temperature). E = efficiency of quenching once the exciton is adjacent to the quenching center. The expressions for K and K are appropriate for a uniform exciton ss sq distribution in an infinite medium. Such is not the case in the wake of a charged particle so the expressions are, at best, only approximate. 3.3.1.1. Initial simplifications For the case of crystalline anthracene typical published experimental values for the coefficients appearing in Equations (3-59) and (3.10) are listed in Table 1. TABLE 1 DIFFUSION AND INTERACTION CONSTANTS D s Kf K. sic Kt K ss K sq = 2 x 10-3(cm2sec-1).35 Dt = 9 x 10(sec'1). = 107(sec-). Ktp Ktic 4 1 ( w -1 37 = 2 x 10 (cm sec1). << 102(sec ). = 102(sec-1).41 is very small. = 5 x 10l(cm3sec-1). = (0 secrad = (0.33 sec-rad-1) = 1.6 - 2.4 x 106(sec-1).38 Kts =.5 - 1.3 x 10-8(cm3sec-1).39 = 68 (sec-lrad-1). Ktt D Ktq The measurement of these constants involved the excitation of pertinent electronic states with optical photons. As a result of the techniques employed,

33 the values correspond to averages for all crystal directions. A notable ex57 ception is the experiment of Levine and Jortner. They determined the triplet exciton diffusion coefficient for the a, b, and c' crystal directions and found it to be isotropic within 20%. The transient quenching coefficients K and K have been proposed to sq tq explain ionization quenching. Since some of the effects of charged. particle excitation are virtually impossible to produce with optical photons, these coefficients have not been measured.and their significance remains conjectural. The importance of various terms in Equations (35.9) and (3.10) can be estimated by use of the experimental values tabulated. above. A comparison of the terms allows immediate simplification of the equations for most purposes. Considering Equation (3.9) it is clear that intersystem crossing from the singlet states to the triplet states is a negligible singlet exciton loss process compared to internal conversion or fluorescent decay to the ground state. The radiation damage term is only significant after the crystal has absorbed an appreciable dose of damaging radiation. Intersystem crossing from triplet states to singlet states is negligible since it is a thermally activated process which proceeds very slowly at room temperature. When only the prompt scintillation component is considered, the contribution of the triplet biexcitonic annihilation term may be neglected in comparison to the singlet biexcitonic loss term. Since the ratio K /Kt is greater than 10 3, the ratio n2/n2 would have to be less than 10-3 for the two terms to s t compete. Such competition in the wake of a charged particle is unlikely because the yield and spatial distributions of ionized. and excited. t-electron

34 22 states should be about the same. Also, electron-hole pairs which produce most of the triplet excitons do not necessarily recombine immediately. Some ejected electrons become trapped and never recombine. The biexcitonic annihilation of triplet excitons is considered partially responsible for the delayed scintillation; thus this process is quite important when the delayed component, rather than the prompt component, is of interest. An examination of the coefficients which appear in Equation (5.10) shows that, at least at room temperature, the loss of triplet excitons due to phosphorescent decay and intersystem crossing to the singlet levels is negligible compared to internal conversion to the ground state. Biexcitonic annihilation competes with internal conversion only in the case of reasonably high concentrations such as exist initially in the track of a heavy charged particle. However, if the singlet exciton concentration is great enough relative to the triplet concentration, as in "flash spectroscopy," intersystem crossing from the singlet population can become important. The radiation damage quenching term becomes significant at a lower accumulated dose than the comparable singlet exciton term, but it is negligible in most instances. 3.3.1.2. Simplified geometry When the specific energy loss is great enough along the track of an incident particle, the clusters and direct excitations overlap to the extent that the initial distribution becomes cylindrical. Once cylindrical geometry is established, axial variations in the excitation and ionization dens

35 ities are negligible along the track compared to the radial variations. Therefore, the concentrations in Equations (3.9) and (3.10) can be considered functions of time and the radial distance from the path of the incident particle only, with the initial conditions being constant for relatively large increments of the track. An expression for the minimum value of specific energy loss (dE/dx)min which results in cylindrical geometry may be obtained as follows. If w is c the average energy dissipated per cluster and FT is the fraction of dE/dx deposited in the track of the incident particle (i.e. not carried off by delta rays) then the average distance (d) between clusters in the track is given by d = ( -T (3.11) T w d c Within the clusters it is reasonable to assume that the probability distribution of the variou s s io a excited molecules is a three dimensional Gaussian 50, 42 centered at some point near the path of the incident particle. ' Samuel 42 and Magee proposed the following initial distribution for the clusters of radicals produced by the electrons ejected in the radiolysis of water. ~(r) = 0 exp[-r /r2], r = 5N 1/3 A (Characteristic radius) where ~(r) is the radical distribution function, 4 is a constant, and N is o o the total number of radicals in a cluster. It is believed that the cluster 50 43 size in water is the minimum possible size. Kuppermann and Belford considered the superposition of an infinite number of equivalent spherical

36 Gaussian distributions with colinear centers. When the centers are separated by twice the characteristic Gaussian radius, the resultant columnar distribution varies less than 3% axially. Thus a simple criterion for the establishment of cylindrical geometry is that value of dE/dx for which d = 2r. This criterion, Equation (3.11) and the expression for r in water yield the desired relation dE/dx w= (1OFTN 1/3 A)-1 (3.12) where N in the case of a solid. is the number of electronically excited molecules and electron-hole pairs. 44 Two independent estimates of w are obtained as follows. Whyte rec cently reviewed, many of the published experimental values for the specific energy expended, by charged particles in the ionization of gases. He concluded that for a wide variety of gases the specific energy expended by electrons, protons and alpha particles is 32 ~ 6 eV per ion pair. This value is essentially independent of particle type and specific energy loss. The frequency distribution for the number of ion-pairs per cluster produced in a cloud chamber shows the average to be 1.62. Thus, the average energy loss per cluster in a gas is 52 ~ 9.7 eV. A comparable value for solids can be ex46 tracted from the experiment of Rauth and Hutchinson. They deduced from the energy loss spectra of a beam of fast electrons (5-20 KeV) which were transmitted through thin plastic and metal foils that the average electron energy loss per primary event (w ) is 60 eV. Assuming that the efficiency of cluster production is the same for the incident electrons and ensuing delta rays, the

57 average energy expended per cluster (w ) is given by = w (l-Fe)/(l-f) (35.15) e where Fe is the fraction of the energy loss carried off by delta rays, and fb is the fraction of the primary events resulting in delta rays.* The e partition Fe for electrons can be calculated in a manner similar to that used for heavy charged particles. A simplified form of Bethe's stopping power formula for electrons is applicable since the velocity of the incident electrons was relatively low (v2/c2 <.079). In an electron-electron collision the most energetic electron after the collision is considered the incident particle for subsequent events; thus the maximum delta ray energy is half the energy (E) of the incident electron. With these considerations and the appro25 priate electron-electron scattering cross section e 1ln(E/2T ) +2 ln(E/2(E-T ) + 2 - E/(E-T ) e 1 0 0 o ln(J E/I) When the value of I for NE 102 scintillating plastic is substituted, Fe is found to range between.314 and.356 for 5 to 20 KeV electrons respectively. The fraction f is simply the ratio of the specific yield of delta rays (dN /dx) to the specific yield of primary events (dN /dx). An expression for dN /dx obtained from the electron-electron scattering cross section is E/2 2te I 1 1 1 dNf/dx = fT m v$ ne [ + (E-T) - T(E-T ]dT 0 e *The energy loss spectra indica ha t practically all primary events are ionizations.

By definition dN/dx is (dE/dx)/w. Introduction of Bethe's simplified expression for dE/dx yields w [1/T - 1/(E-T ) - (1/E) In ((E-T )/T ) 2 In (e/2 E/I) After substitution of the appropriate quantities this ratio is found to vary between 0.0594 and 0.049 for 5 to 20 KeV electrons respectively. Thus, Equation (3.13) can be evaluated. The average energy expended per cluster is found to be about 40 eV. Since this value was deduced for materials similar to anthracene it will be used in the calculation to follow. 47 Newton estimates that there are two excited molecules per electronhole pair. Assuming that there are 1.68 pairs per cluster, a reasonable value for N is - 5. In Figure 6 it is seen that FT for a 5 MeV alpha particle is about 0.56. Substitution of these values into Equation (3.12) gives the following result. (dE/dx)min~ 420 MeV cm1 Even though the assumption of columnar geometry makes Equations (35.9) and (3.10) more tractable, there remains the problem of properly describing the initial radial distribution. The radius of the column of overlapping spheres considered. above represents a lower limit for several reasons. One is the conservative estimate of the radius of a cluster. Another is the assumption that cluster centers are linearly distributed. Finally, the possibility is neglected that some of the clusters produced by delta rays lie near or in the track of the incident particle.

39 3.3.1.3. Initial yields The yield of singlet excitons in the lowest excited level can be obtained from the absolute scintillation efficiency (S ) and related quantities. 4 Birks defines S for pure crystal scintillators as that fraction of the enx ergy deposited in the bulk of a thick crystal by an energetic electron which later escapes from the surface as visible light. Ionization quenching is assumed to be negligible. A useful relation between S and other pertinent x quantities is Sx = (t)ry-) (3-14) where t4 is the average energy of photons escaping from a thick crystal, T is the quantum efficiency of fluorescence, and w is the average energy exs pended by a charged particle for each singlet exciton eventually appearing in the lowest excited level. After a survey of published values for anthracene crystals, Birks proposes 0.04 and 0.68 as the most reliable values for S and ' respectively. (twu) was found from spectroscopic data to be 2.63 eV x s for thick crystals (> 1mm). By use of these values and. Equation (3.14), w s is found to be 44.7 eV per exciton corresponding to a yield of 2.24 x 104 excitons per MeV. Since the delayed scintillation emission contributes only a few per cent in the case of electron excitation, these values can be considered to correspond to the singlets produced during the primary processes. They will also be assumed valid for excitation by heavy charged. particles. An upper limit for the yield of a-electron excitations and ionizations can be obtained by considering the experiments of Swanson and Powell. They

investigated the energy loss spectra of 20 KeV electrons incident normally on very thin films of polystyrene and. similar polymers. Two loss peaks were noted for electrons scattered at zero angle. One at approximately 7 eV and. one at 21.3 eV. The 7 eV peak was attributed. to excitation of zi-electrons in the benzene rings and the 21.3 eV peak to excitation and ionization of crelectrons. Assuming that the latter value is also valid for anthracene and that all energy loss is due to a-electron events, the average energy loss per a-electron excitation or ionization is 21.3 eV. This is equivalent to a yield of 4.7 x 104 a-electron events per MeV. 35.53.2. Biexcitonic Quenching Model In this model the transient quenching due to the temporary disturbances in the wake of the incident particle is neglected. Also, the initial simplifications of subsection 5.5.2 and cylindrical geometry are assumed valid. With these assumptions Equations (3-9) and (3- 10) 6n (r,t) 1 a= D 9r(r )n (rt) - n(r,t) - K n2(r,t) (5.15) st s r 6r s T s s S r n(r,t) - n(r,) - Kttn(r,t) (3-16) where in the absence of quenching by permanent radiation damage T and Tt are the natural lifetimes of the lowest singlet and triplet states respectively. In the case of damage quenching, T = (K +K +K ) 1. Since these equas sf sic tq tions have the same form, an exact analytic solution would satisfy both of

41 them. Such a solution is nonexistent; however, numerical solutions and an approximate analytical solution do exist. The solutions result from various studies of equations of the same form which describe the recombination of ions or the reaction of radicals after an alpha particle passes through a gas or solution. The scintillation problem is discussed in terms of these solutions below. 3.3.2.1. Numerical solutions Two sets of numerical solutions to the radical reaction problem were obtained independently by Fricke and Phillips, 49 and Kuppermann and Belford50 with the aid of fast digital computers. Both sets of results correspond to a similar range of parameters. The solutions have an estimated, accuracy of better than 2% and corresponding solutions agree between the two sets within 1%. Figure 8 shows a plot of the results of Fricke and Phillips which are pertinent to the scintillator problem. The solutions and input parameters have been rephrased in terms related to Equation (3.15). Unfortunately, the range of input parameters is not appropriate for the triplet exciton concentration described by Equation (3.16). The solutions give the light emission integrated from time zero to infinity. The yield (dL/dE) is normalized to that of a 1 MeV electron. Unique solutions are given for each pair of input parameters B and E. The initial radial exciton distribution n (r,o) is ass sumed to be Gaussian. Thus,

4~2 1 0-1 p7 16.1 10.61 4.96 /~.5 0.707 E=(FK /4irD w )(dE/dx) ~ui3 C\J 0 co 0.1 0.2 0.3 0.4 0.5 0.6 0.7 dL/dE G represents the computer solutions of s= D — n -k n ~t s ~ ~ s T S Ss S for B and. E values shown. dLdE=l/T nc n(r, t)derdt r n(r,o)clr FIGURE 8 Computer solutions of the diffusion kinetics equation.

