THE UNIVERSITY OF MICHIGAN COLLEGE OF ENGINEERING Department of Nuclear Engineering Technical Report MEASUREMENT OF FAST NEUTRON SPECTRA IN WATER AND GRAPHITE Lawrence Harris, Jr. ORA Project 07786 supported by: DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE PUBLIC HEALTH SERVICE BUREAU OF STATE SERVICES DIVISION OF RADIOLOGICAL HEALTH GRANT NO. RH-00253-03 WASHINGTON, D.C. administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR April 1967

This report was also a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan, 1967.

ACKNOWLEDGMENTS The development of the spectrometer reported here was initiated by Lt. Col. Glenn G. Sherwood, U.S.A.F., who later carried out the detailed NIOBE calculations. Professor John S. King has directed this work since its beginning. His guidance and encouragement are gratefully acknowledged. Also, Assistant Professor Glenn F. Knoll contributed substantially to the spectrometer development. The cooperation of Messrs. J. B. Bullock, R. D. Martin, and J. Ro Miller, and the reactor operators during the spectrum measurements was outstanding. Dr. H. G. Olson and the Phoenix Memorial Laboratory staff provided considerable assistance throughout this program. Their help is greatly appreciated. Financial assistance was provided by three AEC Special Fellowships in Nuclear Science and Engineering and by grants from the Michigan Memorial-Phoenix Project (Research Grant 215) and the Division of Radiological Health, U. S. Public Health Service (Research Grant RH 00253)o The untiring encouragement and support of my wife, Carole, have been invaluable. ii

TABLE OF CONTENTS Page LIST OF TABLES v LIST OF FIGURES vi ABSTRACT ix CHAPTER I, INTROUDCTION A. Significance of Fast Neutron Spectrum Measurements in Bulk Media 1 Bo Methods for Measuring Fast Neutron Spectra in Bulk Media 2.o Threshold Activation Method 2 2o Time-of-Flight Method 2 35 Nuclear Reaction Method5 4. Proton-Recoil Method6 C. Fast Neutron Spectrum Measurements in Bulk Media 8 IIo SPECTROMETER DESIGN AND OPERATION 12 A, Principles of Design and Operation 12 1o Energy Analysis 12 2. Energy Calibration 14 3. Thick Detector Operation 15 4. Thin Detector Operation 15 B. Detectors 17 1.o Silicon Surface Barrier Detectors 17 2. Depletion Region 20 35 Electron-Hole Pair Generation 23 4, Electron-Hole Pair Collection 24 5, Energy Calibration 25 6. Leakage Current 26 Co Instrumentation 26 Do Signal-to-Background Ratio 29 1, Sources of Background 30 2o Design Considerations 31 35 Influence of Detector Thickness 34 4. Carbon Recoils 39 5. Collimator Effects 39 Eo Efficiency 40 Fo Energy Resolution 47 lo Detector Term 47 iii

TABLE OF CONTENTS (Concluded) Page 2, Radiator Term 49 35 Geometry Term 49 4. System Resolution 55 5. Influence on Measurement 57 Go Energy Range 60 III. EXPERIMENTAL RESULTS 61 Ao Ford Nuclear Reactor 61 1o Reactor Description 61 2o Reactor Power Measurement 61 Bo Water Measurements 63 1l Normalization 63 2, Reactor Power 66 35 Counting Times and Statistics 66 4o Measured Spectra 67 5~ Experimental Uncertainties 69 Co Graphite Measurements 71 1. Description of Graphite Slabs 71 2, Reactor Core Modification 74 30 Normalization and Reactor Power 74 4. Counting Times and Statistics 75 5o Measured Spectra and Experimental Uncertainties 75 IVo COMPARISON WITH CALCULATIONS AND CONCLUSIONS 77 Ao NIOBE Calculations 77 1o Neutron Transport Equation 77 2o Source Terms 79 35 Energy Groups 81 4. Geometry 82 5o Cross Sections 83 60 Comparison with Measurements 83 Bo Conclusions 86 Co Suggested Future Work 87 APPENDICES Ao EFFECT OF CARBON RECOILS 89 Bo COLLIMATOR EFFECTS 96 CO TABULATION OF MEASURED SPECTRA 100 REFERENCES 105 iv

LIST OF TABLES Table Page lo Methods for Measuring Fast Neutron Spectra in Bulk Media 3 2o Fast Neutron Spectrum Measurements in Bulk Media 9 30 Silicon Surface Barrier Detectors 21 4~ Proton Energy Analysis Instrumentation 29 5o Anticoincidence Instrumentation 29 6. Influence of F(rm) on A(cos2t) 55 7. Principal Experimental Uncertainties 70 80 Ratios of Calculated Flux to Measured Flux 84 V

LIST OF FIGURES Figure Page 1o Principal features of proton-recoil fast neutron spectrometer. 13 2o Block diagram of instrumentation used with thick proton detector, 16 30 Block diagram of instrumentation used with thin proton detector showing anticoincidence system that counts only protons stopped in thin detector. 18 4, Calculated energy response of two tandem silicon detectors to protonso 19 5o Block diagram and equivalent circuit for reverse-biased detector, charge-sensitive preamplifier, and amplifier. 28 60 Background count rates for detector positions above and below collimator axiso 32 7o Proton recoil spectrum obtained using thick (1040 microns) detector and thick (2.95 mg/cm2) radiator with collimator against reactor core, 35 80 Signal-to-background ratios ifor proton recoil spectra obtained using thick (1040 microns) detector and thick (2 95 mg/cm2) radiator. 36 9. Ratio of thick detector background to thin detector background. 37 10o Proton recoil spectra obtained using thin (245 microns) detector and thin (1.25 mg/cm2) radiator with collimator against reactor core. 38 11o Calculated efficiency: eR(E) 44 12. Calculated total efficiency: e(E). 45 135 Calculated energy Jacobian: dE/dEpo 48 vi

LIST OF FIGURES (Concluded) Figure Page 14o Radiator-detector geometry used for calculation of f(t) and f(cos2o)o 51 15o Example of construction used for calculation of S()o0 54 16, Calculated distribution function~ f(cos2). 56 17o Calculated energy resolution AE/Eo 58 18o Ford Nuclear Reactor core configurations, 62 19o Spectrometer suspended above FNR poolo 64 20. Collimator positioned 60 cm from FNR core 65 21o Neutron penetration in watero 68 22~ Two views of four graphite slabs. 72 235 Three graphite slabs positioned against FNR coreo 73 24. Neutron penetration in graphiteo 76 25. Range of carbon ions in polyethylene. 94 26~ Ratio of carbon recoil, counts to proton recoil counts, 95 vii

ABSTRACT Detailed knowledge of the energy and spatial distributions of fast neutrons in bulk media is required in radiation shielding, radiation effects, and fast reactor physics. Although computer codes are available to calculate spatially dependent spectra with accuracies presumably limited only by uncertainties in cross sections and source spectra, few spectrum measurements which provide a good test for these calculations have been reported. Here a relatively simple, moderate resolution (12%), differential proton-recoil, fast neutron spectrometer has been developed to measure directed neutron fluxes in the presence of high intensity fission gamma fields of 107 to 10 roentgens/hour. Good signal-to-background ratios are obtained by (1) careful shielding, (2) using silicon surface barrier detectors, (3) positioning the detectors out of the collimated beam of mixed radiation which traverses the thin polyethylene (CHo) radiator, and (4) using tandem detectors in anticoincidence. The efficiency is about 10i6 for neutrons incident on the radiator. Measurements of the energy spectrum from 2 to 12 Mev of normally directed neutrons which leaked from the Ford Nuclear Reactor core and penetrated 0, 20.0, 40.0, and 60.0 cm of H20 and 0, 20.2, 40.4, and 60.6 cm of graphite are reported. The relatively high accuracy of these deep penetration measurements (+10o relative intensity and +20 absolute intensity, +2% energy) makes them useful for testing calculations. Comparison with detailed transport calculations shows good agreement. ix

CHAPTER I INTRODUCTION Ao SIGNIFICANCE OF FAST NEUTRON SPECTRUM MEASUREMENTS IN BULK MEDIA Knowledge of the energy and spatialdistributions of fast neutrons (1 15 Mev) in bulk media is required in the design of radiation shielding,(l4) the study of radiation effects,(57) and the design of fast reactors (8-11) The parallel development of high-speed digital computers with large memory capacity and multigroup computer codes based on transport and Monte-Carlo methods has made detailed calculations of fast neutron spectra feasible. With the more rigorous codes such as NIOBE,(12 14) DTF-IV,(15) and 05R,(16) the accuracy of the calculations is essentially limited only by uncertainties in the cross sections and source represent tation. Unfortunately, due to the difficulty of measuring space and energy dependent fast neutron fluxes, these calculations are usually tested only against integral flux measurements(7) or against other calculations, Clearly the best test of a code, and the representation of the cross sections and the source is a comparison with spectrum measurements, Only by such comparisons can the accuracy of the calculations be establishedo This work reports a method for accurately measuring spatially dependent fast neutron spectra in bulk media, Measurements in two common reactor materials are presented and compared with detailed calculations. 1

2 B. METHODS FOR MEASURING FAST NEUTRON SPECTRA IN BULK MEDIA (l l 9-25) Numerous reviews ('95) of the methods used to measure fast neutron spectra have been published. The current methods used to measure spectra (1-15 Mev) in bulk media are listed in Table 1, Table 1 also gives typical values for the efficiency and resolution reported for each method and indicates which methods require beam extraction, When a beam is extracted, the directional or angular flux is measured; otherwise, the scalar flux is measured. In this section, each method is discussed briefly with emphasis on its limitations, 1 Threshold Activation Method The threshold activation method(26'29) is based on the activation of foils with activation thresholds in the energy region of interest. Its principal limitations are low efficiency and low resolution, The low efficiency results from the small size of the foils used and the low cross sections in the Mev range~ The low resolution is due first to the limited number of materials with suitable activation thresholdsB and well-known cross sections, and secondly to the uncertainties associated with the unfolding of spectra from the activation data. 2, Time-of-Flight Method The time-of-flight (TOF) method consists of measuring neutron flight times over a known flight path. The origin of the flight time is usually defined by using a pulsed neutron source. The application of this technique to spectrum measurements in bulk media has been made possible by