B = R 2/2T D; 0 s s E = (FKS /4rDsw )dE/dx, FT< F 1; n (ro) = (F/w tR2)dE/dx exp[-r2/R2], r < R S S 0 0 0-0 where (dE/dx), w, F and r have been previously defined, F is the effective s T o fraction of the energy loss contributing to the exciton concentration in the column, and R is the characteristic Gaussian radius. There is some uncero tainty in the proper values for R and F because they must account for the delta ray effects in a nonrigorous manner. Since dL/dx = (dL/dE)(dE/dx), it is simple to generate theoretical scintillation response curves from the results shown in Figure 8. The simplest case is when the effective Gaussian radius R is considered constant over the o dE/dx range of interest. Then B is a constant since T and D are presumably s s not functions of dE/dx. Assuming that K and w are constants as well, E ss s varies linearly with dE/dx. Figure 9 shows four d.L/dx versus dE/dx response curves generated under these conditions. Parameters B and E were selected so that the theoretical response would correspond approximately to the experimental results which are also shown in the figure. The relationship between the parameter variations and. the variation of the constants for the four theoretical cases is shown below: Case B E(cm MeV-1) Ds Ro FKqs/Ws (1) 4 x 10-4 3.5 x 10 3(dE/dx) D (1) R(l) (FK /w )(l) (2) 2 x 10 4 1.75 x 10 (dE/dx) 2DS(l) R(l) (FK/w )(1) (3) 4 x 10-4 1.75 x 10-(dE/dx) Ds() R(l) 1/2(FK /w )(1) (4) 16 x 10-4 3.5 x 10-3(dE/dx) D (1) 2R(l) (FKs/ws)(1) s Ss s

0.5 E 0 C?) -0.r1 4-) -C, 0.1 0.05 0.01 0.1 0. 5 1.0 5.0 Specif ic Energy Loss (xl103 MeV cmn'1) 10 are curves generated from computer solutions to the diffusion-kinetics equation. (IL) B = )4x10-4 B = 3.5x10-3 cm MeV' dE/dx (2) B = 2xlO"4, B = l.75x10-3cm MeV_1 dE/dx (3) B = 4xlO-4 B9 = l.75xl0-3 cm MeV'1 dE/dx (4) B = 16xlO-4 B = 3.5x10- cm MeV1 dE/dx - -~-is the curve generated by Birks' formula (KB = 5.28x10-3 cm MeV'1). - -- are curves fitting Schd~tt's alpha particle results5 (Curve labels are the same as in Figure 2. ) FIGURE 9 Scintillation response of anthracene crystals-II.

Here the term labels (1), (2), (3), and (4) correspond to the appropriate case numbers. There are several interesting features about the curves in Figure 9. First, the differential response anisotropy ratio determined from response curves (2) or (3) relative to curve (1) is about the same as that determined experimentally in the same dE/dx range for alpha particles incident in directions parallel to the crystallographic c' and b axes. Therefore, a factor of two variation in D or FK with direction appears adequate to explain the s ss magnitude of the measured response anisotropy. A factor of two variation in R, curves (1) and (4), produces a much smaller effect. Next, it is noted that for certain values of the parameters B and E the absolute magnitude of dL/dx is close to the experimental curves. Also, the variation of dL/dx with dE/dx appears to agree with the general response curve of Birks. However, this type of variation is clearly different from that which Schott observed. The plausibility of the model may be tested by examining the self-consistency of the values for the constants corresponding to the values of B and E which result in approximate agreement between theoretical and experimental response curves. If there is negligible radiation damage T is about s 10-8 seconds. Reliable values for D and w are 2 x 10-3 cm2sec-1 and s s 44.7 x 10-6 MeV per singlet exciton respectively. Thus in case (1) where B = 4 x 10-4, R is uniquely determined and equals 12.6 A. Similarly, E/(dE/dx) = 3.5 x 10-3 cm MeV-1 which requires that FK = 0.4 x 10-cm3sec-1. ss The value of R from above is surprisingly close to the estimated radius o of a cluster, r. Since 1/2 < F < F < 1, K is very near the value detero T- - -- SS

54 mined experimentally. Considering the accuracy with which T, D and K s s ss are known along with the estimate of w, it seems that the constants form a self-consistent set. It is noted that the theoretical results of this model represent only the prompt emission; whereas the experimental curves in Figure 4 include the delayed emission as well as the prompt. While the exact correction necessary in the experimental curves is not known, in general the prompt response would be a fraction of the total light yield shown which decreases slowly with increasing dE/dx. The minimum value of the fraction would not be 4 less than 80% for the dE/dx range considered. This correction would improve the agreement between the experimental and theoretical values of K as dess duced above. The excessive quenching shown by the theoretical response curves at lower dE/dx values could easily be due to the violation of the cylindrical geometry assumption. Likewise, the possibly insufficient quenching at higher values of dE/dx could be corrected if R decreases with increasing dE/dx. Thus, it is concluded that the model considered. here provides a reasonable description of the dynamics of the exciton system which explains both quenching and response anisotropy. 3.3.2.2. Approximate analytical solution When the second order term in either Equations (3.15) or (3.16) is not the dominant loss term, a reasonably accurate approximate analytical solution can be obtained by the method of "forced diffusion." This method was first employed by Jaff51 employed by Jaffe. Essentially the method consists of first neglecting

the second order term in an equation such as (3.15) or (3.16). The resulting equation is linear, and if the initial distribution is in the form of a Gaussian and the medium is infinite, the solution has the form of a Gaussian which spreads spatially and is exponentially damped with time. Finally, the second order term is introduced as a perturbation which is only allowed to provide further damping with time of the Gaussian solution. 52 Recently Blanc et al. applied the technique to the scintillation response problem. They found an expression for the magnitude and time behavior of the prompt scintillation component by solving an equation equivalent to Equation (3.15) using the forced diffusion technique. However, because of the magnitude of the biexcitonic annihilation term required for adequate quenching the approximate solution for this case is probably inaccurate. Fortunately, the second order term is much smaller in the triplet exciton problem. The description of the transient triplet population in the wake of a heavy charged particle as given by a forced diffusion solution of Equation (3.16) has been demonstrated to be appropriate in several cases.53 55 Biexcitonic annihilation of triplet excitons resulting in the direct formation of singlet excitons which promptly decay was assumed the origin of the delayed emission. In particular, the solutions were deemed appropriate for a time greater than 1 microsecond after the primary events; thus any questions about electron-hole recombination and ionization quenching were avoided. For the purpose of analyzing our experimental results it is desirable to have a description of the triplet potion of the triplet population during the evolution of the complete scintillation process so as to include quenching and possible aniso

tropic effects. Therefore, it is assumed that the forced diffusion solution is valid at any time after the formation of the triplet population which is presumed to occur in a short time compared to the time necessary for appreciable triplet diffusion (~ 40 nanoseconds). 53 A general expression for the instantaneous specific light yield (dL(T)/dx) of the delayed component as given by Voltz and Klaustriat is dL(t) 'TsKtts (l/wt..e i t/ ( /wt ) (dE/dx)2exp[-2t/Tt] 2_..t (3.17) dx - 2TR 2 a a ' +E ex E. - E. - - l -) where (1/wt) is the number of triplet excitons eventually formed in the lowest excited level per MeV of energy loss, E = K tt (dE/dx)/8Dtwt, t = R /4D a o t E.(-x) = - f - du 1 x 55 and the other constants are the same as defined previously. King and Voltz deduced that Equation (5.17) describes the published delayed emission decay curves for undamaged anthracene crystals if values for E and t of 0.25 and a 40 nanoseconds are used. If dE/dx = 103 MeV cm-1, w = w, and the values of Ktt and Dt are taken from Table 1, calculations show E to be equal to 0.22 which is surprisingly close to the value above. However, for t to be equal a to 40 nanoseconds, if D is taken from Table 1, R must be equal to 560 A. t o

49 It is conceivable that the subexcitation electrons migrate a substantial distance from the clusters before being finally thermalized. Also, the holes are quite mobile and could diffuse outward from the initial distribution; however, a radial distribution of this magnitude initially upon recombination seems unreasonable. For practical purposes, t << Tt. Likewise, considering the ambiguity a t of the initial conditions it is best to use Equation (3.17) to describe relative light yields with time or other parameters as variables. Therefore, a more usable form is dL(t) (dE/dx) 2exp[-2t/T ] dLt O 2 (5-18) d (_ t+t El( t + _ + E i;t T+ t)a Clearly, the directional anisotropy of the observed delayed emission could arise from a variation of D which would affect E and t in Equation (3.18). Simt a ilarly, radiation damage effects would decrease Tt. 3.3.3. Linear Quenching Model If biexcitonic annihilation in the wake of a heavy charged particle is less significant than was assumed in the previous model, it is possible that temporary quenchers such as dissociated molecules account for the observed quenching and response anisotropy. Presumably the quenching occurs during a time which is short compared to the natural lifetimes of the lowest exciton states; thus it is convenient to investigate both Equations (3.9) and (3.10) during two separate time intervals. The appropriate simplifications of sub

50 section 535.31.1 and the assumption of cylindrical geometry are considered valid for both intervals. 5.3.5.1. Short time interval (10-13 sec < t < 10-9 sec) During this time period quenching by the transient quenching agents is assumed to dominate all other exciton removal processes. Both Equations (3.9) and (3.10) reduce to the form shown below for the singlet exciton concentration. -t s s K )n(rt) - K s(rt)n (rat) (3.19) Here the time and spatial dependence of the transient quenching coefficient have been indicated. The quantitative estimates involved in the analysis of Equation (5.19) are significantly different in the case of singlet excitons from the case of triplet excitons; therefore, the discussion immediately following pertains only to singlet excitons. Relevant comments about the triplet exciton concentration are deferred to the end of the discussion. Even though Equation (3.19) represents a considerable simplification of the original equation, further simplification is necessary before an analytic solution can be obtained. Initially the spatial distributions of the excitons and quenching agents are quite similar; however, during the time interval specified the exciton distribution spreads considerably while the quenching centers remain fixed. This evolution suggests that Equation (3.19) be solved separately for the fixed column defined by the quenchers and for the surrounding region which is free of quenchers.

51 A simple solution to the equation can be obtained with the assumptions: (1) A column of effective radius (R ) is defined by the initial distributions of quenching centers.and excitons (r < R < R ). (2) Once an exciton migrates out of the column (r = R ) it does not return. This corresponds to the condition that n(r,t) vanishes at r = R + \. e (3). The quenching centers are uniformly distributed within the column (r < R ). They are not destroyed upon quenching an exciton and persist until the excitons within the column have escaped or have been quenched. (4) Initially the radial exciton distribution can be represented by the zeroth order regular Bessel function of the first kind. The first zero of the Bessel function is required to occur when r = R + X so that assumption (2) above is fulfilled. The solution to Equation (3.19) under these conditions is n (r,t) = (const.)(exp[-(K + + D )t]) J (2 r), r < R (35.20) s sq R~+? s o R e+ - e where J (2.405 r) is the zeroth order Bessel function of the first kind of o R +\ e parameter (2.405/(R +\)). The singlet excitons which escape from the column are free to migrate and decay naturally just as those formed by a fast electron. Therefore, the prompt components of dL/dx for a heavy charged particle is proportional to that fraction (f ) of the initial exciton yield ((dE/dx)/ws) which escapes e t -9 from the column. Since the quenching rate K is necessarily large, 10-9 secsq onds is essentially infinite when considering the decay of n (r,t) within the s column. If f is the fraction of the exciton yield which is quenched, then e f = (l+f /f )1 since f + f =1. Application of Fick's law at the surface. e q e e q of the column (r = R ) results in e

52 f = dt/f (-D V n(r~t))d' e surface r =R s r t)d - d e s where dS is an element of area on the surface of the column, and V is the r radial part of the gradient operator. Similarly f t 1 dIE> cl-torRK n(rt)dr q column o <r <Re sq d - -e s where d 3r is a volume element within the column. By the use of Green's theorem and the explicit expression for n (rt) 5 00 45d fd( jO~2D n(r,,t)d33Q~7 e o column o<r<R +R_ D d Now' t f K e sq q.4o5 ' D +k s and dL dE/dx dx Kt 1+ sq 5D e Where (1/Ws has been removed by normalization of the light yield to that of a 1 MeV electron. For both the band and hopping model expressions given in subsection 3.5.1 for K it is noted that Kt can be considered the product sq sq

55 of a constant (K) and the concentration of quenching centers N. Assuming that wt is the energy expended per transient quenching center, sq t 1 dE K = K0 d) sq \ t dx sq Now dL = dE/dx 3 dx K dE (3.21) 1+ Wsq 2 dx (sq R ) + where K = a V for the band model, and K = Nh /N for the hopping model. This expression has the same form as Birks' semiempirical formula which has been found to describe most experimental results quite well. Kallmann and Brucker as well as Birks himself have made qualitative comments about the origin of the quenching term (KBdE/dx) in Birks' formula. However, to the knowledge of this author Equation (3.21) above is the first form of the equation in which all terms are expressed as functions of clearly defined parameters. The conditions which are necessary for simple diffusion theory to be valid must be added to the previous list of assumptions. In terms of exciton migration they are: (5) The probability of exciton scattering per unit time (K ) must be significantly greater than the probability of quenching per unit time. Subsequently the requirement K /K < 0.2 will be invoked. (6) Diffusion theory is not accurate within several scattering mean free paths of a boundary in the media.