TABLE 1 METHODS FOR MEASTJRING FAST NEUTRON SPECTRA IN' BULK MEDIA Method Beam Extraction Detector Efficiency Resolution 1i Threshold Activation Not Required Foils Low Low 2o Time-of- Liquid Organic 10-8 -10-6 Flight (TOF) Required Scintillator(33) (includes 10% collimation) 30 Nuclear Reaction Ao Li6 (n,)H Not Required (but Silicon Surface 10-7 -10 or 21% at 3 Mev used in this example) Barrier Detectors 10-9 -10-8 2% at 14 Mev in Sandwich (includes Configuration(36) collimation) B. He3(n,p)H3 Not Required He Filled Pro- 10-4 _10-3 3% - 5% portional Counter( ) 4, Proton Recoil Ao Integral Not Required Liquid Organic 0o15 - O0o40 32% at 1 Mev Scintillator(49) 9% at 14 Mev B. Differential Required Silicon Surface 3-6 x 10-6 or 24% at 2 Mev Barrier Detectors 3-6 x 10-9 15% at 3 Mev in Tandem (includes 12% at 12 Mev Configuration(57) collimation)

4 the development of high intensity, nanosecond scale, pulsed neutron sources. The high intensity is required because of the long flight paths necessary for good resolution and because of the limitation imposed on the repetition rate by the increase of the pulse width along the flight path, For measurements in nonmultiplying media,(9,30,31) an electron linear accelerator (LINAC) is generally used to bombard lead or depleted uranium targets with 530 Mev electrons to generate bremsstrahlung. This in turn generates up to 1013 neutrons per second with a near fission spectrum by (y,n) and (y,f) reactionso Flight paths are usually 50 to 60 meters long. For measurements in multiplying media,(91032) less intense sources are required. The neutron yield obtained from a positive ion accelerator through the H2(d,n)He3 and H3(d,n)He4 reactions is adequate for some measurements, With current TOF apparatus used with LINAC sources, the principal limitations on resolution are due to (1) counting statistics which require channel grouping to make statistical uncertainties less than some specified value(33) and/or (2) uncertainty in the mean time and the variance in time for neutrons to slow down and migrate from the source to the entrance of the flight path(34) According to Russell, et al,(30) this latter effect is small but nonnegligible (-10 ns above 0,5 Mev) in hydrogenous media, but it may lead to 440% energy resolution for measurements in a large shield of high A elements such as leado If this is true, a 50-meter flight path is too short for these measurements, Profio(33) points out that the main shortcomings of his TOF technique

5 are the uncertainties in the detector efficiency and the transient gamma background. In order to surpress the latter, a 3.14-cm thick depleted uranium plate was interposed in the flight path during measurements. The effect of the depleted uranium is indicated by spectrum measurements made with and without the filter. Addition of the filter reduced the measured 1 Mev flux, presumably after correction for attenuation by the filter, by a factor of three. The measured 10 Mev flux was reduced by 20%. These results indicate the gamma background may be causing substantial errors. 3. Nuclear Reaction Method The nuclear reaction method uses either the He3(n,p)H3 reaction (Q = +0.76 Mev) or the Li6(n,z)H3 reaction (Q = +4.78 Mev) to produce charged particles whose total energy is equal to the energy of the neutron plus the Q of the reaction. This energy is measured using semiconductor (3~-39) (40,41) scintiation detectors,(3539) gas proportional counters,(441) or scintillation crystals. (42,43) The semiconductor detectors are arranged in a sandwich configuration with either a thin Li6F film(35-37) or He3 gas at up to 995 psi pressure(38,39) between them. A sum-coincidence circuit is used to obtain signals proportional to the full energy of both reaction products and to remove noncoincident background. The positive Q of both reactions also assists in gamma discrimination. Use of the Li6F film is complicated by competing reactions and by Li6 (n,a)H reactions induced by thermal neutrons for which the reaction

6 cross section is very high. Similarly, the use of He gas is complicated by competing reactions (especially elastic scattering which produces He3 recoils). 4. Proton-Recoil Method The proton-recoi-l method consists of measuring the energy of elastically scattered protons. The proton energy, Ep, is related to the neutron 2 energy, E, by the relation, E = E cos 2, where r is the n-p scattering angle in the laboratory system. If all of the scattered protons are counted, an integral proton spectrum is obtained. This must be differentiated or unfolded to obtain the neutron spectrum. In early applications of the integral proton-recoil method, integral proton spectra obtained with stilbene scintillation crystals were differentiated, (44) More recently, sophisticated unfolding techniques have been developed to convert integral proton spectra obtained in stilbene scintillator crystals(4'46) and liquid organic scintillators(4749) and in hydrogen filled and methane filled proportional counters(50-52) to neutron spectra. Pulse shape gamma discrimination is usually used in conjunction with these detectors, The chief limitations of the integral proton-recoil method are that the unfolding techniques require precise detector response functions in order to be accurate, and the background due to gamma interactions and neutron interactions other than single n-p scattering is difficult to determine precisely,

7 In contrast to the integral proton-recoil method, if only those protons scattered through d*o about o0 are counted, a differential proton spectrum is obtained. Since this is related to the neutron spectrum 2 through Ep = E cos o the conversion to the neutron spectrum is straightforward. With this method, a thin hydrogeneous material, such as polyethylene (CH2), is located in a neutron beam and the protons scattered into some solid angle are intercepted by a detector for energy analysis. The neutron beam is extracted from the source with a collimator system. The hydrogeneous film or proton radiator is made thin to reduce the proton energy losses in it and thus permit good energy resolution. The detectors are usually scintillator crystals(53'54) or semiconductor detectors,(5557) (58,59) although Cialella ) has reported using magnetic energy analysis. Radiators may be used in series to increase efficiency, and detectors may be used in series to reduce background with coincidence or anticoincidence(57) techniques. Tandem detector devices are usually called telescopes. The spectrometer developed as part of this work is a differential proton-recoil device.(57) The detectors are silicon surface barrier diodes as used by Furr and Runyon,() and like Herdade, et al., () they are located off the collimator axis. The collimator efficiency is 10-3 and the detector efficiency varies from 3 to 6 x 10-6 in the energy range 2 to 12 Mev. The resolution is 24% at 2 Mev, but improves to 15% at 3 Mev and to 12% at 12 Mev. For measurements from 2 to 6 Mev, a 1.25 mg/cm2 thick

8 polyethylene radiator is used with a 245-micron thick detector. A second detector aligned behind the first one, is used to identify protons which are not stopped in the first detector and, by means of an anticoincidence arrangement, to block signals from the first detector due to these protons. The signals must be blocked because the energy deposition in the first detector does not represent the total proton energy. For measurements from 4 to 12 Mev, a 2.95 mg/cm2 radiator is used with a single 1040micron thick detector. The principal advantages of this type of spectrometer are its low gamma sensitivity, its well-known absolute efficiency, the straight forward conversion from proton spectra to neutron spectra, and the essentially unbounded upper energy limit (available by use of multiple thick detectors and/or a large n-p scattering angle). The main disadvantages are its low efficiency and the lower energy limit of about 1 Mev (due to poor resolution resulting from relatively large proton energy losses in the radiator). C. FAST NEUTRON SPECTRUM MEASUREMENTS IN BULK MEDIA Measurements of fast neutron spectra in bulk media which are perhaps the best reported in the literature are summarized in Table 2. Other measurements(43'7377) were omitted because they are less suitable for testing detailed calculations. Of the measurements listed in Table 2, several are more useful than the others as tests. First, Verbinski and Bokhari's(337) spectra (No. 4) are the most detailed measurements of reactor neutron spectra in H20O that have been published. However, comparison with the NIOBE and