54 (7) Exciton scattering is assumed isotropic. However, the assumption of isotropic scattering must be violated since of all the factors appearing in Equation (3.21) D is the only one that could s vary enough with direction to produce the observed response anisotropy. Neglecting the 15% difference between prompt and total light yield, it can be shown that Equation (5.21) approximately describes the results of Tsukada et al. for protons incident in the c' and b crystallographic directions if the coefficient of dE/dx in second term in the denominator equals 4 x 10-3 and 7 x 10-3 cm MeV-1 respectively. This relation is equivalent to the following requirement. t K 4 x 103 cm MeV1 dE < sq < 7 x 10-3 cm MeV -) (35.22) dx Y - vdx/ ( + s e Another constraint arises from the assumption that quenching within the column is complete well before fluorescent decay becomes significant. This requirement is met if Kt > 1010 sec. (3-23) sq - Elimination of K between requirements (5) and (3.22) results in sq d< ( 2Ks/( + D (4 x l0- ). (3.24) e Similarly, combination of requirements (3.22) and (3.23) leads to

(7) Exciton scattering is assumed isotropic. However, the assumption of isotropic scattering must be violated since of all the factors appearing in Equation (3.21) D is the only one that could s vary enough with direction to produce the observed response anisotropy. Neglecting the - 15% difference between prompt and total light yield, it can be shown that Equation (3.21) approximately describes the results of Tsukada et al. for protons incident in the c' and b crystallographic directions if the coefficient of dE/dx in second term in the denominator equals 4 x 103 and 7 x 10-3 cm MeV-1 respectively. This relation is equivalent to the following requirement. t K dE 4 x 10-3 cm MeV'- dE < sq < 7 x 10-3 cm MeV d-y) (3.22) dx -- 2 4 +V s e Another constraint arises from the assumption that quenching within the column is complete well before fluorescent decay becomes significant. This requirement is met if t 10 -1 K > 10 sec. (3.23) sq - Elimination of K between requirements (5) and (3.22) results in sq dE< 2Ks/( + D (4 x l03)-l (3.24) e Similarly, combination of requirements (3.22) and (3.23) leads to

55 10/ (7 x 10-3 ) < Ds < d (3.25) e Unless the radial extent of the original column in the wake of a heavy charged particle has been badly underestimated, assumption (6) above implies that the exciton scattering mean free path must be of the order of the intermolecular spacing (a 5 A) for the method of this section to be applicable. 0 Assuming that the scattering mean free path is approximately 5 A, the band model of exciton migration should become equivalent to the hopping model.3 Therefore, further analysis of the inequalities requires the introduction of t only the hopping model expressions for D, K and K. Combination of ins s sq equalities (3.24) and (3.25) and use of the appropriate expressions results in 1.4 x 1012 e dE e < 0 (3-.26) h where d is the root mean square hopping distance which is essentially the scattering mean free path. The number of exciton hops per second N is equivalent to the number of scattering events per second. Results of two independent measurements are compatible with a value for N of 4 x 10+12 sec 1. 57 Considering assumption (6) and the fact that X is probably negligible compared to R, a reasonable value for(R + \)/d is 5. Substitution of these values into relation (3.26) results in the following inequality. 9 MeV cm-1 _ dE/dx < 1250 MeV cm-'. Since as shown in subsection 3.3.1.2 the assumption of cylindrical geometry is not valid for dE/dx values less

56 than about 400 MeV cm-1, it is clear that the lower limit on dE/dx is greater than the inequality above shows. Nevertheless, this range of dE/dx values corresponds to protons with energies of 1 MeV or less and alpha particles in the energy range of 4~ to - 25 MeV. The constraints applied, above can also be used to determine the magnitude of the number of quenching centers necessary to provide an adequate amount of quenching. From requirement (3.23) and the hopping model exprest sion for K it is noted that sq ' 1 \dE q h 7dx 10'~ < 'sq (3.27) N tR2 m e If E = 1, dE/dx = 400 MeV cm-1, X is negligible and R = 25 A, and N = 1012 sec- 1 it is found that 1/wt = 2.06 x 104 quenchers per MeV. Similarly, from sq requirement (5) q h dx sq < 0.2 N JtR2N m e h Considering that dE/dx = 1250 MeV cm-1 and the same values for the other constants as before, it is found that 1/w < 1.32 x 105 quenchers per MeV. It sqis noted that the order of magnitude suggested for (1/w ) by the calculations sq above is the same as that deduced for the upper limit of a-electron excitations per MeV of energy loss. Allowing for the approximate nature of the assumed solution of Equation

57 (3.19) and the numerical estimates employed, it appears that this model gives a plausible description of ionization quenching and response anisotropy for a limited range of dE/dx values. The diffusion kinetics of the triplet population can be treated in a manner analogous to that exploited above, and if assumptions (1) through (4) are met, an expression identical in form to Equation (5.21) is obtained. However, in attempting to relate such a result to the delayed emission observed, it is necessary to introduce the result into the biexcitonic model discussed in subsection 3.3.2. At least it is necessary if the ultimate role of triplet-triplet exciton annihilation in the delayed component is accepted. This additional complication seems unwarranted. for our purposes. 5.5.3.2. Long time interval (10-9 sec < t < a) It was assumed in subsection 5.5.5 that the transient quenchers become ineffective before 10-9 seconds has elapsed after the primary events. Thus, after 10-9 seconds, the remaining singlet exciton population is free to migrate and decay by the natural processes of internal conversion and fluorescence assuming that accumulated radiation damage has not resulted in an appreciable number of lurking permanent quenchers. In any case, the prompt decay and light emission will follow a single exponential as observed experimentally. We will assume that the delayed. emission is adequately described in the discussion of subsection 533.2.

CHAPTER 4 THE SCINTILLATION RESPONSE TO PROTONS AND CARBON IONS 4.1. INTRODUCTION In this chapter an investigation of the directional scintillation response of large anthracene crystals to energetic heavy charged particles is elaborated. The experimental method was based on the internal generation of recoil protons and carbon ions with energies in the MeV range by the scattering of fast monoenergetic neutrons from the nuclei within the crystal. A two detector fastslow coincidence system with variable detector geometry and a variety of discrimination capabilities was employed to select scintillations for analysis arising from monoenergetic protons or carbon ions recoiling in a particular direction relative to the crystal axes. The energy and direction of the selected recoils were continuously variable within certain ranges. In addition, this method of excitation avoided surface effects which can arise when using externally incident particles having a short range in anthracene. The neutron source and detector geometry is illustrated in Figure 10. A photograph of the actual system is shown in Figure 11. Fast neutrons with nearly the same energy were produced at the point labeled "source." Detectors I and II consisted of scintillators I and II directly coupled to photomultiplier (PM) tubes with scintillator I being the anthracene crystal under investigation. The centroids of the neutron source and the scintillators defined a horizontal scattering plane. A small fraction of the source neutrons were scattered from scintillator 58

6o FIGURE 11 Pictorial view of experimental apparatus.

61 I into the solid angle subtended by scintillator II and subsequently interacted in the second detector. For these events, when the corresponding signal from detector I was delayed by approximately the flight time of the neutrons from scintillator I to scintillator II, the signals from the two detectors were in coincidence. A schematic of the electronic system used to select and analyze linear signals from either detector is shown in Figure 12. Before a linear signal corresponding to a scintillation event was analyzed, it was required to pass a fast linear gate and the slow linear gate of the multichannel analyzer (MCA). In the coincidence mode of operation the opening of the fast gate required the proper time relationship between the timing pulses from detectors I and II. The fast signal from detector II was also subjected to amplitude requirements. By use of the pulse shape discrimination (PSD) circuit, the gate of the MCA could be restricted to open only when the signal from detector II corresponded to the detection of a neutron. In the ideal case, the energy and direction of the selected recoiling nuclei in scintillator I were uniquely defined by the energy of the incident neutrons, type of scattering, and the scattering angle (a). However, the finite dimensions of the neutron source and the scintillators introduced a spread in both the energy and direction of the recoils. Also, there was a spread in the source neutron energieso Other deviations from the ideal case arose from chance coincidences and inelastic scattering events. Therefore, the limited resolution of the method prevented the observation of any effects well resolved in direction such as channeling in the crystal.

62 Linear Signal -w~ Space Charge Limited _ h Signal + I (PSD) - - Delay line 4- t Polarity and approximate pulse shape FIGURE 12 Electronic system-I.

4.2. EXPERIMENTAL ARRANGEMENT 4.2.1. Scattering System The nuclear reactions, 1H2(H2,n)2 He3 and 1H3(H2,n)2He4 which served as the fast neutron sources were produced in the target assembly of the Texas Nuclear Corporation neutron generator shown in Figure 11. The generator is of the Cockroft-Walton design, and was operated at a deuteron accelerating potential of 140 kilovolts. Effectively "thick" deuterium and tritium impregnated titanium targets were utilized. The average energies of the neutrons which were emitted in the forward direction were 2.8 and 14.6 MeV respectively. The mechanical support arrangement used to align and adjust the scattering geometry is evident in Figure 11. The cylindrical axis of the anthracene crystal was oriented to coincide with the horizontal scattering plane. The cylindrical axis of detector II was vertical. Freedom of motion was provided as follows: (1) Rotation of the anthracene crystal about its horizontal cylindrical axis. (2) Rotation of the anthracene crystal about a vertical axis through its center. (3) Movement of detector II about the anthracene crystal in the horizontal scattering plane. A cathetometer was used for the initial alignment of the source and detectors and also for periodic checks thereafter. Calculations indicated that the brass shadow shield reduced the number of unscattered source neutrons which reached detector II by a factor of - 102. Structural components were made principally of aluminum and as light in weight

64 as possible in order to reduce the scattering probability for neutrons in the vicinity of the detectors. 4.2.2. Detection and Analysis Systems An RCA 8575 (bialkali photocathode) PM tube was employed in detector I. This tube was selected because of a favorable dark noise spectrum, fast response, and a high quantum efficiency in the wavelength range of the fluorescence of anthracene (4000 - 5000 A). A fast timing signal was taken from dynode 12 of the tube, and a linear signal from the anode. The anthracene crystal of interest constituted the remainder of detector I. A 1" high by 1" diameter cylindrical crystal was used in the measurements reported in this chapter. It was convenient to attach one of the polished ab cleavage surfaces of the crystal to the flat face of the PM tube; optical coupling was provided by Dow Corning 20-057 compound. The remaining surfaces of the crystal were packed with 1/16" of MgO which served as a reflector and then covered with a 1/32" thick aluminum cap for mechanical support. Detector II consisted of a 2 " h14 by.?" diameter encapsulated NE 213 liquid scintillator coupled to an RCA 6810A (S-11 response) PM tube. The NE 213 liquid scintillator had the desirable features of high scintillation efficiency, fast light emission, and excellent pulse shape discrimination (PSD) characteristics. When PSD was required for rejection of gamma ray scintillations, the standard heavy duty voltage divider was replaced by one of Owen's design. 58 A linear signal was taken from dynode 12 and a fast timing signal from dynode 13 or the anode of the PM tube depending on whether or not PSD was employed.

65 As illustrated in Figure 12, timing pulses from detectors I and II were introduced into discriminator-trigger circuits I and II. These circuits provided low level and, in the case of trigger II, simultaneous high level leading edge triggering. Low level triggering provided accurate timing information while the high level allowed a veto of the timing signal if pulse amplitude requirements were not met. If, after appropriate delays, the fast timing signals arrived in coincidence within the resolution time of the coincidence circuit, a gate generator was actuated which opened the fast linear gate. Distortion of the linear signals resulting from pulse pile-up was minimized by the fast linear gate, limiter, and stretcher amplifer sequence since the majority of the pulses were rejected before significant integration. A frequency-compcrnsated variable attenuator was inserted preceeding the fast linear amplifier to make the amplitudes of the pulses from detector I or II compatible with the requirements of subsequent components. The PSD circuit, amplitude discriminator, gate generator, and the internal gate of the multichannel analyzer comprised the "slow" portion of the coincidence system. Pulses from the PSD circuit were subjected to amplitude discrimination by the input trigger level of a cathode ray oscilloscope (CRO). Upon triggering, the subsequent "gate pulse out" signal from the CRO actuated a pulser which served as the gate generator for the MCA gate.