TABLE 2 FAST NEUTRON SPECTRUM MEASUREMENTS IN BULK MEDIA Energy Range Shield Number Group Year Neutron Source Method (Mev) Medium Geometry Penetration Distances Calculations/Comparison Ref. 1 ORNL 1953 BSR-I Reactor Diff. n-p 1.3-10 H20 Infinite 0,5,20 & 30 cm at 0~ None (60) 2 ORNL 1954 BSR-I Reactor Diff. n-p 1.3- 8.5 Graphite Slab 0 & 32.7 cm at 0~ None (61) 3 ORNL 1963 LINAC/Pb Target TOF 1 -13 LiH Slab 0,10,20& 27. 5 cm at 0~ NIOBE/Fair (62) 4 ORNL 1964 BSR-I Reactor Li6(n,c)H3 1 -11.5 H20 Infinite 0,10,20,30,40 & 50 cm at 0~;20 NIOBE & DTK/Fair (56,37) & 40 cm at 41~; 10,20,30 & 40 cm at 52~ 5 ORNL 1967 LINAC/Pb Target TOF 1 -12 H 0 Slab 0,20 & 40 cm at 0~; 10,20 & 30 cm at 30~ NIOBE & DTK/Good (37) 6 ORNL 1967 TSR-II Reactor Int. n-p 0.7-10 Liquid N Slab 0,61.0 & 91.4 cm exp[-Zt(E)t]/Excellent (49) 7 ORNL 1967 TSR-II Reactor Int. n-p 1.8-10 Liquid 0 Slab 0,61.0 & 91.4 cm exp[-Ft(E)t]/Excellent (49) 8 ORNL 1967 TSR-II Reactor Int. n-p 0.7-10 Graphite Slab 0,11.0,20.3 & 30.5 cm exp[-t(E)t]/Excellent (49) 9 ORNL 1967 TSR-II Reactor Int. n-p 0.7-10 Pb Slab 0 & 15.2 cm exp[- t(E)t]/Excellent (49) 10 GA 1964 LINAC/U Target TOF 0.5-15 Liquid H Cylinder 0,6.4,11.4,17.8,26.7 & 33.0 cm at 0~, None (63,64) 15~,37~,53~, & 780~ 11 GA 1964 LINAC/U Target TOF 0.5-15 CH2 Infinite 0,5 & 15 cm at 0~; 30 cm at 160,320 & 60~ GAPLSN & GGSN/Poor (65,66) 12 GA 1966 LINAC/U Target TOF 0.5-15 CH2 Sphere 0,15 & 30 cm at 0~; 30 cm at 11.5~,20.1~, GAPLSN & GGSN/Fair (33) 35.5~ & 55.7~ 13 GA 1966 LINAC/U Target TOF 0.5-12 Graphite Infinite 0,20.3,35.6,50.8 & 66.1 cm at 0~ None (07) 14 USSR(I) 1963 Thermal Reactor Int. n-p 1 -10 CH2 Slab 0,10,20,30,60 & 80 grams/cm2 Moments/Fair (68) 15 USSR(I) 1964 Thermal Reactor Int. n-p 1 -11 Graphite Slab 0,22.5,45,92.5 & 135 cm Moments/Poor (69) 16 USSR(I) 1964 Thermal Reactor Int. n-p 1 -11 Pb Slab 0,12,24,49 & 74 cm None (69) 17 USSR(I) 1964 Thermal Reactor Int. n-p 1 -11 Fe Slab 0,10.4,20.4,40 & 65 cm None (69) 18 USSR(I) 1965 Thermal Reactor Int. n-p 1 -12.5 Concrete Slab 0,10,30,60 & 100 cm None (70) 19 uSSR(II) 1964 Po-Be Int. n-p 1.5-10 H20 Semi-Infinite 0,10,20,30 & 40 cm Moments/Fair (71) 20 USSR(II) 1964 Po-Be Int. n-p 1.5-10 H20 Slab 0,10,20 & 30 cm None (71) 21 USSR(II) 1965 Po-Be Int. n-p 2 -10.5 C2 Slab & 45 cm None (72) 22 USSR(II) 1965 Po-Be Int. n-p 1.5-10.5 Al Slab & 44 cm None (72) 23 Mich. 1966 FNR Reactor Diff. n-p 2 -12 H20 Infinite 0,20.0,40.0 & 60.0 cm at 0~ NIOBE/Excellent (57) 24 Mich. 1966 FNR Reactor Diff. n-p 2 -12 Graphite Slab 0,20.2,40.4 & 60.6 cm at 0~ NIOBE/Good (57)

10 DTK* calculations shows only fair agreement. Of note is a dip which appears at 3.5 Mev in the calculations and at 4 Mev in the measurements. Since this dip results from the elastic scattering resonance of oxygen at 3.5 Mev, it appears the spectrometer energy calibration was in error. Also, the NIOBE calculations show another dip at 7.3 Mev which does not appear in the measurements. In this case, it seems the NIOBE cross sections used were in error because current oxygen cross sections(78) do not show a sizable resonance near 7.3 Mev. Secondly, Verbinski's(37) recently reported spectra (No. 5) of (y,n) and (y,f) neutrons which penetrated water in slab geometry show good agreement with NIOBE and DTK calculations. However, the comparison is somewhat biased because the measured spectra were individually normalized to the calculated spectra for convenience in comparing spectrum shapes. Thirdly, Profio's(33) spectra (No. 12) of (y,n) and (y,f) neutrons in a paraffin sphere (15.2 cm ID and 76.2 cm OD) were measured in very clean geometry. Even so, comparison with GAPLSN** and GGSN*** calculations shows only fair agreement. Fourthly, Clifford, et al. s(49) recently reported spectra (Nos. 6-9) of reactor neutrons which traversed several samples were measured in narrow beam geometry. Thus, only uncollided neutrons were counted. These *DTK is an early LASL version of DTF-IV. **GAPLSN is a General Atomic version of DTF-IV. ***GGSN is a faster running version of GAPLSN which permits downscattering only.

11 measured spectra depend only on the spectrum of neutrons incident on the sample, the sample thickness, and the total cross section of the sample material. Comparison with calculated spectra, Nt(E) = No(E) exp [-Zt(E)t], shows agreement which ranges from good to excellent depending on which of several sets of total cross sections was usedo Although these measurements provide excellent tests for the total cross sections, they give no information on slowing down sourceso Thus, in view of the apparent absence of reliable measurements to test calculated spectra which include scattered neutrons, the spectrum measurements (Nos. 25 & 24) reported here should be very usefulo At the deeper penetrations, they are in fact dominated by scattered neutrons, For example, the ratio of scattered neutrons to unscattered neutrons ranges from 100 at 2 Mev to 1 at 12 Mev for the neutrons which penetrated 60 cm of H200

CHAPTER II SPECTROMETER DESIGN AND OPERATION A. PRINCIPLES OF DESIGN AND OPERATION The principal features of the proton-recoil, fast neutron spectrometer developed for these measurements are shown in Figure 1. During operation, the spectrometer is submerged in the open pool of the Ford Nuclear Reactor, the 2 megawatt research reactor at The University of Michigan. Fast neutrons from the FNR core stream through the collimator to a proton radiator. The radiator is a thin polyethylene (CH2) film from which about one out of every 10 incident neutrons elastically scatters a proton to the detector. The detector system generates a voltage pulse whose height is proportional to the energy of the incident recoil proton. 1. Energy Analysis The energy of the recoil protons is related to the energy of the neutrons incident on the radiator by applying the laws of conservation of kinetic energy and linear momentum. Neglecting the small difference between proton mass and neutron mass, this results in the following ratio: proton energy - cos2 neutron energy where * is the n-p scattering angle in the laboratory system. This relation assumes that prior to being scattered, the protons are free and at rest. These assumptions are reasonable for hydrogen nuclei 12

10 10 10 61 cm 41cm cm-tmc -- 305cm Evacuated Neutron Collimator (Entrance: 10.2cm I D, Exit: 1.9cm ID) Aluminum Electron Filter Steel Gamma Shield (18 cm OD) H Lead Gamma Shield (25cm OD) Aluminum Charged Particle Baffle Brass Radiator Holder Wheel Silicon Surface Barrier Proton Detector Evacuated Detector Chamber (25 cm I D) - Motor Evacuated Beam Trap (8cm ID) Figure 1. Principal features of proton-recoil fast neutron spectrometer.

14 held in place by ev bonds and scattered by Mev neutrons. Since the hydrogen nuclei are scattered from within the radiator, they lose some energy before leaving it. If the remainder of their energy is deposited within the detector, then for neutrons with energy E which scatter protons from the radiator through an angle r to the detector, E Cf i (i)^ + r a X ffD4l^WR DETCTOR This equation assumes the region between the radiator and detector is evacuated and the detector window is very thin. Because the protons are scattered through some angles in $5 about 4, there are small variations in cos 2o Also, since the protons travel various distances in the radiator before escaping it, there are variations in the proton energy losses in the radiatoro Thus, it is necessary to rewrite the above equation in terms of average values in the following approximate form. E i + -- (i) To simplify the notation, define Hence the neutron energy, 2 Enery 2. Energy Calibration The energy calibration of the spectrometer is based on the above re

15 lation. The proton energy deposition in the detector, Ep is measured with a calibrated detector system. This calibration is described in Section II-B-5. The proton energy deposition in the radiator, 6Ep, is generally much less than Epo Ep is calculated using range-energy data(79-81) or energy loss data(53'81) for protons traversing an average radiator thickness of /2)tR sec 4, where tR is the radiator thickness. Determination of sec 4 and cos24 requires a careful measurement of the radiator-detector geometry and the calculation of their average values as determined by the angular dependence of n-p scattering. Details of this calculation are in Section II-F-3. 35 Thick Detector Operation In order for the detector response to be proportional to the incident recoil proton energy, the proton must be stopped in the depletion region. A detector thick enough to stop all incident protons is designated a "thick" detector in this connection. Since the measured neutron spectra decrease exponentially above 9 Mev, a detector thick enough to stop protons scattered by 14 Mev neutrons responds essentially as a thick detector for measurements to 12 Mev, A block diagram of the instrumentation used with this detector is shown in Figure 2. 4o Thin Detector Operation As willbe demonstrated in Section II-D-3, the use of a thin detector results in important background reduction. Of course, a thin detector does not stop all incident protons~ Thus, in order to accept only those detector

CH2 THICK 2PON PROTON RADIATOR DETECTOR RADIATOR NEUTRONS' PROTONS PREAMP BIAS AMP MULTICHANNEL ANALYZER Figure 2. Block diagram of instrumentation used with thick proton detector.

17 signals due to protons stopped in the thin detector, the two-detector, anticoincidence arrangement shown in Figure 3 is used. The energy response of the two tandem detectors is indicated in Figure 4. As these figures indicate, protons which traverse the thin detector and deposit enough energy in the second detector to exceed the discriminator level (0.5 Mev), trigger a coincidence pulse which blocks the signal from the thin detector, The dashed lines of Figure 4 show this anticoincidence arrangement should operate satisfactorily for proton energies up to 4.9 Mev. This corresponds to neutron energies up to 6 1 Mev. The detectors are described in the next section and their instrumentation is covered in detail in Section II-Co Bo DETECTORS Semiconductor devices were first used for nuclear radiation detection by Van Heerden(2) in 1945o His bulk type detector has been succeeded by the junction type detector first reported by McKay3) in 19490 It was 1960 before extensive use of the latter detector was reported (84,85) Today surface barrier and diffused junction detectors of intrinsic and lithium-ion-drifted silicon and germanium are used widely. The detectors used with this spectrometer are intrinsic silicon surface barrier detectors. 1. Silicon Surface Barrier Detectors These detectors were chosen because of their following characteristics^ thin windows, linear response, high resolution, fast response, high stability, low gamma sensitivity, and compact size. Details of the detectors

18 CH2 THIN PROTON PROTON RADIATOR DETECTOR DETECTOR FOR,_____ | ____ PROTONS WHICH PASS THROUGH NEUTRONS PROTONS THIN DET OR BIAS PREAMP PREAMP BIAS AMP _ M AMP DISC DI SC. COINCIDENCE COINC PULSE CLOSE GATE SIGNAL MULTICHANNEL PULSE GAT ANALYZER Figure 3. Block diagram of instrumentation used with thin proton detector showing anticoincidence system that counts only protons stopped in thin detector.

6 5-HIGHEST ENERGY INCIDENT PROTON FOR WHICH ANTICOINC DENCE SYSTEM OPERATES / /ENERGY DEPOSI TED IN >4W / - -\ /SECOND DETECTOR 24 | /ENERGY uZ 3 |~ /~DEPOSI TED L 3 IN FIRST DE- - /TECTOR (245 5/ MICRONS THICK) 2 DISCRIMINATOR LEVEL / FOR SECOND DETECTOR I 0 1 2 3 4 5 6 7 8 9 10 ENERGY OF PROTONS INCIDENT ON FIRST DETECTOR (MEV) Figure 4. Calculated energy response of two tandem silicon detectors to protons.

20 are given in Table 35 The operation of these detectors is based on the properties of the depletion region in a semiconductor diode operated with reverse bias, Electron-hole pairs generated in the depletion region by ionizing radiation are collected to provide a direct measure of the energy deposition in this region. The theory of these detectors deals primarily with the establishment of the depletion region and the generation and collection of electron-hole pairs. Although the theory is covered in the literature, ( 89) the essential ideas will be reviewed briefly here, 2, Depletion Region When n-type and p-type crystals of the same material are placed together, electrons diffuse from the n-type into the p-type crystal and holes diffuse in the opposite direction. The region in which this diffusion occurs is characterized by a depletion of the majority charge carriers and the presence of the resulting space charges due to the bound impurity sites (donors and acceptors)o Reverse biasing (plus to n-type and minus to ptype) the junction widens the depletion region. Hence, because the region is depleted of the majority charge carriers, its conductance is low and very little current flows through it, Forward biasing the junction removes the depletion region and current flows freelyo This action is the basis for the semiconductor diode rectifier. The depletion region of the semiconductor diodes is not formed by placing two crystals together, Rather, for the silicon surface barrier detector, a p-type surface layer is formed on a single n-type silicon crystal by ox

TABLE 3 SILICON SURFACE BARRIER DETECTORS Depletion Crystala Detectorb Leakagec 5.5 Mev AlphaC Thickness Depth Area Resistivity Bias Capacitance Current Resolution Detector (mm) (mm) (cm2) (ohm-cm) (volts) (picofarads) (microamps) (Kev) Manufacturer Thick Detector 1.040 1.040 1.77 12,000 375 20 1.2 30 ORTEC Thin Detector 0.245 0.245 1.77 5,700 55 80 0.7 40 ORTEC (First Tandem Detector) Second Tandem 1.0 0.16 3.0 4,700 35 200 0.7 60 G. G. Sherwood Detector Univ. of 4ich. aIntrinsic n-type Silicon bVDET Vo + VSUPPLY - ILRLRL = 22 megohms, VO - 0.5 volt CMeasured in Evacuated Test Chamber at 22~C dOak Ridge Technical Enterprises Corp.

idation. The depletion region extends into the n-type crystal. The approximate thickness of this region is found by solving Poisson's equation for constant space charge density and using the reverse bias and zero electric field as boundary conditions. This thickness is x = (kV/2j Ne)l/2, where k is the dielectric constant of the crystal, V is the reverse bias, e is the electronic charge, and N is the charge density due to impurity sites. If all impurities are ionized, the resistivity of the crystal is p = 1/tNe, where. is the majority charge carrier mobility, Thus, x =(p Vk [/2r)1/2 shows the depletion thickness varies as the half power of the crystal resistivity and the reverse bias. The capacitance of the depletion region is approximately that of a parallel plate capacitor of the same thickness with a silicon dielectric, Thus, the capacitance per unit area, p - 4,r1S s e4i^ ] 1) When the crystal resistivity and breakdown voltage are sufficiently high, the reverse bias can be increased until the depletion region extends from the p-type surface layer to the other side of the n-type crystal. The resulting fully depleted detector has three advantages over the partially depleted one. First, with the reverse bias somewhat higher than that required for full depletion, the thickness of the depletion region and hence the detector capacitance are insensitive to bias fluctuations, Secondly, with thin windows on both front and back, essentially all of the energy lost by charged particles traversing the detector is deposited in the depletion.

25 region. Thirdly, the pulse rise time is reduced as the undepleted region of the detector is reduced. This is because the undepleted region contributes to the series resistance of the detector and the time constant of the detector equivalent circuit varies as this resistance. As indicated in Table 3, both the thick and thin detectors are fully depleted. 3. Electron-Hole Pair Generation The average energy required to generate an electron-hole pair in the depletion region is predicted by Shockley(90 91) to be ~ s, E9 + rER where Eg is the energy gap between the valence and conduction bands, ER is the energy of the highest frequency optical mode phonon, and r = (Li/LR), the ratio of the mean free path between ionizing collisions, Li, and the mean free path for phonon collisions, LR. For silicon at 300~K, Eg = 1.12 ev. With r = 17.5 and ER = 0.063 ev, E = 3.57 ev. Until recently, all measurements indicated that E was independent of the mass, charge and energy of the ionizing particle. However, careful measurements by an Italian group(92) give ec = 3.61 + 0.01 ev for the 5.49 Mev alphas of Am241 and e = 3.79 + 0.01 ev for the 0.365 Mev conversion electrons of Sn11. These results have been substantiated by a U. S. (95) group(93 who found ec = 3.60 + 0.01 ev for the same alphas and ce = 3580 + 0.01 ev for the 1.05 Mev conversion electrons of Bi207. Both sets of results are for silicon at 300~K (Eg = 1.12 ev) and with the data extrapolated to 0~~~~~~~~Or

24 infinite collecting electric field to eliminate the influence of trapping andrecombination. The approximately 5% difference in E and Ee is not explained by Shockley's model. Even so, the agreement with the predicted 3o57 ev gives some credence to his model. 4o Electron-Hole Pair Collection The collection of electron-hole pairs is impeded by two mechanisms: trapping and recombination. These phenomena usually occur at imperfection sites in the crystal. Trapping of the charge carriers refers to the immobilization of the carriers at trapping centers. If the mean carrier lifetime is on the order of or less than the amplifier clipping time, a substantial portion of the signal is lost. The loss of charge carriers by recombination is most likely to occur in the vicinity of the particle track where the ionization density is highest. This recombination takes place before the electrons and holes in the ionized column are separated by the applied electric field. Hence, recombination increases with increasing ionization density and decreasing electric field. The principal consequence of trapping and recombination is to reduce the collection efficiency and energy resolution of the detector. The collection efficiency, r = Q/Ne, gives the ratio of the charge Q on the collecting electrode to the charge generated by the release of N electron-hole pairs. Here N = E/e, where E is the energy deposited in the depletion region and e is the mean number of ion pairs generated per unit energy deposited in this region, Most junction detectors can be biased suf

25 ficiently for r to be very nearly 100%. 5. Energy Calibration The energy calibration of the detectors and their instrumentation is based on the use of a precision pulse generator to determine the zero energy 241 channel and the use of the 5.49 Mev* alphas of Am241 to fix the channel width. The pulse generator, whose output is linear, was capacity coupled to the preamplifier input and the pulse amplitudes were varied to obtain a plot of pulse height versus channel number. The intercept of this plot was the zero energy channel. The linearity of this plot demonstrated the linearity of the preamplifier, amplifier, and ADC combination. The use of alphas to determine the channel width for protons is based on the assumption that Tp/Ep = l/EA. It is generally considered that the difference between qp and Pa is too small to be measured with present techniques. However, a recent measurement(97) gives cp/Ea'- 0.99. At the time of data reduction, this result was unavailable. Hence, in the absence of other data to substantiate it, this 1% is neglected. Future measurements of Ep/Ea for silicon may indicate the desirability of correcting the channel width for a small difference between ep and Ea. An approximate verification of the calibration procedure was made using the 1.05 Mev(98) conversion electrons of Bi207. Two previously described measurements give Ee/ca = 1.050 + 0.004 and 1.056 + 0.004. Assuming then *Am241 alpha spectrum: 5.4870 Mev (86.0%), 5.4455 Mev (12.7%), 5.5880 Mev (1.5%), and 20 others (<0. 5%). (94-96)

26 that C /e = 1o055 and e/Tp = 1.000, the 1.05 Mev electrons should be counted in the channel calibrated for 1,00 Mev protons. This response was observed. 60 Leakage Currents Another important characteristic of reverse biased junctions is the current flow in'the absence of radiation. This current, called bulk current, must be sufficiently small that heating of the crystal is negligible. The bulk current has two components: the drift current due to the diffusion of minority carriers into the depletion region and the generation current due to the thermal generation of minority carriers in the depletion regiono In addition to the bulk current through the depletion region, some current flows around its edgeo This edge leakage or surface leakage current depends on many factors including the design and construction of the detector, treatment and contamination of its surfaces, and ambient conditions such as temperature, humidity, and pressure. The sum of the bulk current and the edge leakage current is called the reverse current or leakage current, It must be much smaller than the signal currents resulting from radiation interactions in the depletion region if the signal-to-noise ratio is to be sufficiently high to permit good energy resolution, Leakage currents for the detectors used here are given in Table 35 Co INSTRUMENTATION Integrating or charge-sensitive preamplifiers are used with these junction detectors, This type of preamplifier is favored because its output

27 is very nearly independent of the detector capacitance. This is indicated in Figure 5 which shows the block diagram and equivalent circuit for a reverse-biased detector, charge-sensitive preamplifier, and amplifier. Here the amplifier output voltage pulse due to the collection of charge Q at the detector VAM = A(Q/C), where C = CCD + CA + (G+i)CF]/ G CF, G is the voltage gain of the preamplifier input section (with feedback capacitance CF), A is the combined voltage gain of the preamplifier (after the input section) and the amplifier, CD and CA are the capacitances to ground of the detector and the preamplifier input (including stray), respectively. This equation is derived for negative G. To follow convention,(99) IG1 is written as G. For G = 2000, (i.e., IGI = 2000), CD = 80pf (as for thin detector), and CA = 20 pf, C = 1.01 CF and V = 0.99 A(Q/CF). In order to keep CA small, the preamplifiers were located within 1 ft of the detectors. This was done by putting the preamplifiers in a watertight box that was attached to the top side of the detector chamber. Each preamplifier was connected to an amplifier in a temperature controlled instrument room through a 200 ft length of RG-71 doubly shielded, 93 ohm coaxial cable. The multichannel pulse height analyzer and anticoincidence system were located in the same instrument room. Block diagrams of the instrumentation are given in Figures 2 and 3. Details on the components are given in Tables 4 and 5.