66 4.3 - EXPERIMENTAL TECHNIQUES 4.3.1. Practical Considerations 4.3.1.1. Scattering relations Figure 13 illustrates the relationship between an ion recoil direction (~) and the crystal axes (a,b,c, and c'). Angles 9 and 0 are polar coordinates with the polar angle 6 measured from the crystal (cylindrical) axis c'. The azimuthal angle 0 is measured in the ab plane counterclockwise from the a axis. Energy and direction calculations were based on the following simple relations in the laboratory system of coordinates. 4E M E ~ 2 (4.1) P 2 (M+2)2 Cos ME sin2P = E sin2a (4.2) (M+l) (cos c( ~ (1 + os (M-l))2) (3) where: E = energy of an incident neutron. E = energy of the neutron after scattering. = angle through which the neutron is scattered. E = energy of the recoil ion. P = angle between the ion recoil direction and the incident direction of the source neutron. M = mass of the recoil ion relative to that of the proton. a+P = jT/2 (for recoil protons).

67 +C', e=O +c, 0=1800 4, e34~42' +b, =900 e=900 +a, =0 e=9o~ Crystallographic axes are a, b, c and c'. The ion recoil direction is p. FIGURE 13 Relationship between ion recoil direction and crystallographic axes,

68 4.3.1.2. Experimental limitations Experimental conditions imposed stringent limitations on the usefulness of the recoil ion excitation technique. The minimum practical recoil energy was dictated by the geometry of the system which introduced a spread in recoil energies (AE) and directions (zA:). These variations were directly related to a spread in neutron scattering angles (za) which resulted from the finite dimensions of the target and scintillators I and II. An indication of the energy spread zAE is given by the energy resolution (R E()).* In the case of recoil protons an explicit expression for R (a) obtained from Equation (4.1) is R E(a) = 2(ctn a),za. From this expression it is clear that the resolution increases rapidly with a decrease in a when a is small. To find the energy resolution for the carbon ion recoils, it was necessary to solve Equations (4.1), (4.2), and (4.3) for each particular set of scattering conditions. Since the maximum carbon recoil energy was less than 1 MeV for 2.8 MeV source neutrons, carbon recoil scintillations were analyzed only for 14.6 MeV source neutrons. The angular spread decreased when the source to detector I and the interdetector spacing was increased; hence, the energy resolution improved. However, these distances were ultimately limited by the interaction rates in detectors I and II. The optimum detector spacing based on reasonable data acquisition times and an acceptable angular spread was determined empirically in preliminary experiments using recoil protons. It was noted that a significant *Defined as the ratio of AE to the recoil energy for a particular neutron scattering angle a.

69 increase in the spacing beyond that selected as optimum resulted in a negligible change in the measured anisotropy. The directional response results presented in this chapter were obtained with a source to detector I distance of 50 cm. Interdetector spacings of 70 cm and 30 cm were used for proton and carbon ion measurements respectively. The smaller separation in the case if recoil carbon ions was possible because of the neutron scattering dynamics. The minimum practical neutron scattering angle for recoil proton measurements was 55~ which resulted in 0.92 MeV protons for 2.8 MeV source neutrons and 4.8 MeV protons for 14.6 MeV source neutrons. Similarly, the minimum scattering angle used in the recoil carbon ion measurements was 83~ which resulted in 2 MeV carbon ions. Approximate calculations for these cases indicate an energy resolution of 3355 for recoil protons and 27% for recoil carbon ions. The corresponding angular spreads are 6~ and 7,5~. The pulse height resolutions* of the peaks in the measured spectra corresponding to.92 MeV and 4.8 MeV recoil protons and 2 MeV recoil carbon ions were approximately 43%, 355 and 47% respectively. However, it is noted that the measured pulse height resolutions were increased by the statistical effects of scintillation light emission, detection, and subsequent electronic amplification and analysis. Also the peaks were broadened by any nonlinearity in the energy response of the scintillator. The maximum scattering angle was also restricted. Whereas the energy resolution was greatly improved, the differential elastic scattering cross sections of the hydrogen and carbon nuclei decreased for large scattering *Defined as the full width of the pulse height peak at half the maximum value (FWHM) divided by the mean pulse height of the peak.

70 angles. The resultant decrease in the intensity of the scattered neutrons was accompanied by a decrease in the detection efficiency of detector II. Since the scattered neutrons were less energetic at large scattering angles, fewer of the corresponding pulses in detector II were above the discrimination threshold of trigger II. Primarily because of these effects, the maximum practical recoil energy in scintillator I was 1.88 MeV (a=55~) for protons when 2.8 MeV source neutrons were used and 3.5 MeV (a=128~) for carbon ions with 14.6 MeV source neutrons. The upper limit for recoil protons with 14.6 MeV source neutrons was not determined. 4.3.1.3. Empirical investigation of perturbations Approximate calculations indicate that in the case of 2.8 MeV source neutrons (the most extreme case) approximately half the neutrons which reached scintillator II after scattering in scintillator I had been scattered twice in scintillator I with at least one of the two events resulting in a recoil proton. The effects of multiple scattering were examined in a preliminary experiment in which the responses of two 1/2" high by 1/2" diameter cylindrical anthracene crystals were scanned using 2.8 MeV source neutrons and the method discussed in this chapter. The probability of multiple scattering was appreciably less in the small crystals than in the larger crystal used in the final measurements. Therefore, any significant effects of multiple scattering should have been apparent when comparing the scintillation pulse height spectra for similar proton recoils in the crystals. No noticeable difference in the relevant peaks in the spectra was observed. It was concluded that the scintilla

71 tion pulses produced in scintillator I by multiple scattering must have had a broad slowly varying spectrum in the range of the peak corresponding to single scattering events. To demonstrate that the mechanical system was not contributing to the measured anisotropy, the large anthracene crystal was replaced after a series of proton recoil response scans by a cylinder of Pilot B plastic scintillator of the same size. The results of a response scan identical to one made with the anthracene crystal showed no anisotropy to within ~ 1.5%, about the same as the uncertainty of all the scans. 4.3.2. Timing and Discrimination The coincident events of interest were a small fraction (~10-4) of the total number of scintillations occurring in either scintillator I or II. A list of the interactions in scintillator I of significance in the experiment is shown in Table 2. A proper balance of the source intensity, hence the count rate in each detector, and the time resolution of the fast coincidence system allowed the rejection of most of the uncorrelated events in both scintillators. However, as can be seen in Table 2 additional selectivity was required to eliminate the correlated but undesired events. The pulse height and pulse shape discrimination associated with detector II and time of flight discrimination of the fast coincidence system provided the required selectivity. It is convenient to discuss the features of the fast coincidence timing and the discrimination requirements arising with the two different source neutron energies separately.

72 TABLE 2 SIGNIFICANT INTERACTIONS IN SCINTILLATOR I Radiation Interaction in Scint. I Consequences 2.8 MeV Source Neutrons Elastic Scattering (i) High rate of uncorrelated scintillations in scintillator I (2) Occasional true coincidence event of interest Capture Gamma Rays Compton Scattering (1) High rate of uncorrelated scintillations in scintillator I (2) Occasional correlated Compton events in both scintillators Scattered Source Neutrons Elastic Scattering (1) High rate of uncorrelated scintillations in scintillator I (2) Occasional production of a true coincidence event (In Addition to the above the following events occur with 14.6 MeV source neutrons.) 14.6 MeV Source Neutrons Inelastic Scattering C'2(n,n'7)C12 (1) -6.8-9 55 MeV scattered neutrons produce occasional true coincidence events (2) 4.533 MeV gamma rays produce occasional correlated events Inelastic Scattering Gamma Rays Compton Scattering (1) High rate of uncorrelated scintillations in scintillator I (2) Occasionally correlated Compton events in both scintillators

73 4.35.2.1. Fast timing Several factors influenced the timing uncertainty of the fast coincidence timing system. One was the variation in the time of flight of neutrons which were scattered from scintillator I to scintillator II resulting from the spread in neutron energies and the difference in flight paths because of the finite size of the detectors. Another factor was the "slewing" of the timing pulse from the fast trigger circuits resulting from the shape and amplitude nonuniformities of the fast timing pulses from the detectors. In the most extreme case (recoil carbon ions) the timing uncertainty was measured using a time to amplitude converter. The resolution* of the true coincidence peak in the resultant pulse height spectrum or "coincidence curve"** was 4.55 nanoseconds. During the response measurements, the coincidence system was operated with relatively large timing resolutions*** of 50 and 40 nanoseconds for recoil proton and carbon ion cases respectively so that a minimum number of the desired true coincidences would be missed. The optimum delay of the timing pulse from trigger I for a coincidence with a corresponding true coincidence timing pulse from trigger II was obtained from a coincidence curve for the system. A new curve was obtained experimentally when any significant changes were made in a, P, D2, trigger levels, or PM tube gain. *Full width at half the maximum count rate. **Plot of counts per unit time versus delay between the timing signals from triggers I and II. ***Time within which two timing signals must reach the coincidence circuit in order for a coincidence logic signal to be generated.

4.3.2.2. D - D Source neutrons In recoil proton measurements with 2.8 MeV source neutrons the relatively low energy of the scattered neutrons made the low level detection efficiency of detector II critical. The detection efficiency of detector II increased rapidly with decreasing neutron energy in the zero to several MeV range. This variation in efficiency enhanced the coincidence probability for the larger recoil proton energies in scintillator I (lower energy scattered neutrons) relative to the lower recoil energies. Judicious adjustment of the high level amplitude discriminator of trigger II was required to offset this effect and thereby to preserve the symmetry of the recorded pulse height spectra. PSD could not be employed to reject gamma rays because the system had a negligible detection efficiency for low energy neutrons. However, the flight time of the neutrons scattered from scintillator I to scintillator II was relatively long (> 57 nanoseconds) compared to that of gamma rays (2.5533 nanoseconds). Therefore, the fast coincidence system with a time resolution of about 50 nanoseconds effectively eliminated by time of flight discrimination any coincidence events resulting from gamma ray scattering from detector I to detector II. 4.3.2.3. D - T Source neutrons The discrimination requirements were most demanding during recoil carbon ion measurements. Inelastic scattering of the 14.6 MeV neutrons from the carbon nuclei in the anthracene crystal produced undesired but true coincidence events. The energies of the inelastically scattered neutrons reaching detector

75 II varied between -8.5 and 7.3 MeV for the scattering angles employed. Amplitude discrimination eliminated such coincidences, but only with a large loss in detection efficiency for the elastically scattered neutrons. A more severe problem was the true coincidences arising from the associated 4.533 MeV deexcitation gamma rays. The directional emission probability and the pulse height spectrum in scintillator II was similar to that of the neutrons elastically scattered from the carbon nuclei. The PSD system provided rejection of the 4.43 MeV and lower energy gamma rays. It was operated at a bias level such that neutrons which produced a scintillation pulse smaller than a 0.35 to 0.4 MeV electron were rejected. This bias level provided a high gamma ray rejection ratio* without an excessive loss in detection efficiency for neutrons with energies greater than a few MeV. The rejection ratio was determined in direct measurements to be 650 to 1 for the 2.5 MeV and lower energy gamma rays emitted by Th-2352 daughter products. The rejection ratio for 4.43 MeV gamma rays was demonstrated to be adequate in an experiment with the 4.43 MeV gamma rays emitted by a Pu-Be neutron source.** The gamma rays emitted by the neutron source arise from the same isomeric state in carbon-12 as that excited by inelastic neutron scattering. 4.3.2.4. Selected spectra During the preliminary 14.6 MeV source neutron measurements, the linear pulses from detector II were analyzed with the trigger levels, timing, and *The number of gamma rays rejected per gamma ray counted. **A radioisotope neutron source utilizing the alpha particles emitted by Pu to produce the nuclear reaction Be9(a, n7)C12.

76 coincidence gating arrangement identical to that used for analysis of the recoil pulses in detector I. The "companion spectra" so obtained were consistent with the scintillation pulse height spectra expected for neutrons scattering in scintillator II after being elastically scattered from carbon or hydrogen nuclei in scintillator I. Two companion spectra are shown in Figures 14 and 15 for neutron scattering from respectively carbon and hydrogen nuclei. Also shown in the figures are the "singles" spectra obtained with the shadow shield in place and the PSD system in operation. In the carbon recoil case the singles spectra with the shield removed and the PSD system inoperative is included to illustrate the effect of the shield in reducing the count rate in detector II. In one case the minimum pulse height analyzed was determined by the high level of discriminator-trigger II. In the other case the minimum pulse height was determined bythe bias level of the trigger employed in the PSD system. 4.3.35. Measurements All anthracene crystals used in this investigation were grown by the Harshaw Chemical Company. The large 1" high by 1" diameter cylindrical crystal to which the results presented in the subsection 4.4 pertain was selected because of maximum optical clarity and freedom from internal cracks. The orientation of the crystal axes was determined by the "precession" method of x-ray diffraction. The results were confirmed by noting the effects of the optical birefringence which arises becausen of the monoclinic structure of the crystal. A scan of the scintillation response was effected as follows. First, the ion recoil energy and recoil direction A were fixed by the choice of the source

77 1o0 0~0 010 102 00 I 0 I 5 6 7 8 9 10 11 12 13 1 4 15 1 1Proton Eneigy (MeV) I 0 20 40 60 80 100 120 Channel Number (1) is the singles spectrum with no shadow shield or PSD. (2) is the singles spectrum with the shadow shield and PSD. (3) is the companion spectrum for selected recoil carbon ions in scmntillator I (3 MeV carbon ions, 11.6 MeV scattered neutrons). -— is the pulse height corresponding to'the high level threshold of discriminator-trigger II. FIGURE 14 Scintillation pulse height spectra in scintillator TI-I.