CB RL CHARGE SENSITIVE AMPLIFIER VAMP + _'-+ PREAMPLIFIER G(2000 ---- A(32ARs ~RD-1- ____,,CF(6pf) RD5 TTCD RL T=CA RF(4.4 M) VAMP (22MS1) (20pf) Q VAMGAQ A Q AMP CD+ CA+(G+I)CF CF Figure 5. Block diagram and equivalent circuit for reverse-biased detector, charge-sensitive preamplifier, and amplifier.

29 TABLE 4 PROTON ENERGY ANALYSIS INSTRUMENTATION Component Manufacturer Model Preamplifier Tennelec 100A Amplifier Nuclear Data 150F Multichannel pulse height analyzer ADC Nuclear Data 150F Memory Nuclear Data 150M TABLE 5 ANTICOINCIDENCE INSTRUMENTATION Component Manufacturer Model Preamplifiers Tennelec 100A Amplifiers Sturrup 101 Discriminators Sturrup 501 Coincidence unit Sturrup 1401 Gate unit Nuclear Data 150F Do SIGNAL-TO-BACKGROUND RATIO Since low signal-to-background ratios (S/B) have been the principal limitation encountered in most measurements of reactor neutron spectra, the improvement of the S/B has been one of the main objectives in the development of this spectrometer system. Here the signal refers to those counts which result from neutrons entering the source end of the collimator, travel

30 ing through the collimator without being scattered, and then scattering protons from the radiator to a detector which is thick enough to stop them. The background, as it is customarily defined, refers to all nonsignal counts. 1. Sources of Background It is useful to consider the background as consisting of two components; nonsignal counts associated with the radiator and all other nonsignal counts. The latter component is measured by removing the radiator and is usually found to be the larger one. It is due to charged particles resulting from gamma and neutron interactions which occur within the detector and in the shielding and structural material in the vicinity of the detector. Data which indicates that gamma interactions within the detector dominate at higher energies and gamma interactions in material around the detector dominate at lower energies will be presented. The nonsignal counts associated with the radiator are due to (1) protons scattered from the radiator with such high energy that they are not stopped in the detector, (2) carbon ions scattered from the CH2 radiator by neutrons, and (3) protons scattered from the radiator by neutrons which either entered the collimator through the side wall rather than through the source end or entered the collimator through the source end, but were scattered in the collimator wall before reaching the radiator. The first case is designated as a nonsignal count because the measured proton energy is less than the energy of the proton incident on the detector. The third case, although not usually designated background in the literature, is designated such here because it does not qualify as

31 part of the above defined signal. 2, Design Considerations. As previously stated, most of the background counts usually result from gamma interactions within and near the detector. Hencethe spectrometer was specifically designed to reduce this source of backgound. The principal features are shown in Figure 1. This spectrometer has been operated 7 8 with the source end of its collimator in fission gamma fields of 107 to 10 roentgens/hour. The longevacuated, conical collimator extracts a well-defined neutron beam from the reactor. It also allows the detector chamber to be far enough from the reactor core so that the pool water is an effective shield, The effectiveness of the water shielding was demonstrated by a measurement of the background count rate with the collimator removed. The measurement showed that only 10 to 20% of the background counts from 2 to 5 Mev are due to radiation which did not enter the detector chamber through the collimatoro The cylindrical steel and lead shields assist in the collimation of fission gammas. The desirability of this collimation is indicated in Figure 6, This figure shows the detector count rate without radiator as a function of the detector position above and below the collimator axis, This data was taken with only the lead shield installed. The background reduction by a factor of over a hundred along with a signal reduction of only 10% dictated the use of an off-axis detector position. The detector was positioned with its center 4,2 cm above the collimator axis and 10o2 cm

32 120 DETECTOR DIAMETER: /.9 CM 10 ~ COLLIMATOR THROAT DIAMETER. 1.9CM 100 |0 90 H I80 0 H 70 t __ 60O z ~ 500 LFigure 6 Background count rates for detector positions above and w 40 -30 20 I0O -4 -3 -2 -I 0 +1 +2 +3 +4 DISTANCE CENTER OF DETECTOR ABOVE COLLIMATOR AXIS IN CM Figure 6. Background count rates for detector positions above and below collimator axis.

33 from the center of the radiator positiono The resulting angle between the radiator-detector centerline and the collimator axis was 24,~ As a result of the suggestion by Dro Fo C. Maienschein of ORNL to increase the thickness of the gamma shield, the steel shield was addedo Its addition reduced the background counts from 2 to 5 Mev by 44%, The electron filter is a 50-mil thick aluminum plate located over the front of the collimator throat to reduce the number of electrons streaming into the detector chamber. It reduces the background counts from 2 to 5 Mev by 36%I The charged particle baffle shields the detector from charged particles originating in the rear portion of the collimator throat. The beam trap reduces backscattering to the detector, The radiator wheel is a thin brass plate with six equally spaced 2, 1-cm diameter holeso They are slightly larger than the 1,9-cm diameter of the collimator throat, The wheel can be rotated and stopped so that, the center of any one of the holes is aligned with the collimator axiso Various thickness polyethylene radiators can be mounted over these holes on the collimator side of the radiator wheel. For these measurements, only 1.25 mg/cm2 and 2o95 mg/cm2 thick CH2 radiators were used, A blank wheel position was aligned with the collimator axis for the measurement of the background counts not associated with the radiator, The evacuated detector chamber is much larger than that required to house the detector, radiator wheel, and motoro The extra volume provides free space around the detector to reduce charged particle events in material near the detector~

34 30 Influence of Detector Thickness The limitation imposed by a low S/B is illustrated by the data of Figure 7o The S/B for this data and for data taken with 60 cm of water between the reactor core and collimator is shown in Figure 8. The lower S/B for the latter data indicates the background is dominated by gamma interactions since water attenuates fast neutrons (the signal) more than it does gammas (the background)o The S/B for the latter data also demonstrates that reliable data (i.e., S/B > 1) cannot be taken with this radiator-detector combination through 60 cm of water in the energy range from 2 to 5 Mev, Resolution considerations prohibit the use of a thicker radiator to improve the S/B in this energy region. An alternative is to use a thinner detector. The effect of using a detector of the same area but with its thickness reduced by a factor of four is shown in Figure 9o These curves show that the ratio of background counts for thick and thin detectors is equal to the ratio of - their thicknesses at high energies but is much greater at lower energies, Thus, since the detector areas are equal, the background at high energies is proportional to the detector volume. This indicates gamma interactions within the detector are the main source of background at these energieso At the lower energies, the curves indicate the background is dominated by gamma interactions in material outside the detectors. Data taken with the thin detector is shown in Figure 10. The coincidence spectrum shows the energy lost in the thin detector by protons which are not stopped in it. The anticoincidence system discussed earlier prevents

55 ~~106~ ~0 105 r —-- 0 0 0 04 _~ * 0 00. * 0 1 I04_______0_____ ^WITH RADIATOR o - 0S -0. 0L 0 0 o 103 --------— ^ —------------ * 0 0 0 0 103 000,% % ~~~o tO 0 WITHOUT 0.. % 0 0 0 *,'~0' 0 ~ 0 D S0 Figure 7. Proton recoil spectrum obtained using thick (1040 microns) detector and thick (2.95 mg/cm2) radiator with collimator against reactor core.

36 24 -- 22 S (COUNTS WITH RADIATOR)-(COUNTS WITHOUT RADIATOR) 20- B (COUNTS WITHOUT RADIATOR) 18 16 COL LIMA TOR AGAINST REA CTOR CORE 14B 2 10 I 8 4 60 CM OF WA TE IBETWEEN COLLIMA TOR AND CORE 2 1 2 3 4 5 6 7 8 9 10 PROTON ENERGY IN MEV Figure 8. Signal-to-background ratios for proton recoil spectra obtained using thick (1040 microns) detector and thick (2.95 mg/cm2) radiator.

37 250 oI GS( 1 I< DETECTOR AREAS ARE EQUAL Go 1 BACKGROUND COUNT 200 RATES ARE NORMALIZED S |\ l8 \ ~TO REACTOR POWER I I O 0 1i o 150 QI 0 I_ \ \ a \ \ C 50 COL LIMATOR\ 20 CM OF WATER C.) ~ REACTOR \ \ AN CORE o COR CORE 0 ~ 0 I 2 3 4 5 ENERGY IN MEV Figure 9. Ratio of thick detector background to thin detector backgound.

oq.oDsj q.suTS'B ao'-BUIaTTTOO qqTb aoq.19Tpsa (gMO/Sm ^F*T) UTqq puse ao;oDa;p (suoTopu'l ) uTqT. SuTsn pauTS.qo SoDG(Is T'TOoGI uoq-o, I'OT 01 mST (A3 V) A983N3 NOIOd L 9 S t ~ __ I 0-0 —--. —---------- 001 I0 i. < Sl~n~D * |< 01 O0 00I** I S g*I I _ o 0* 0 0 - 0 I I I 2 ~*.. * __.***0. 0 OJ 0O 0 * 0 n0 0 — OiviIavi HtoM I 0 0I0. 0H0M 0 ~ O0. - - 4 S iNn -.l z _____ 0 S01 0ItIIQI N ----— It- 000001 0'9~O.I.I(IV;M -l0 ~ O0~~~~~~~~~r

39 these counts from being recorded. Alternately, they can be recorded separately as shown in Figure 10 and subtracted along with the counts recorded with the radiator removed. Use of the thin detector and anticoincidence system permits measurements above 2 Mev through 60 cm of water to be made with S/B > 1. 4. Carbon Recoils It is shown in Appendix A that the background due to carbon recoils depends on the neutron energies of interest and on the shape of the spectrum being measured. For a hypothetical neutron spectrum which is constant from energy 4.24 (EC)min to Emax, and zero thereafter, the maximum background occurs at the lowest neutron energy of interest, Emin. For the present measurements, Emin = 2 Mev and (EC)min = 1.5 Mev. If Emax is 14 Mev, the maximum background due to carbon recoils is 4%, and if Emax is 18 Mev, it is 6%. These are conservative estimates, of course, since the actual measured spectra decrease rapidly with energy above the minimum energy, 4.24 (EC)min = 6.36 Mev, required to scatter 1.5 Mev carbon recoils to the detector. 5. Collimator Effects There are two effects which occur when the collimator walls are not black. First, some of the neutrons which exit the collimator entered it through the source end but were scattered in the collimator wall before reaching the exit. Secondly, some of the neutrons that reach the collimator exit initially entered the collimator through the side wall rather than *The lowest carbon recoil energy of interest is (EC)min = (Ep)min = (Emin cos2J - 8Ep), and 4.24 is the ratio of the incident neutron energy to the carbon recoil energy.

40 through the source end, In Appendix B, these effects are estimated by use of a crude model to introduce 4.8% and lo7% errors, respectively, when using the long conical collimator of this spectrometer. Because the background due to carbon recoils and collimator effects is relatively small and the corrections are difficult to determine, no corrections were made for these measurements, Eo EFFICIENCY The efficiency of the spectrometer can be defined either in terms of the neutron angular flux at the source end of the collimator or in terms of the neutron flux incident on the radiatoro These two efficiencies, of course, differ only by the collimator efficiency, For the first case, the total efficiency e(E) is defined as the number of neutrons with energy E counted per unit time per unit neutron angular flux incident on the source end of the collimator and directed about the collimator axis toward the radiator: ~(E)- t CE(S) gi(2) where: C(E )dE is the count rate in counts per sec. due to protons which are P p scattered from the radiator to the detector by neutrons with energies in dE about E and which deposit energies in dE about Ep within the detector. cp(E)dE is the number of neutrons with energies in dE about E per sec

41 2 per cm per steradian incident on the source end of the collimator and directed about the collimator axis toward the radiator. For the second case, a similar expression is used to define ER(E), the number of neutrons with energy E which are counted per unit time per unit neutron flux incident on the radiator. R~(E - 4, (5) where: cpR(E)dE is the number of neutrons with energies in dE about E per sec per cm directed about the collimator axis toward the radiator and incident on the radiator. e(E) and GR(E) are related by defining the collimator efficiency, 4 (F.) ~c - ~ te) -(4) In order to simplify the evaluation of cC and CR(E), the following assumptions are made: a. The radiator is positioned over the exit end of the collimator. b. The distance from the source end of the collimator to the exit end is large compared with the largest dimension of these two apertures, c, The distance from the radiator to the detector is large compared with the largest dimension of these two components. d. The anisotropy of n-p scattering in the center-of-mass system is negligible for the neutron energies of interest, (This is reasonable because n-p scattering is essentially 100% s-wave scattering up to 10 Mev and

42 is still 99% s-wave scattering at 14 Mev.)(100) e. The radiator is sufficiently thin so that neutron attenuation and multiple n-p scattering are negligible. From its definition, ^e s. s l _i t1 T l a Lc where: Q is the solid angle subtended at the radiator by the source end of the collimator in steradians, AC is the area of the source end of the collimator in cm2. LC is the distance from the source end of the collimator to the radiator end in cmo Also from its definition, ir( E9c ( C in cw where: (NHtRAR) is the number of hydrogen atoms in the radiator. H NR is the number of hydrogen atoms per milligram of radiatoro t is the thickness of the radiator in milligrams per cm R AR is the radiator area in cm2 EnP(-. is the differential cross section for neutrons with energy E dS2 to elastically scatter protons through the laboratory angle 4 with respect to the direction of the incident neutron, averaged with respect to A, in cm2 per hydrogen atom per steradian,

43 AD Q = A is the solid angle subtended at the radiator by the detector D L D in steradianso AD is the area of the detector in cm2. LD is the distance from the radiator to the detector in cm. From assumption (d), e^.p(~^) (g(u) _ (^ where: a (E) is the cross section for neutrons with energy E to elastically n-p scatter protons in cm2 per hydrogen atom. cos 4 is the cosine of the laboratory scattering angles averaged with respect to t. Combining these terms, (e-7} = X(Rt8 co ) E) i n (5)F C Taking the product ECER(E) to get the total efficiency, ~~(~} = X(NAt?^- (S R ^ } c; r^ Wtevat di.; (6) An outstanding feature of these efficiency expressions is that the energy dependent term, a p(E), is very well known (< + 1%). Figures 11 and 12 show eR(E) and c(E) as calculated using the following constants~ NH = 0.86 x 1020 H atoms/mg R t = 1.25 and 2o95 mg/cm2 AC = M (5ol cm)2 = 81.7 cm2

7x10I6 CALCULATED EFFICIENCY: NUMBER OF NEUTRONS COUNTED PER UNIT TIME PER UNIT NEUTRON 6 _____________ FLUX INCIDENT ON RADIATOR 5 ________ __________ _________^ 2.95 MG/CM2CH2 RAD/ATOR 4 z?\.^5 AG/CM22 CH2 RADIATOR 2 012 3 4 5 6 7 8 9 10 II 12 NEUTRON ENERGY (MEV) Figure 11. Calculated efficiency: ~R(E).

7xlO-9 7 \ 109 CALCULATED TOTAL EFFICIENCY: NUMBER OF NEUTRONS COUNTED PER UNIT TIME PER UNIT NEUTRON ANGULAR FLUX INCIDENT ON SOURCE END OF COLLIMATOR AND 6 ------ \ - DIRECTED ABOUT COLLIMATOR AXIS TOWARD RADIATOR 5 Ir 4 ---,_ i- f | 2.95 MG/CM CH2 RADIATOR u 3 o 1.25 MG/CM2 6CH2 RADI/AT TOR 02 I _____ 2 3 4 5 6 7 8 9 10 II 12 NEUTRON ENERGY (MEV) Figure 12. Calculated total efficiency: e(E).

46 AR = t(0,95 cm)2 = 2.84 cm2 2 2* AD = (0o75 cm) = 1,77 cm LC = 315 cm LD = 10o2 cm cos = fcopsf(t) d* = 0.91 cos2 = fcos2f(t) dr = 0,83 sec f = Jsecrf(t) d* = lo10 The last two quantities are used to evaluate E = E cos2 - 5E and P P 5Ep (1/2S)fRdEdx)dx (1/2)t sec (dE) The normalized scattering b R *Ll Ax E frequency, f(4)d*, is derived and evaluated in Section II-F-3, From the definitions of eR(E) and e(E):, the differential fluxes ~Q~JE) C.(El (7) The differential count rate, C(E ) = N(E )/At AE,, where N(E ) is the p P P p number of counts accumulated during At in the channel whose width is AEp and whose midpoint is Epo To find dE recall P _ P dEp r Thus, As. / -gf where *Detector area was measured by counting Am241 alphas with and without an aluminum mask (1.29 cm2 aperture) in front of detector.

47 Since the latter derivative is negative, E, I - ___ _l____ __ _ (9) dEp - ^^ This Jacobian was calculated and the results are shown in Figure 135 Fo ENERGY RESOLUTION The spectrometer energy resolution is defined as AE/E, where AE is the FWHM of the spectrometer response function for monoenergetic neutrons of energy Eo Here the neutron energy E = (E +8Ep)/cos2o The resolution is found using the relation where u = u(xl, x2, x3, 000)0 Thus, (E;) P 2). (A) E + 10) lo Detector Term The detector term, AE /E cos2g, is the smallest and is negligible at all but low energies (6% at 2 Mev, 3% at L Mev) Table 3 gives.AE as 30 and 40 Kev for the thick an ththin detectors, respectively, in an evacuated test chamber0 When they are installed in the spectrometer and it is submerged in the reactor pool as it is during normal operation, LAEF of both

1.28 1.26 1.24 1.22 1.20 /.25 MG/CM2CH2 RADIATOR 1.18 dE 1.16 d-Ep 114 2.95 MG/CM2 CH2 RADIATOR 1.12 1.10 1.08 - 1.06 1.04 1.02 1.00 2 3 4 5 6 7 8 9 10 I 1 12 NEUTRON ENERGY (MEV) Figure 13. Calculated energy Jacobian: dE/d:Ep.