78 X10 102 II 10 0 \ C) 00 0 (2) -~ U, ) —1 1 0 1 0 20 Channel Number 0 01234 Proton Energy (MeV) 1 20 40 60 80 100 120 Channel Number (1) is the singles spectrum with the shadow shield and PSD. (2) is the companion spectrum for selected recoil protons in scintillator I (7.3 MeV protons, 7.3 MeV scattered neutrons). ---- is the pulse height corresponding to the PSD bias level. FIGURE 15 Scintillation pulse height spectra in scintillator II-II.

79 neutron scattering angle. Then the discriminator settings and coincidence timing delays were optimized. Finally the scintillation pulse height spectra were obtained for various orientations of the crystal axis relative to P. rTypically, 0 was fixed and then 0 was varied between 0~ and 360~. Usually, e and 0 were changed by 30~ increments. The centroid of the peak in the pulse height spectrum was assumed to correspond to the idealized recoil case. Several low intensity gamma ray sources (Cs-137, Na-22, Co-60. and Th-232 daughters) were used for calibration and linearity check of both detectors and associated discriminator-triggers as well as the linear signal analyzing system. The pulse height corresponding to the half-maximum point in the fall-off of the "Compton edge" in the recoil electron scintillation pulse height spectrum was assumed to represent the maximum energy of the "Compton electrons." The response of anthracene to electrons is a linear function of energy for energies greater than 20 KeV. For calibration purposes the low energy nonlinearity was neglected and the response assumed to be linear for all energies. The error resulting from this assumption was less than 0.5%. Response func59 tions for NE 213 deduced by Bachelor et al. were used to correlate the gamma ray calibration data and the proton response of detector II. Detector I and the analyzing system were calibrated before and after each neutron scattering measurement. Typical variations in the response of the system during a measurement were less than 2%. The gain of detector II was routinely checked and adjusted when necessary during a series of scans to avoid any significant variation of the detection efficiency for the selected scat tering events. The low probability of the occurrence and detection of the

80 scattering events of interest required high reaction rates in both scintillators for reasonable data acquisition times. However, the rates were limited by the stability and discrimination capabilities of the electronic systems as well as the chance coincidence rate. Neutron source intensities on the order of 109 neutrons per second proved to be practical. Typical single rates in detectors I and II were 104 and 5x103 counts per second (cps) respectively; whereas true coincidence rates varied from 0.1 cps in the recoil carbon ion measurements to 1.0 cps in the recoil proton measurements. A fast gate width (effectively the light collection time) of 0.8 microsecond and a slow gate width of 2 microseconds were employed in the measurements. Chance coincidence rates ranged between 5 and 50% of the true coincidence rates. Pulse height resolution of the elastic scattering peaks in the scintillation pulse height spectra varied between 35 and h47 for carbon ion recoils and from 20 to 40% for recoil protons. Figures 16 and 17 show peaks for carbon ions and protons. The chance coincidence spectra which are included were obtained by introducing an excessive delay in the timing signal from trigger I. In the recoil proton case a singles spectrum is also shown. 4.4. EXPERIMENTAL RESULTS The directional scintillation response of the 1" high by 1" diameter anthracene crystal was measured for recoil protons with energies of 0.92, 1.88, 4.8, and 7.3 MeV, and recoil carbon ions with energies of 2, 2.5, 3, and 3.5 MeV. Table 5 provides a summary of the response anisotropy ratios deduced from the results. Ratios are given for all recoil energies. Each value rep

81 80 0 70. 60. 60 v(2) 30 F WM Centroid O 0 0 - ) 0 10 20 30 40 50 60 70 80 90 100 Channel Number (1) is the chance coincidence spectrum. (2) is the true coincidence spectrum for 35 MeV recoil carbon ions (a = 111~, P = 32~, 0 = 90~, 0 = 1150). FIGURE 16 Recoil carbon ion scintillation pulse height spectrum in anthracene crystal.

82 140 X200 120 100 (3) 80: Pulse height 26.1% resolution 60 4-) 40 -Centroid 20 -- 0 0 20 40 60 80 100 120 Channel Number (1) is the singles spectrum. (2) is the chance coincidence spectrum. (3) is the true coincidence spectrum for 7.3 MeV recoil protons (a=P=4~5, e=O). FIGURE 17 Recoil proton scintillation pulse height spectrum in anthracene crystal.

83 TABLE 5 RESPONSE ANISOTROPY RATIOS I Ion Energy Ratio of Maximum Response to that in Direction of: and type a axis b axis c' axis 2 MeV C 1.21 1.68 2.5 MeV C 1.20 1.62 5 MeV C 1.22 1.65 1.04 3.5 MeV C 1.22 1.63 0.92 MeV H 1.16 1.54 1.02 1.88 MeV H 1.12 1.43 1.02 4.8 MeV H 1.06 1.27 1.0 7.3 MeV H 1.05 1.25 1.0 resents the response to protons or carbon ions with recoil directions giving the maximum response divided by the response for recoil directions parallel to one of the crystallographic axes (a, b, or c'). 4.4.1. Directional Response Scans Figures 18 and 19 illustrate the results of response scans with 0.92 and 1.88 MeV recoil protons. Results obtained with 3 MeV recoil carbon ions are shown in Figure 20. Recoil directions relative to the crystallographic axes are given in terms of the coordinate system shown in Figure 13. The response is indicated for all azimuthal angles and for polar angles of 30~, 60~, and 90~. The response curves are drawn so as to be symmetric about the ac crystal plane of symmetry as well as to fit the data points indicated. Incomplete scans were made with 4.8 and 7.3 MeV protons. Results of azimuthal scans for a polar angle of 90~ are shown in Figure 21. For recoil carbon ion energies

84 00 0 C) 0 -b O ^ e-=900 A__~ e = 60 0 0 e%9 = 30 0 oO8 L. -a FIGURE 18 Directional response of anthracene crystal to 0.92 MeV protons.

85.\, +a 00 o081 o ~ 0 90~ -a A ~ -=60~ o ~ 0-300 FIGURE 19 Directional response of anthracene crystal to 1.88 MeV protons.

86 o 8=300 FIGURE 20 Directional response of anthracene crystal to 15 MeV carbon ions.

87 0 Arooo, 0 0 0-7.3 MeV Protons A-. MeV Protons 0?00 0 +b 0 - b 0081 - -a E) = 90o FIGURE 21 Directional response of anthracene crystal to 4.8 and. 7.35 MeV protons.

88 other than 5 MeV the response was measured only for recoil directions parallel to the a and b crystal axes and the direction of maximum response as estimated from the 5 MeV scan. Figure 22 illustrates the variation of the response in the ac plane for 0.92 and 7.3 MeV recoil protons and 3 MeV recoil carbon ions. The points indicated in the plot for 0 < 90~ were either measured, or obtained from the intersection of the ac plane with response curves such as those shown in Figures 18 through 21. Mechanical limitations restricted 0 to 90~ or less during the measurements; therefore, points for 90~ < 0 are inversions of the points for 0 < 90~. It is difficult to ascertain the exact recoil direction giving the maximum response in any of the cases. The direction appears to lie in the ac plane inclined about 30~ from the c' axis toward the a axis. All data points represent the estimated centroid of the peak in the recoil ion scintillation pulse height spectra. In cases where more than one measurement was made for a particular set of conditions, the data points are the averages of the measurements. In several trial measurements corrections were made in the recorded pulse height spectra to remove the chance coincidence contributions. These corrections had a negligible effect on the estimated centroids of the peaks in the spectra. Moreover, it was quite impractical to take chance coincidence spectra for each recoil direction, and corrections for subsequent measurements based on one chance spectrum were inaccurate. Therefore, the centroids of all peaks were estimated without subtracting real or hypothetical chance coincidence contributions. In all cases the peak pulse heights were normalized to the pulse height corresponding to a 1 MeV Compton

89 e -~ t+c'1. -a 0 00 008 0 X12 esos o092MVRci Protons Points for 0)> 900 are inversions of points for E0 < 900. FIGURE 22 Directional response of anthracene crystal to 0.92 and. 7.15 MeV protons and. 3 MeV carbon ions.

90 recoil electron in the same crystal. The justification for connecting the experimental points in the plots for relatively widely varying values of t is based on extensive preliminary experiments. Scans of the recoil proton response of a smaller 1/2" high by 1/2" diameter anthracene crystal were conducted with smaller angular increments between recoil directions and better angular resolution. In particular, recoil directions about the b crystal axis and in the ac plane were investigated. No significant structure was noted; hence, more data points than those used in the measurements indicated above seemed unnecessary. 4.4.2. Energy Response In Figure 235 the normalized response is plotted for proton and carbon ion recoil directions parallel to the a, b c' crystal axes, and the direction which gave the maximum response. The points were deduced from the results obtained with 0.92, 1.88, 4.8, and 7.3 MeV protons and 2, 2.5. 53 and 3.5 MeV carbon ions. Birks' Formula* with carefully selected quenching parameters was used to generate the curves which seem to describe the proton results. The appropriate values of the quenching parameters are indicated in the figure. To simplify the formula the specific energy loss dE/dx in units of MeV mgm 1 cm2 was assumed to be given by the expression 0.294 E-3/4, (E in MeV) which was suggested by Tsukada et al. L(Normalized Response) =; KdE

9' 10 U, 0 0 -Cal 1.0 N E 0 0.1I Recoil Direction Parallel to: - -o- c' axis -— a axis..~-b axis0 - -0- direction of maximum response Quenching paramaters usl d -2 in Birks' formula (MeV- mgm cm 1X10 Response jto Carbon Ions C =800190 C=00153 C = 0.0113 Response f/ to Protons1 0.1 1.0 Energy (MeV) FIGURE 23 1 0 Directional response of anthracene crystal as a function of energy.

92 The carbon ion response points illustrated in Figure 25 may be described by the expression L = CE where L is the normalized response, C in a constant depending on the recoil direction, and E is the recoil energy in MeV. Curves generated with this formula are shown in the figure along with the corresponding values of C. 4.5. DISCUSSION OF RESULTS The results of this chapter provide an additional basis for the evaluation of the three models of the scintillation process developed in Chapter 3. The static and dynamic cases are considered separately. 4.5.1. Static Quenching The analysis presented in subsection 5.2.2 is extended by considering the recoil proton and carbon ion results. Figure 24 shows a plot analogous to Figure 7 which includes the curves from Figure 7 and a new curve obtained from a Birks' formula description of the proton data of the present chapter. Results from the recoil carbon ion data are shown also; however, because of the relative uncertainty in dE/dx and FT in the carbon ion case, only two points are shown. Both correspond to carbon ions in the 2.5 to 3.5 MeV energy range for which the dE/dx values are nearly constant. One point is based on a value of 0.6 for FT which was indicated by the calculations of subsection 3.2. The other point is for an FT value of 1, corresponding to the case of no energy loss through delta ray production. It is evident from Figure 24 that the weighted directional difference in specific light yield, as obtained from a wide range of experimental results, cannot be described as a single exponential

93 0.5 - - (2) T:0.6 -II.01 _ (4)..05 l l | I l I l l l. 0 1 2 3 4 5 6 7 8 9 10 dE/dx (X 103 MeV cm-1) (1) is calculated from the proton results of Tsukada et al. (2) is calculated from the alpha particle results of Sch5tt.5 (3) is calculated from the proton results presented in this chapter. (4) are calculated from the 2.5 to 5.5 MeV carbon ion results presented in this chapter. FIGURE 24 Weighted difference in specific light yield as a function of specific energy loss-II.

94 function of dE/dx, nor as the difference of two such functions. Therefore, an anisotropic yield of excited Ei-states or anisotropic static quenching, as formulated in Chapter 3, is an inadequate explanation for the experimentally observed directional light yield. 4.5.2. Dynamic Quenching For the evaluation of the dynamic quenching models it is convenient to consider the plots shown in Figure 25. The specific response for proton recoils parallel to the a, b, and c' axes has been generated from the Birks' formula description of the results of this chapter. Specific response curves for carbon ion recoils in the same three directions were obtained from linear expressions which described the experimentally observed directional yields as a function of recoil energy. Two of the specific response curves obtained from the computer solution of the biexcitonic quenching model equation are also included in Figure 25. Four significant features are noted about the plots in the figure. (1) A continuation of the Birks' formula description of the proton data describes the magnitude of the 2.5 to 3.5 MeV carbon ion results as well. (2) Because of the "saturation" nature of the Birks' formula description, the specific response anisotropy ratio for a proper fit of the low energy proton data is about the same for all higher values of dE/dx. (5) The variation of the specific response of the recoil carbon ions with dE/dx is not described by Birks' formula. (4) The two curves corresponding to the biexcitonic quenching model have nearly the same shape as those of the Birks' formula description which was shown in 5.5.5 to be analogous to the formulation of the linear quenching model.