49 detectors increases to about 60 Kev. This increase is probably due to ground loops. Also, AEa increases to 140 Kev during some periods. During the same periods, a one megacycle ripple is observed on the preamplifier output. The appearance of this ripple has been found to correspond to the broadcasting time of a local, daytime radio station which transmits at 1.05 megacycles. Since spectrum measurements were taken about equally during day and night, an average AEa is 100 Kev. This value is used for AEp. As before, cos24 = fcos24f(t)dV = 0.83. Hence, AEp/E cos2* = 120 Kev/E. 2. Radiator Term The radiator term, A(5Ep)/E cos24, is the dominant term at low energies, but becomes negligible at high energies. It can be estimated by neglecting the variations in t and assuming all protons are scattered through some mean angle 1. Then the response function is a rectangular function whose tRsect maximum energy is E cos2 and whose minimum energy is E cos24- fo (dE/dx)dx. tRsec T Thus, the width of this rectangular function is A(&Ep) = / (dE/dx)dx R t sec t(dE/dx) p. Replacing sect by sect = jsecc f(t) d4 = 1.10, A(&Ep) = ^p" p 2 &Ep and A(3Ep)/E cos2 ~ 2.41 Ep/E - 1.32 tR (dx /E. 3. Geometry Term The last term, A(cos2V)/cos27, is called the geometry term because it is determined primarily by the scattering angles allowed by the collimatorradiator-detector geometry. However, it also depends on the angular dependence of the n-p scattering cross section. As before, the scattering is

50 assumed to be isotropic in the CMCSo Also, the neutrons are assumed to be normally incident on the radiator. The small angular: divergence of the long, conical collimator makes the latter assumption very good. Thus,the geometry term is determined by the radiator-detector geometry and the cosine of the laboratory scattering angle. This term is independent of neutron energy, and it is the dominant term at high energies, A(cos2l) is the FWHM of the normalized distribution function f(cos24), where f(cos2r)d(cos2*) = f(4) dt and f(n)d* is the fraction of the counts due to protons scattered in d1 about,o To find f(t), consider a beam of neutrons normally incident on the differential radiator area, dAR, shown in Figure 14o The resulting current of protons scattered in d* about V from dAR to the differential detector area, dAD, is JR (EIE rn 9,1)0RJA: An (ir,7" AY)11 SllR S where: Jn (E, r, )dEdAR is the number of neutrons with energies in dE about E which are normally incident on dAR per second. J (E, r, 6, t) dEdARdQD is the number of protons elastically scattered by neutrons with energies in dE about E from dAR into dQD per second, Assuming Assuming djL 31~~~~'r

S(re,4l) dAD = (r, 8, )dp DETECTOR P=Htan' RADIATOR Rr dAR=rdrd8. _ DI J —---— COLLIMATOR AXIS — k —-- H J-H FRONT VIEW SIDE VIEW Figure 14. Radiator-detector geometry used for calculation of f(t) and f(cos24).

52 and;rn(Er, ) = J;(E) F(r9) g (E~, B)<w J S 2R d:p(E) Jn o()1E F r,) 5(r, C,) ) oR fiO, a Vy Define: AR 5 (, ) R. P F, r), r, ONe ) z Substituting, Define: P(a,^) )y S r( Ely P(E,W)at: s tARi/rH) %,(el 5(t) Srt^^ But, IP(EY)1S f W ( ) c _ j 4) Rca s O where the normalization constant where the normalization constant To find f(cos24), recall f(cos24) d(cos24) = f ()dr. Since d(cos2) -2 cos * sin r dr, f(cos24) = -(Z/2)S (f) cot t d, The determination of f(x) and f(cos24) requires S(r). The function S(4) must be evaluated for a specific radiator-detector geometry and a

53 given F(r,G). Here it is assumed that F(r,G) = F(r). Thus, 5w) i I F() s5 (r> ^t) l^^ p r This integral is evaluated by the following graphical-numerical method, Draw to scale the front view of the radiator and detector shown in Figure 14o Then draw concentric circles within the radiator that divide it into m equal areas. Next, draw radii which divide each of the m areas into n equal areas, This procedure is illustrated in Figure 15 for m=3 and n=12o Each of the resulting mn = 36 areas is equal. Due to the symmetry, only the 18 areas in the right half of the radiator are used. Arcs with radii which correspond to various values of 4 are swung from the centers of these areas to intercept the detector area. From Figure 14, the arc radius, p(r) = H tan 4o Figure 15 shows arcs drawn from area (m,n) =(3,5) for integral values of ro The intercept of 0(24~) with the detector area is S(r, 8g, 24~). A set of arcs with radii corresponding to integral values of r was drawn for each of the radiator areas (m,n) The length of each intercept with the detector area was measured to get S(rm, G,9,f) Using these values of S(rm, nn, t)S(4) = (^AR/A-R) Z F(rm) S(rm, en), m,n where (PR/1R s ((/i^) Thus, i( m: ( i//) C 2 F(, (, 6 V) and (ffi;X (^c (3/3bh cotW ^ ^{ E FttH <; M.. d An

54 S(tr3, —- 26~ 250 240 230 220 210 DETECTOR 200 190 ---- 180 170 p(240)=H tan 24~ (r3,85) RADIATOR Figure 15. Example of construction used for calculation of S(W).

55 The latter function was evaluated and plotted. The FWHM of this function is A(cos2)., It was evaluated for three cases to find the influence of the radial function F(rm)o The results are shown in Table 6o TABLE 6 INFLUENCE OF F(rm) ON A(cos24) Case F(rl) F(r2) F(rj) A(cos2t) A(CoI) cos24 I 0o333 o0333 Oo333 o0lO8 O 130 II Oo500 o 333 Oo 67 Ool00 O 120 III 1.000 0 0 O O083 Oo100 The function, f(cos24) is shown in Figure 16 as calculated for case IIo Due to the cylindrical collimator throat, the F(rm) used for this case is expected to be a good estimate of the actual F(rm)o The results shown in the table indicate that the uncertainty in 4(cos2)V), introduced by the uncertainty in F(rm), is less than 10%o The average values of cost, cos24, and sect calculated using f(4)d* are relatively insensitive to the choice of F(r m) L4o System Resolution The detector, radiator, and geometry terms are combined to get the system resolution as followso

56 0.20 0.18 0.16 0.14 0.12 0.10N 0nI (cos2)=o 006 0.06 0.04 0.02 0 LI I I I_ X 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 cos 2'I Figure l6. Calculated distribution function: f(cos2r).

57 The resolution (ioeo, FWHM in per cent) is shown as a function of neutron energy in Figure 17 for the two radiator thicknesses used. Due to the better resolution at low energies, the thin radiator is used with the thin detector for neutron energies from 2 to 6 Mevo The thick radiator and thick detector are used together for neutron energies from 4 to 12 Mev. 5o Influence on Measurement The effect of the spectrometer resolution on measured neutron spectra depends on the FWHM and shape of the resolution function and on the shape of the neutron spectra. Since the fission spectrum decreases approximately exponentially at high energies, it is of interest to know how the resolution influences the measurement of an exponential spectrum. To estimate this effect, the resolution function is assumed to be Gaussiano Thus the measured spectrum, d (,E).-0( (.,Ei where (I) E Using R = AE/E and o(E) = E/2o355 = RE/2.355, evaluation of the integral gives dp{E|) ^ e, t3'33) (12) For a = (1.290 Mev)-1 = 0.7752 Mev-1 and R = 0.12, cpm(E)/p((E) = 1o03 for E = 6 Mev and lo 12 for E = 1.2 Mev.

28 26 24 22 20 HZ 18 2.95 MG/CM2 CHz RADIATOR LiL 0 16 o-14 I 12 /.25 MG/CM2 CH2 RADIATOR LL- 10 6 4 2 B 10 I I l l I I m 2 3 4 5 6 7 8 9 10 II 12 NEUTRON ENERGY (MEV) Figure 17. Calculated energy resolution: AE/E.

59 The slope of the measured spectra is Using the same a and R, Jj7L = -,75 Ilev -' - (e,3Y M's ^r E S lev -Io.3(o/) Ney r /II p/ayeI For comparison, the slope of the actual spectrum is, _ _ X -^ a 775R Etch s - ((^< 1^^ S9)' Gt ~> The above ratios show the spectrometer resolution causes the measured flux to be greater than the actual flux at a given energy, and the slope of the measured spectrum to be less than that of the actual spectrum. The influence of a change or uncertainty in the resolution on the measured slope is given by the following relation. A(AL~) I 1 d-_ (1L) (^/4) s S- R Using the same a and R again, ^o y mad slo p e ) in t s isen s F.blt s~- - p- 4} 4-4i) Thus, a 10% change or uncertainty in the resolution results in a change or uncertainty in the measured slope in the opposite sense by less than 0O5%~

60 Go ENERGY RANGE As has been indicated, the energy range of the spectrometer is from 2 to 12 Mevo The lower limit is determined by two factors. First, the signal-to-background ratio, which increases with decreasing energy, drops below one at about 2 Mev for most of the measured spectra. Secondly, the resolution becomes poorer at lower energies. The upper limit is also determined by two factors, The low efficiency and the few neutrons with energies above 10 Mev result in poor statistics at these energies unless very long counting times are used, Also, the detector must be thicker than the range of the highest energy protons of interest. The above considerations indicate the complex nature of the spectrometer energy range, It depends on the thickness and geometry of the radiators and detectors, and on the intensity and energy dependence of both the source and the background,

CHAPTER III EXPERIMENTAL RESULTS Ao FORD NUCLEAR REACTOR The spectrum measurements in water and graphite were made in the Ford Nuclear Reactor (FNR) pool using core leakage neutrons as the fast neutron source. 1o Reactor Description *The FNR is an open pool type research reactor operated at power levels up to 2 megawatts at The University of Michigan. It is very similar to the Bulk Shielding Reactor I (BSR-I) at Oak Ridge National Laboratory. The volume fractions of the standard fuel element are 0.2% uranium (95% U255), LLlo6o aluminum, and 58.2% water. The H20 serves as moderator, coolant, reflector, and shieldo The reflector system also includes a tank of D20 on the north core face and graphite reflector elements on other faceso Different core configurations were used for the water and graphite measurements. The two configurations are shown in Figure 1.8. 20 Reactor Power Measurement The measured spectra were normalized to reactor power. Reactor power was measured by stopping the secondary coolant flow while the reactor was operating at a steady state power level and observing the rate at which the pool water temperature increased as the primary coolant water returned to the pool. The average reactor power, At where AT/At is the rate of the pool water temperature increase, m is the mass of the water in the pool and the primary cooling system, and cp is the 61

62 TDIR R R F F F F F/S F F F F F F F FLC F FC D20 62 cm NORTH ZERO COLLIMATOR TANK POSITION FOR F F/F F/ F WATER MEASUREMENTS F F F F F TD F F FTS_______ 10 cm -- 40 cm, 32cm - 2cm -- _ R TD R R RTS R F F IF F/sF R F F F F RFF/CFF/CF D20 62 cm NORTH R F F F F F TANK ZERO COLLIMATOR R F F/C F F/ C F POSITION FOR GRAPHITE MEASURE- R F F F F F MENTS RTlD F JF T F FUEL ELEMENT (FUEL HEIGHT:60 cm) R REFLECTOR ELEMENT (GRAPHITE) F/S FUEL ELEMENT WITH CENTRAL CHANNEL FOR SAMPLES F/C FUEL ELEMENT WITH CONTROL ROD IN CENTRAL CHANNEL TS TUBE FOR SAMPLES TD TUBE FOR DETECTOR DURING REACTOR STARTUP Figure 18. Ford Nuclear Reactor core configurations.