95 0.5 _._ KB =.006 -KB =.0064 L Response to E KB =.0092 Protons ~o ) x C =.0183' Specific Energy Loss (X 0 eV c =.0153 coil directions of the protspons and carbon ions. ~~1The carbon ion response curves were obtained from a linear description and E = 1-75xlO 3 cm MeV 1 dE/dx= JScintillation response of anthracene crystals-I 051 2.5-3.5 _ t Carbon Ion 2 0.5 0 Energy (MeV) Proton Energy (MeV) 0.1 1.0 10 Specific Energy Loss (X 103 MeV cm- ) Curve labels (a, b, or c') indicate the crystal axis parallel to the recoil directions of the protons and carbon ions. of the results of this chapter using the values of C indicated. (1) is the response generated from the computer solutions (Figure 8) for B = 4xlO-4 and E = 3.5x10-3 cm MeV'1 dE/dx. (2) is the response generated from the computer solutions for B = 2xlO-4 and E = 1.75xlO-3 cm MeV-1 dE/dx. FIGURE 25 Scintillation response of anthracene crystals-III.

96 The basic assumptions of the linear quenching model developed in subsection 3.3.3 are violated if dE/dx is greater than ~1250 MeV cm-. Qualitatively, this limitation arises because the effective volume of the column of excitation along the track of a heavy charged particle does not get larger as dE/dx increases. For large values of dE/dx, almost all the molecules within the track are damaged and act as quenchers. Hence~ in the hopping exciton model of exciton diffusion, the probability of a quenching encounter per hop in the column is close to unity and the diffusion concept is no longer valid. Therefore, the agreement between the continuation of the curves from Birks' formula and the carbon ion results does not demonstrate the success of the linear quenching formulation unless the estimates of column radius or exciton hopping distance are erroneous. An alternate explanation for the apparent success of Birks' formula is suggested by the similarity between this description and the description provided by the computer solutions for the biexcitonic quenching model. The bases of the biexcitonic model are not as restrictive as those of the linear quenching model. It accomodates both the band and hopping exciton concepts. Because of the absence of serious contradictions or limitations of the model, it is concluded that anisotropic singlet exciton diffusion with the resultant anisotropic biexcitonic quenching rate is the source of the directionally dependent light yield. The fact that a factor of two variation in the diffusion coefficient produces a calculated variation in the yield of more than the maximum observed implies that exciton migration need not be highly anisotropic. The order of the magnitudes of the diffusion coefficients required is:

97 Dab > Dbc > D, where the subscripts indicate the plane perpendicular to the track of the exciting particle. In the specific case of the proton response for dE/dx = 800 MeV cm-1 shown in Figure 25, the following relation between the diffusion coefficients may be obtained from the computer solutions presented in Figure 8. D ab = 1.69 D, and Dbc = 1.51 D, when the solution ab ac bc' ac' parameters B and E equal 4xlO04 and 2.8 respectively for recoils parallel to the b axis.

CHAPTER 5 RADIATION DAMAGE EFFECTS ON THE DIRECTIONAL RESPONSE 5.1. INTRODUCTION This chapter describes an experimental investigation of the effects of permanent radiation damage on the directional anisotropy of the prompt and delayed scintillation components in an anthracene crystal. A collimated beam of 5.3 MeV alpha particles was used for excitation. The scintillation light emitted during the time intervals 0 to 0.1 microsecond and 1 to 8 microseconds after the incidence of an alpha particle was measured for a variety of directions of incidence parallel to the ab crystal plane. Although the surface condition of the crystal and the efficiency of the light collection of the detection system required considerable attention, alpha particle excitation was much superior in these measurements to the neutron scattering technique described in the previous chapter because a low background was essential. A 1/4" high by 1/2" diameter cylindrical anthracene crystal was mounted in a conical reflecting cavity viewed by a single photomultiplier tube. The crystal could be remotely rotated about the cylindrical c' axis. Simultaneous analysis of the prompt and a selected portion of the delayed scintillation yield, as detected by the PM tube, was provided by the electronic system. Such pulse shape analysis was controlled by an associated discriminator-trigger which after appropriate delays actuated three gate generators and subsequently the operation of three linear gates. Two of the gates iso98

99 lated the prompt and delayed part of the scintillation signal from the PM tube, and the third provided both pulse height discrimination and simultaneous analysis of the prompt and delayed signals. The effects of radiation damage were determined by repeated measurements of the anisotropy of the prompt and delayed emission components as the cumulative Co-60 gamma ray radiation dose was incrementally increased from zero to 1000 kilorads. 5.2. EXPERIMENTAL ARRANGEMENT 5.2.1. Reflecting Chamber A cross sectional view of the conical cavity in which the crystal was placed is illustrated in Figure 26. The cylindrical crystal was positioned in the apex of the cavity with an ab cleavage face resting on the horizontal end of a vertical coaxial shaft which allowed 360~ rotation. All surfaces within the cavity, except the crystal and PM tube face, were covered with five coats of Nuclear Enterprise TiO2 reflecting paint which provided diffuse reflection. As shown in Figure 26, the small diameter horizontal passage between a Po-210 alpha source and the crystal provided adequate collimation. The angular spread in the directions of the alpha particles incident on the crystal was estimated to be less than 2~. The collimator and the shaft which supported the crystal were designed so that the alpha particles impinged normally on the cylindrical crystal surface at a point equidistant from the ends. The chamber was maintained at a pressure of less than 40 microns of Hg by a mechanical vacuum pump during alpha particle excitation. It was separated from the pump by a

100 iotomultipl i er Tube Polonium 210 Alpha Particle "0" Ring To Vacuum Pump Collimator for I Alpha Particles Shaft "0" Ring FIGURE 26 Reflecting Chamber.

101 liquid nitrogen cold trap to protect the crystal and the interior of the chamber from backstreaming vapors. 5.2.2. Detection and Analysis System The electronic system is illustrated in Figure 27. It consisted mainly of the components used in the experiment described in the previous chapter. However, the 512 channel MCA was replaced with a 1024 channel MCA with two dimensional analysis capabilities. Three signals were obtained from the PM tube. Dynode 11 provided a fast timing pulse, and dynode 9 provided a low level linear signal. A high level signal was obtained from the anode which was linear, at least during the time interval in which the delayed scintillation component was measured. The timing pulse was analyzed by a discriminator-trigger allowing high and low level leading edge triggering. When the amplitude requirement set by the high level threshold was satisfied, a set of accurately timed logic pulses were generated. Three of these pulses were utilized, after suitable delays to actuate the gate generators controlling the opening of three linear gates. Linear gate I passed only the prompt portion of the low level linear signal; linear gate II passed the delayed portion of the high level signal. The internal gates in the two independent halves of the MCA comprised gate III and allowed simultaneous rejection or analysis of the signals passed by gates I and II. The electronic system preceding gates I and II produced a minimum amount of pulse shape distortion of the prompt portion of the low level signal and

102 IDi scrimi nator-Tri gger EG&G TD101/N - 'ik7 psec I a Gate Ger Tektronics.Pt '~l~ec L ieratorlI Aser Type 114 I Gate Generator III E.H. Pulser Model 133 -J.Gate Generator II 1/2 EG&G-TRlO4S/N _ _ I _ _ 4ft tv ~ 5- 0 Vo tg Di1/ vide PM Tub Reflecting Chamber Stret Coincidence Circuit EG&G-Cl 02A/N NOR Output + Linear Gate I EG&G-LGlOl/N Limiter EG&G-Ll 02/N ] ZL -- -iI -H Fast-Linear Inverting Amp., 1/2 ANIOI/N Fast Linear Amplifier EG&G AN101/N Linear Gate IIStretcher Amplifier II.EG&G-LGl 02/N;cher Amplifier I 'G&G-SAl105/N.4I [ _ _ __ E l ___ __ DelIay l ine - Polarity and approximate pulse shape F Concidence Input5' MCA Gates 1024 Channel MCA-ND 150 FIGURE 27 Electronic system-IT.

the delayed portion of the high level signal. Therefore, subsequent integration of the pulses by stretcher amplifiers I and II provided signals with amplitudes proportional to the total light yield of the prompt and delayed portions of the scintillation yield as defined by the timing and duration of the two gate pulses. Since a finite time was required for the discriminator-trigger circuit to analyze a timing pulse and initiate the operation of the gate generators, gate I was normally biased open. When the trigger circuit was actuated, after a fixed delay the output of gate generator I closed the gate for the duration of the prompt and delayed signal. Spurious low level pulses below the threshold of the discriminator-trigger passed by gate I because of the normally open condition, were ultimately rejected by the closed gate at the MCA input. 5.3. EXPERIMENTAL TECHNIQUE 5.3.1. Electronic System Parameters Since the prompt scintillation emission component in anthracene decays rapidly (-30 nanosecond decay constant in a thick crystal), less than 4% of the prompt yield occurs at times greater than 0.1 microsecond after the primary events. Therefore gate I was closed 0.1 microseconds after a timing pulse with the required amplitude arrived at the discriminator-trigger. Subsequently, gate II was set to open 1 microsecond after the activation of the trigger and to remain open for 7 microseconds. Although the delayed emission persists longer than 8 microseconds after a primary event, the method employed for measuring the delayed component was not sensitive enough to improve the accuracy

104 of the results by longer light collection times. The RC of stretcher amplifier I was limited by construction to 10 microseconds; however, since all the charge accumulation occurred during the 0.1 microsecond gate I was open, negligible charge was lost during the collection time. A value of 300 microseconds was selected for the integrating time constant (RC) of stretcher amplifier II so that an insignificant amount of charge would be lost during the collection time. Gate III was timed to open for a 2 microsecond interval, 9 microseconds after the actuation of the discriminator-trigger; thereby, the output signals from both stretcher amplifiers were sampled after integration was complete. The resultant coincident pulses were analyzed simultaneously by the MCA in the two dimensional mode of operation or singly as desired. The timing uncertainty of the trigger-gating combination was observed to be several nanoseconds which was negligible considering the characteristic times of the events enumerated above. Adequate amplificationof the delayed response signal as the fluorescenoe efficiency of the crystal decreased due to radiation damage required that the PM tube high voltage be increased from 2400 to 2800 volts. When the dose exceeded 500kilorads, meaningful measurements of the delayed component were no longer possible. 5.3.2. Empirical Investigation of Perturbations Two potential sources of error in the measurement of the delayed component

105 were tafter-pulsing"* and nonlinear response of the PM tube when operated under high gain conditions. An estimate for the upper limit of the after pulse contribution was obtained by assuming that the magnitude of the after-pulsing is proportional to the magnitude of the prompt pulse. Therefore, when the prompt signals produced by gamma rays and alpha particles were the same, the magnitude of the noticably smaller delayed pulses resulting from the gamma rays was certainly the upper limit for any after pulsing contribution. This information was deduced from the results of a two-dimensional analysis of the prompt and delayed light yields while the crystal was subjected to simultaneous gamma ray and alpha particle excitation. The continuous prompt versus delayed response pulse height spectrum resulting from the gamma rays also gave an indication of the linearity of the delayed pulse height signal regardless of the degree of saturation of the prompt high level output. Figure 28 shows a topographical plot of such a two dimensional analysis. It can be seen that the pulse height of the centroid of the delayed component spectrum for the alpha particles is about ten times as great as that of the gamma rays which produce the same size prompt component. Thus, at least 90% of the alpha particle delayed signal was not due to after pulsing. Also, the centroid of the pulse heights of the delayed gamma ray components appear to be linear over the complete range of corresponding prompt pulse heights which were examined. Additional proof of the linearity of the delayed response signal was obtained by measuring the delayed response anisotropy over a PM tube high voltage *Large spurious pulses occurring over a period of a few microseconds after a a true pulse.

106 _00 I m I I 10 -Gamma Pays 200 500 -------- 1000 - _ ~X -x._x-X Prompt Signal Pulse Height -l 0 I I i I I I I 0 10 20 Channel Number - are curves through the points with two-dimensional coordinates (channel numbers) for which the numbers of counts indicated would be observed during the two hour counting period. -x-x- are curves through the centroids of the delayed component spectra corresponding to one channel wide portions of the prompt component spectrum. - - indicates the channel number of the centroid of the prompt component spectrum for alpha particle excitation. * indicates the channel number of zero delayed signal pulse height. FIGURE 28 Two-dimensional prompt and delayed scintillation component pulse height spectrum for gamma ray and alpha particle excitation.

107 range of 2400 to 2800 volts. Although the gain and thus the degree of saturation of the prompt high level signal changed considerably with the variation in high voltage, the anisotropy of the measured delayed response remained essentially constant. 5.3.3. Measurements The 1/4" high by 1/2" diameter crystal which was investigated in the experiments described in this chapter was obtained from the Harshaw-Chemical Company. It was optically clear and free from internal cracks. Before a scan of the directional response, the crystal was etched for two minutes in Benzene. Initially, the orientation of the a and b crystal axes was estimated by noting the optical birefringence effects; however, the symmetry of the measured directional scintillation yield was subsequently used for orientation purposes. As observed on a Tektronix 585 CRO (~4 nanoseconds rise time), the delayed scintillation emission as detected by the PM tube and passed by the linear gate consisted primarily of small intermittent individual spikes probably corresponding to single photons. Because of the size and relative infrequency of the pulses, the delayed signal after integration was quite sensitive to electronic drifts, particularly in the DC base line (pedestal) of the fast linear gate. Calibration before and after a measurement was essential. Likewise, more reliable values of the prompt response were obtained with frequent calibration. Two dimensional analysis proved to be impractical for a complete response scan because of the involved sequence of calibrations which was required; therefore, this type of analysis was only used in preliminary experi

108 ments. All response scans reported in subsection 5.4 were obtained by analyzing the components individually in separate series of measurements. Figures 29 and 50 show corresponding prompt and delayed pulse height spectra obtained by individual measurements. Pulse height resolutions of the prompt component peaks were around 17%. The resolutions of the delayed component peaks were usually about 45%. Count rates of several hundred cps were found to be an optimum compromise between pulse pile-up, system drift and data acquisition time. 5.3.3.1. Calibration techniques Several gamma ray sources (Cs-137, Na-22, Co-60) were used for absolute calibration and to determine the linearity of the system. Normalization and constant recalibration of the prompt component pulse height spectra were expedited during an extended series of measurements by making an absolute normalization before and after the series. During the measurements the relative response to alpha particles for various orientations of the crystal was determined by alternating measurements between the initial orientation and other orientations each differing by a fixed angular increment. The same technique of alternating directional measurements was applied to the delayed component investigation. However, the sensitivity of the system to electronic drifts required additional calibration checkso The following method was utilized. First the crystal was excited with Co-60 gamma rays which resulted in a scintillation pulse height spectrum which was continuous up to the "Compton edge." Next, the fast timing signal was split and sent to both triggers. The original trigger operated as usual; whereas the second trigger

109 200 'E a) 4,.C =: (o SaJ 4J c) c: (0 jC 0 I 10 20 30 40 50 Channel Number FIGURE 29 Prompt scintillation component pulse height spectrum. 200 (O C,' =4 'E L. o qai 1 100 Cso c — cC _u S(U) c:3 0 (1) 0 10 20 30 40 Channel Number FIGURE 350 Delayed scintillation component pulse height spectrum.

110 was set to "multiple pulse." Since the number of standard size output logic pulses in the multiple pulse train was proportional to the time the PM timing pulse was above the threshold of the trigger, the continuous spectrum of scintillation pulses resulted in an assorted number of logic pulses in each train. The pulse trains were properly delayed and substituted for the high level (delayed signal)PM output and then pulse height analysis conducted as usual. The resultant pulse height spectra in the MCA consisted of a number of equally spaced sharp peaks from which any change in the channel number of zero pulse height or gain was quickly determined. 55.3.3.2. Radiation damage The 10,000 curie Co-60 gamma ray facility of the Phoenix Memorial Laboratory at The University of Michigan was used to produce permanent radiation damage in the anthracene of interest in large increments. During the irradiation, the crystal was placed 18 cm from the centerline of the cylindrical source. In this position the measured dose was 70 kilorads per hour. The Co-60 gamma 4o ray attenuation length in anthracene is ~10 cm; therefore, the damage was produced uniformly throughout the crystal. The permanent radiation damage was assumed to increase linearly with the cumulative dose since it has been noted4 that at room temperature there is a negligible annealing of the effects of damage on the fluorescence efficiency. The decrease in the scintillation efficiency of the crystal after an increase in gamma ray dose was determined by comparing the light yield before and after each irradiation with that of a Pilot B plastic scintillator of the same size.

1ll 5.4. EXPERIMENTAL RESULTS A scan of the prompt response of the anthracene crystal to 5.5 MeV alpha particles was conducted for directions of incidence parallel to the ab crystal plane as the dose of Co-60 gamma rays absorbed by the crystal was increased incrementally from 0 to 1000 kilorads. The delayed response was correspondingly measured for alpha particles incident in directions parallel to the a and b crystallographic axes. Before the crystal was damaged, both the prompt and the delayed responses were maximum for incident directions parallel to the a crystal axis and minimum for directions parallel to the b axis. Since the directions of maximum and minimum prompt response were noted to be unchanged with radiation damage, it was assumed that the same held true for the delayed component. Table 4 gives a summary of the measured effects of damage on the prompt, delayed, and total anisotropy ratios. The ratios represent the response for alpha particles incident in directions parallel to the a crystal axis divided by the response for directions parallel to the b axis. The abrupt increase in the prompt response ratio when the dose was increased from 215 to 290 kilorads is attributed to a concurrent change in the daily adjustment procedure used with the linear gate-stretcher amplifier component. It is noted that the ratio was essentially constant before and after the change. Moreover, it is seen that the total response anisotropy ratio varied little with dose. However, the 10% increase in the delayed response ratio as the dose was increased from 0 to 500 kilorads is apparently real.

112 TABLE 4 RESPONSE ANISOTROPY RATIOS II Response for Alpha Particles with Incident Directions Parallel to the a Axis Relative to that for Incident Directions Parallel to the b Axis. Dose (Krad) Prompt Component Delayed Component Total 0 1.35 1.06 1.37 70 1.37 1.06 145 1.539 1.09 215 1.56 1.14 290 1.45 1.12 1.57 555 1.43 1.14 1.36 495 1.46 1.17 1.39 1000 1.46 1.42 5.4.1. Response Scans with no Damage Figure 51 shows the yield of both the prompt and delayed components as a function of incident direction for the case of no radiation damage. The relation between the incident direction 3 and the crystallographic axes is the same as that indicated in Figure 135. In Figure 31 the prompt response data points are the results of a single scan; whereas the points in the delayed response plot were obtained by averaging the results of several partial scans. As in the previous chapter, the curves shown in the figure are based both on the data points and the symmetry of the crystal about the ab plane. In this section the prompt and delayed scintillation response is normalized to the prompt response of the crystal in an undamaged condition to a 1 MeV compton electron.

113 e = go 0 - Prompt component (0 -.1 psec) 900 V ' Delayed component (1 - 8 psec) FIGURE 351 Prompt and delayed directional scintillation response of anthracene crystal to 5.5 MeV alpha particles.

5.4.2. Response After Radiation Damage Figure 32 shows the results of the 360~ scans of the prompt response conducted between each irradiation with the high intensity Co-60 gamma ray source. From a polar plot of this data the orientation of the a and b crystal axes was easily estimated. Then, in all cases other than for the undamaged crystal, the delayed component was measured only for directions of incidence parallel to these axes. The effect of radiation damage on the magnitude of the prompt and delayed scintillation yield is illustrated in Figure 553. The case of alpha particles incident parallel to the a axis is considered. Two quantities are plotted as a function of absorbed dose. One plot corresponds to the prompt scintillation yield with no damage (L~ ) divided by the yield for various values of absorbed P dose (L (D)). A linear fit of the points generated in this manner from the experimental results is provided by the expression L~ /L (D) = 1 + AD where A is a constant and D is the cumulative dose. As indicated in Figure 33 an appropriate value for A is 4.4 x 10-3 Krads 1 when D is measured in kilorads. The second plot shows the variation of the delayed scintillation yield (L ) d relative to the prompt as a function of absorbed dose. The ordinate values of the second plot represent the ratio of the delayed scintillation yield to the prompt for the case of no damage (L~ d/L ~) divided by the ratio of the delayed yield to the prompt for various amounts of absorbed dose (Ld(D)/L (D)).

"15 1. C (1) (2) (3) (4) ci) (A) 0 0~ U, *1)~ -0 (5) (6) (7) (8) 0.1 I I I I- A I 1800 2400 3000 0 600 1200 1800 Response Scan (L) (2) (5) (14) (5) (6) (7) (8) Dose (Krad) 0 70 215 290 3555 1495 1000 FIGURE 52 Effects of radiation damage on the prompt directional scintillation response.

7 6 - 4O 0 L3 /Lp(D) = 1 +AD / A = 4.45 X 10-3 Krads 0 0 (Ld/Lp)/(Ld(D)/Lp(D)) 0 100 200 300 400 500 600 700 800 900 1000 Dose (Krads) Ratios 4/Lp(D) and (La/Lp)/(Ld(D)/Lp(D) are derived from measurements of the prompt and delayed response of the anthracene crystal to 5.53 MeV alpha particles incident in directions parallel to the a axis. is the prompt and Ld the delayed response with no damage. Lp(D) and Ld(D) are the corresponding quantities for various doses D. FIGURE 33 Variation of prompt and delayed scintillation response with Co-60 gamma ray dose.

117 5.5. DISCUSSION OF RESULTS 5.5.1. Prompt Component The 26.4% variation in the prompt response of the undamaged crystal for 5.3 MeV alpha particles incident in directions parallel to the ab plane is in reasonable agreement with the value of 21.2% Schumacher and Flammersfeld obtained with 8.78 MeV alpha particles. From Figure 355 it is noted that the dose which reduced the prompt light 4o yield to one-half the original value is 210 kilorads. Weiss et al., deduced a corresponding value of 500 kilorads using uniform optical photon excitation throughout the bulk of several crystals. Considering the effects of reabsorption, the present prompt response results indicate the linear singlet removal rate (k + k + k ) was increased as a result of the 1000 kilorad dose sf sic sq from 10s sec-1 to 2.8x108 sec-. None of the models in Chapter 3 imply a change in the measured prompt anisotropy ratio with an increase of this amount, and none was observed. 5.5.2. Delayed Component An important feature of the results presented in this chapter is the apparent 10%o increase in the directional variation of the delayed scintillation emission with a 500 kilorad dose. However, such a trend is predicted by the "forced diffusion" solution of the triplet exciton diffusion-kinetics equation discussed in the biexcitonic quenching section, 5.3.2. Equation (3.18) was integrated numerically for a range of values for the characteristic diffusion time t, triplet lifetime Tt, and for the parameter E. The parameters t and at a

118 E are inversely proportional to the triplet exciton diffusion coefficient, and Tt varies inversely with dose. For t equal to 60 nanoseconds and E/t equal a a to.06, the numerical solution indicates that a 500 kilorad dose would reduce the delayed scintillation yield by the amount measured if Tt = 9.9 microseconds. D This value of Tt corresponds to a value for the damage quenching rate kt of tq.202 sec-1 rad-1 which is comparable to a corresponding value of.33 sec-1 rad-1 deduced from the results of Weisz et al. 4 The numerical solutions also show that for k =.202 sec-1 rad-1 and E/t =.06, a decrease in t from 60 tq a a to 40 nanoseconds results in a 5.6% decrease in the scintillation yield of an undamaged crystal and a 0l decrease after a 500 kilorad dose. Thus, if t a (or Dt) is assumed directionally dependent, these caluclations are consistent with the observed increase in the anisotropy ratio of the delayed scintillation component with damage. The relative magnitude of the effective triplet exciton diffusion coefficients necessary to explain the observed directional variation is D, > D bc where the subscripts ac' and bc' indicate the plane perpendicular to the track of the exciting particle.

CHAPTER 6 CONCLUSIONS 6.1. THIS STUDY The analysis of the scintillation process presented in this dissertation indicates that the directionally dependent scintillation phenomena in crystalline anthracene arises from anisotropic diffusion of singlet and triplet excitons. Measurements of the prompt response of a large anthracene crystal for 0.92 MeV recoil protons and 2 to 3.5 MeV recoil carbon ions show the percentage variation in the directional response to be nearly the same. Yet, for the recoil carbon ions the average specific energy loss is an order of magnitude greater, and the light yield per MeV an order of magnitude less than the corresponding quantities for 0.92 MeV protons. Anisotropic diffusion of singlet excitons is found to control the rate of biexcitonic annihilation, providing the right magnitude of directionally dependent quenching over a wide range of specific energy loss. By treating the anisotropic diffusion problem with effective isotropic diffusion coefficients, it is found that a variation of two in the value of the diffusion coefficient is more than sufficient to explain the experimental observations. Experimental data indicates that singlet exciton migration is most rapid in a plane nearly parallel to the ab plane and least rapid in the ac crystal plane. Another result from this investigation is the first measurement of the absolute scintillation yield of anthracene for carbon ions in the 2 to 53.5 MeV 119

120 energy range. A diffusion controlled biexcitonic annihilation rate for triplet excitons explains the measured directional dependence of the delayed scintillation emission as a function of radiation damage. A 33% variation in the effective triplet diffusion coefficient in planes normal to the ab crystallographic plane is adequate to produce the experimentally observed 5.6% directional variation in the response for an undamage crystal. Moreover, the magnitude of the increase in the directional variation of the delayed component as the crystal was progressively damaged by Co-60 gamma radiation is predicted within a factor two. 6.2. SUGGESTED EXPERIMENTS At least three separate experiments are suggested upon consideration of the study presented here. First, it would be desirable to determine the diffusion tensor for singlet excitions in anthracene directly. This type of measurement would probably require some unique method involving excitation with optical photons. Second, a more feasible experiment than that above would be the careful measurement of the directionally dependent delayed scintillation emission in the presence of a strong magnetic field. The role of charge transfer (CT) excitons in the delayed emission process could possibly be clarified. If the CT excitons are intermediate states which are involved between the recombination of electron-hole pairs and the formation of triplet excitons, migration could take place before the formation of the triplets. This mechanism might explain the broad initial triplet exciton distribution implied by the results of King and

121 Voltz described in subsection 3.3.2.2. Finally, by use of an accelerator capable of producing a wider range of source neutron energies, the response of anthracene or other organic crystals to energetic carbon ions could be investigated over a wider energy range by the scattering method of Chapter 4. Further knowledge of the variation of the light yield with energy is necessary for a better understanding of the fundamental processes involved in a scintillation event.

REFERENCES 1. C. D. Swartz and G. E. Owen, "Recoil Detection in Scintillators, " Fast Neutron Physics, Part I (Interscience Publishers, Inc., New York, 1960) p. 228. 2. W. F. Kienzle and A. Flammersfeld, "Die Anisotropie der Szintillationslichtausbeute organischer Molekuleinkristalle fur a-Strahlen," Z. Phys., 165, 1 (1961). 3. J. M. Robertson, "Structure of Naphthalene and Anthracene," Rev. Mod. Phys., 30, 155 (1958). 4. J. B. Birks, The Theory and Practice of Scintillation Counting (The Macmillan Company, New York, 1964). 5. W. Schott, "Die Szintillationslichtausbeute energiereicher Deuteronen und a-Teilchen in organischen Kristallen," Z. Phys., 179, 428 (1964). 6. K. Tsukada, S. Kikuchi and Y. Miyagawa, "Directional Anisotropy in the Characteristics of the Organic-Crystal Scintillators, II," Nucl. Instr. and Meth., 37, 69 (1965). 7. F. D. Brooks, "Organic Scintillators," Progress in Nuclear Physics, Vol. 5 (Pergamon Press, London, 1956), Chap. VII. 8. J. Kloppenburg and A. Flammersfeld, "Energieverlustmessungen in Anthrazen, Terphenyl und Plastikszintillator fur Protonen und Deuteronen im Energiebereich von 100 bis 900 KeV.," Z. Phys., 196, 424 (1966). 9. W. Whaling, "The Energy Loss of Charged Particles in Matter," Encyclopedia of Physics, Vol. 34 (Springer-Verlag, Berlin, 1958), pp. 193-215. 122

123 10. R. Voltz, J. Lopes da Silva, G. Laustriat and A. Coche, "Influence of the Nature of Ionizing Particles on the Specific Luminescence of Organic Scintillators," J. Chem. Phys., 45, 3306 (1966). 11. K. Wick and A. Flammersfeld, "Channelingeffekte bei der Lichtausbeute von Anthrazen bei Beschuss mit a-Teilchen," Z. Phys., 204, 164 (1967). 12. W. Brandt, R. Dobrin, H. Jack Jr., R. Laubert and S. Roth, "Channeling Studies Through Characteristic Radiations," Can. J. Phys., 46, 537 (1968). 135 W. R. Falk and L. Katz, "Fluorescence Decay Time Measurements of Organic Scintillators," Can. J. Phys., 40, 978 (1962). 14. P. G. Sjblin, "The Scintillation Decay of Anthracene Excited by Alpha Particles and Electrons," Nucl. Instr. and Meth., 63, 253 (1968). 15. P. E. Gibbons, D. C. Northrop and 0. Simpson, "The Scintillation Phenomenon in Anthracene: II. Scintillation Pulse Shape," Proc. Phys. Soc., 79, 373 (1962). 16. A. Schmillen, "Fluorescence Decay Times of Organic Crystals," Luminescence of Organic and Inorganic Materials (John Wiley and Sons, Inc., New York, 1962), p. 30. 17. K. Tsukada and S. Kikuchi, "Directional Anisotropy in the Characteristics of the Organic-Crystal Scintillators," Nuclo Instr. and Meth., 17, 286 (1962). 18. F. Brinkmeier, "Zeitliches Abklingen des Szintillationslichts von Anthrazen-und p-Terphenyleinkristallen bei Beschuss mit a-Teichen als Funktion der Einschussrichtung," Z. Phys., 190, 316 (1966).

124 19. R. Hofstadter and J. A. McIntyre, "Measurement of Gamma-Ray Energies with Two Crystals in Coincidence," Phys. Rev., 78, 619 (1950). 20. D. E. Lea, "Physical Properties and Dosimetry of Different Radiations," Actions of Radiations on Living Cells (Cambridge University Press, Cambridge, England, 1955), Chap. I. 21. E. J Hart and R. L. Platzman, "Radiation Chemistry," Mechanisms in Radiobiology, Vol. I (Academic Press, Inc., New York, 1961), Chap. II. 22. F. Hutchinson and E. Pollard, "Physical Principles of Radiation Action," Mechanisms in Radiobiology, Vol. I (Academic Press, Inc., New York, 1961), Chap. I. 23. M. Pope, "Charge-Transfer Exciton and Ionic Levels in Organic Crystals," J. Polymer Sci. Pt. C., Polymer Symposium, (USA), No. 17, 233 (1967). 24. P. Avakian and R. E. Merrifield, "Triplet Excitons in Anthracene CrystalsA Review," Mol. Crystals, 5, 37 (1968). 25. H. A. Bethe and J. Ashkin, "Passage of Radiations Through Matter," Experimental Nuclear Physics, Vol. I (John Wiley and Sons, Inc., New York, 1953), Part. II. 26. W. S. Snyder and J. Neufeld, "On the Passage of Heavy Particles Through Tissue," J. Rad. Res., 6, 67 (1957). 27. J. Linhard and P. V. Thomsen, "Sharing of Energy Dissipation Between Electronic and Atomic Motion," Radiation Damage in Solids, Vol. I (IAEA, Vienna, 1962), p. 65.

125 28. L. C. Northcliffe, "Passage of Heavy Ions Through Matter," Annual Review of Nuclear Science, Vol. 13 (Annual Reviews, Inc., Palo Alto, California, 1963), p. 81. 29. R. L. Platzman, "On the Primary Processes in Radiation Chemistry and Biology," Symposium on Radiobiology (John Wiley and Sons, Inc., New York, 1952), Chap. VII. 30. J. L. Magee, "Elementary Processes in Action of Ionizing Radiation," Comparative Effects of Radiation (John Wiley and Sons, Inc., New York, 1960), pp. 142, 1435. 31. W. Helfrich, "Destruction of Triplet Excitons in Anthracene by Injected Electrons," Phys. Rev. Letters, 16, 401 (1966). 52. E. L. Frankevich and B. M. Rumyantsev, "Charge-Transfer Excitons and Delayed Fluorescence of Anthracene," Phys. Stat. Sol., 30, 329 (1968). 33. R. M. Sternheimer, "The Density Effect for the Ionization Loss in Various Materials," Phys. Rev., 88, 851 (1952). 34. F. A. Black, "The Decay in Fluorescence Efficiency of Organic Materials on Irradiation by Particles and Photons," Phil. Mag., 44, 263 (1953). 55. 0. Simpson, "Electronic Properties of Aromatic Hydrocarbons III. Diffusion of Excitons," Proc. Roy. Soc., A238, 402 (1956). 36. J. Jortner, S. A. Rice and J. L. Katz, "Triplet Excitons in Crystals of Aromatic Molecules," J. Chem. Phys., 42, 309 (1965). 37. M. Levine and J. Jortner, "Diffusion of Triplet Excitons in Crystalline Anthracene," J. Chem. Phys., 45, 1951 (1966).

126 380 SO Z. Weisz, A. B. Zahlan, M. Silver and R. C. Jarnagin, "Radiationless Transition Rate Constant Determination from Delayed Fluorescence," Phys. Rev. Letters, 12, 71 (1964). 39. M. Pope and J. Burgos, "Autoionization and Exciton Annihilation in Anthracene," Mol. Crystals, 3, 215 (1967). 40. S. Z. Weisz, P. Richardson, A. Cobas and R. C. Jarnagin, "Triplet Sampled Radiation Damage," International Symposium on Organic Scintillators, Argonne National Laboratory, 1966. 41. S. Singh, W. J. Jones, W. Siebrand, B. P. Stoicheff and W. G. Schneider, "Laser Generation of Excitons and Fluorescence in Anthracene Crystals," J. Chem. Phys., 42, 5530 (1965). 42. A. H. Samuel and J. L. Magee, "Theory of Radiation Chemistry. II. Track Effects in Radiolysis of Water," J. Chem. Phys., 21, 1080 (1953). 43. A. Kuppermann and G. G. Belford, "Diffusion Kinetics in Radiation Chemistryo II. One-Radical-One-Solute Model; Calculations," J. Chem. Physo, 36, 1427 (1962). 44. G. N. Whyte, "Energy Per Ion Pair for Charged Particles in Gases," Rad. Research, 18, 265 (1965). 45. A, Ore and A. Larsen, "Relative Frequencies of Ion Clusters Containing Various Numbers of Ion Pairs," Rad. Research, 21, 331 (1964). 46. A. M. Rauth and F. Hutchinson, "Distribution in Energy of the Primary Energy Loss Events of Electrons in Condensed Media," Biological Effects of Ionizing Radiation at the Molecular Level (IAEA, Vienna, 1962), p. 25,

127 47. A. S. Newton, "Mechanisms of Chemical Effects of Ionizing Radiation," Radiation Effects on Organic Materials (Academic Press, Inc., New York, 1963), Chap. III. 48. N. Swanson and C. J. Powell, "Excitation of it-Electrons in Polystyrene and Similar Polymers by 20 KeV. Electrons," J. Chem. Phys., 39, 6350 (1963). 49. H. Fricke and D. L. Phillips, "High-Speed Computations in Diffusion Kinetics. III. Solute Depletion in the Cylindrical One Radical- One Solute Model," J Chem. Phys., 34, 905 (1961). 50. A. Kuppermann, "Diffusion Kinetics in Radiation Chemistry," The Chemical and Biological Action of Radiations (Academic Press, Inc., London, 1961), Chap. III. 51. G. Jaffe, "Zur Theorie der Ionisation in Kolonnen," Ann. Phys., 42, 303 (1913). 52. D. Blanc, F. Cambou and Y. G. de Lafond, "Cine'tique de la composante rapide de la scintillation dans un milieu organique pur. Application au cas de 1'anthracene," C. R. Acad. Sci., 254, 3187 (1962). 55. T. A. King and R. Voltz, "The Time Dependence of Scintillation Intensity in Aromatic Materials," Proc. Roy. Soc., A289, 424 (1966). 54. R. Voltz and G. Laustriat, "Radioluminescence Des Milieux Organiques I. Etude Cinetique," J. Physique, 29, 159 (1968). 55. R. Voltz, H. Dupont and G. Laustriat, "Radioluminescence Des Milieux ItJ! Organiques II. Verification Experimentale de L'Etude Cinetique, J. Physique, 29, 297 (1968).

128 56. H. Kallmann and G. J. Brucker, "Decay Times of Fluorescent Substances Excited by High-Energy Radiation," Phys. Rev., 108, 1122 (1957). 57. H. B. Rosenstock, "Energy Transfer in Organic Solids," J. Chem. Phys., 48, 532 (1968). 58. R. B. Owen, "Pulse-Shape Discrimination Identifies Particle Types," Nucleonics, 17, No. 9, 92 (1959). 59. R. Batchelor, W. B. Gilboy, J. B. Parker and J. H. Towle, "The Response of Organic Scintillators to Fast Neutrons," Nucl. Instr. and Meth., 13, 70 (1961). 60. D. J. Brager, "The Fricke Dosimeter: Dose Rate Calibration of 10,000 Curie Co-60 Source," (Unpublished Report, The University of Michigan, 1968). 61. M. Schumacher and A. Flammersfeld, "Szintillationslichtausbeuten organischer Molekulkristalle fur a-Strahlen und Elektronen," Z. Phys., 178, 11 (1964).

UNIVERSITY OF MICHIGAN 3 9015 03483 2397II 3 9015 03483 2397