63 specific heat of water For the FNR, (1/mc ) = 8 65~F/megawatt hour; This method assumes (1) nonfission heat sources are negligible, (2) heat losses are negligible, and (3) the pool- water is mixed thoroughly. These assumptions are apparently valid and the method is quite reliable and accurate (+5) (101) Bo WATER MEASUREMENTS As indicated in Figure 18, the spectrum measurements were made on the south side of the coreo The spectrometer was submerged in the reactor pool and the collimator axis was aligned with the north-south core centerline, A photograph of the spectrometer suspended above the pool is shown in Figure 19. Figure 20 shows the submerged collimator 60 cm from the souith core face, The demineralized pool water ranged from 355C to 435C during the measurements, lo Normalization In order to reduce the influence of flux shifts within the core due for instance to control rod withdrawal during xenon buildup, the spectrum measurements were normalized directly to the fast neutron leakage flux from the south core face. The spectra were then normalized to reactor power by relating the leakage flux to a single calorimetric measurement of reactor power for the same core configuration used during the spectrum measurements. The fast neutron leakage flux was monitored by activating aluminum wires and counting the Al27 (na) Na24 reaction* product gammas (137 and *This reaction was used because its threshold is in the Mev range (3.26 Mev)(26) and the half life of its product is well known (+0o13%)(102) and much longer than the half lives of other reaction products presento The other reactions are the A127 (n,p) Mg27 reaction with threshold at lo89 Mev and the A127(n,7) A128 reaction. The half life of Na24 is 14o97 hours whereas the half lives of Mg27 and A128 are 9 o4 minutes and 2~3 minutes, respectivelyo Hence, the activated aluminum wires can be allowed to decay until the only significant reaction product remaining is Na24o The effect of Na23 (n,-) Na24 reactions which result from thermal neutron capture by sodium impurities in the aluminum wires was minimized by using high purity aluminum and by covering the aluminum with 10 mil cadmium.

aec~~~~~***~~~~~r~~~~f *c~:-~cx: o*: a a CI ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 4: ~~~6Fiur 19. Spctomte susened abov FNB pool.rra rrrr

O! 11 |~~~~alN Figure 20. Collimator positioned 60 cm from RNR core.

66 2o75 Mev) with a 3" x 3" NaI (T1) crystal. Four wires were positioned 30 cm from the core for each activation. The wires were mounted at 90~ intervals on the circumference of a ring (30-cm diameter) that was centered on the north-south core centerline. With the wires in these positions, it was found that when the collimator was against the core, the aluminum activation was approximately 33% higher than it was without the collimator present. This undesirable perturbation was negligible at the other collimator positions, but did introduce an estimated +5% uncertainty in the normalized amplitude of the zero spectrum measurement. 2. Reactor Power The FNR was operated at 2 megawatts for all of the measurements except those with the collimator against the core. The latter measurements were made at 0.2 and 0.5 megawatt using the thick detector and thin detector, respectively. The lower power levels were used to limit the counting rates and thus reduce pile-up distortion. This distortion, was monitored by ob241 serving the width of the Am alpha peak. Negligible broadening (< 10%) was observed at the power levels used. 35 Counting Times and Statistics The water measurements were: made during a four-week period. The initial measurements were made with the collimator against the reactor core. For the measurements from 2 to 6 Mev made using the thin detector and thin radiator, three 20-minute foreground counts and three 20-minute background counts were taken in alternating sequence. After the zero spectrum was measured, measurements were made with the collimator 20, 40, and finally 60 cm from the reactor core. The measurement from 4 to 12 Mev for the 60cm spectrum made using the thick detector and thick radiator, required the longest counting time. Here six 10-hour foreground counts and six 5-hour background counts were taken in alternating sequence. Due to the few number of neutrons at the higher energies, the statis

67 tical uncertainties were largest at these energies. At 10 Mev the standard deviation (sigma) of a single point varied from 3.2% to 6.0%, and at 12 Mev it ranged from 6.5% to 12.9%. 4, Measured Spectra A machine plot of the measured spectra of FNR leakage neutrons which penetrated 0, 20.0, 40.0, and 60.0 cm of pool water is. shown in Figure 21. Each measured point was obtained by subtracting the normalized background counting rate (without radiator) from the normalized foreground counting rate (with radiator). Then, as indicated by Equation (8), the resulting counts per second per Mev of proton energy per megawatt of reactor power were divided by the total efficiency in cm2 steradian and by the energy Jacobian in Mev of neutron energy per Mev of proton energy. The resulting angular flux is expressed in neutrons per second per cm2 per Mev (of neu-4 tron energy) per steradian (directed normally to the: south.core:f ace).per. megawatt (of reactor power). The semilog plot of Figure 21 is characterized by three principal features. First, the FNR leakage spectrum falls off exponentially above 5 Mev as the fission spectrum does, Secondly, the attenuation of lower energy neutrons is much greater than that of the higher energy neutrons due pri:marily to the higher elastic scattering cross section of hydrogen at the lower energies. Thirdly, the progressively deepening dip in the spectra at about about 3 Mev is due to the elastic scattering resonance of oxygen at that energy, The scatter of the data at the higher energies.isj.due to

68 1012 IE \ NEUTRON PENETRATION IN H 0! a NORMAL TO REACTOR CORE z 5cs \^~~~~~- NIOBE 76 GROUP CALCULATION ^~~< "~ ~~I+ EXPERIMENTAL POINTS 10 10 Cf) U N z 5L 10, - 10. II I, 0 I CM x 0^ ^ ^^ ^^ ^ ^^~~~~~~~~0.0 CM 106 0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 NEUTRON ENERGY (MEV) Figure 21. Neutron penetration in water.

69 counting statistics. The calculated spectra shown in Figure 21 are discussed in Chapter IVo 5o Experimental Uncertainties The principal experimental uncertainties are summarized in Table 7. The uncertainties associated with the background were limited by restricting the reported data to that with signal-to-background ratios above one, Even so, with the collimator effects included, these uncertainties may be as high as + 10% at 2 Mev, The influence of the spectrometer resolution was to convolute the actual spectra with the spectrometer response function, ioe,, the measured spectra are averaged over the energy width of the response function. The averaging process results in loss of spectral detail and, as shown in Chapter II for an exponential spectrum like the fission spectrum above 5 Mev, the slope of the spectrum may be modified, The importance of the latter effect in determining the slope of the fission source spectrum is discussed in Chapter IVo Excluding these resolution effects, the total relative and total absolute uncertainties in the amplitudes of the measured spectra are typically +10% and +20%, respectively. Counting statistics increase these percentages somewhat at neutron energies above 10 Mev, and background uncertainties make them slightly higher at neutron energies near 2 Mev, The +2% uncertainty in the spectrometer energy calibration is due mainly to the uncertainties in the mean squared cosine of the n-p scatter

70 TABLE 7 PRINCIPAL EXPERIMENTAL UNCERTAINTIES Ao Proton Recoil Spectra Measurement Detector Energy Calibration: + 1% *Background: Avg. + 5%, Max. + 10% at 2 Mev *Counting Statistics: Avg. + 3%, Max. + 13% at 12 Mev for water Max, + 253 at 12 Mev for graphite Bo Conversion from Proton Spectra to Neutron Spectra Spectrometer Energy Calibration (includes detector): + 2% Efficiency: + 5% Co Normalization Reactor Power Measurement: + 5% *Aluminum Activation: + 2% except + 5% for 0 cm water Do Shield Geometry *Thickness: + 1.5%, + 0.75%, + 0.5% for 20, 40, 60 cm water + Oo 5 for graphite *Density: + 0.2% for water + 2% for graphite Eo Spectrometer Resolution *Denotes uncertainties associated with relative measurements.

71 ing angle (cos24 = 0.83+0.01) and the mean energy required for protons to generate an electron-hole pair in silicon (p = ea + 1%). C. GRAPHITE MEASUREMENTS The graphite measurements were made with graphite slabs mounted against the south core face. 1. Description of Graphite Slabs The graphite was high density, fine grained, HLM grade (Great Lakes Carbon Corp.). Its measured density* was 1.74 + 0.04 grams/cm3. Each slab was 20.2 cm x 62.5 cm x 62.5 cm. These dimensions include the 0.655-cm thick 6061 aluminum plate which completely encased each slab to keep it dry while submerged in the FNR pool. Two views of four of the slabs fabricated for this experiment are shown in Figure 22. Figure 23 shows three of the slabs positioned against the south core face during measurements at 2 megawatts. The collimator axis was aligned with the north-south core centerline as for the water measurements. The graphite slabs were suspended from above the reactor pool. The tube attached to the top side of each slab was provided for off-gassing.** IThe supplier specified an average density of 1.72 grams/cm3 for this grade **Little off-gassing was observed except from the slab nearest the core for a short period after the reactor reached full power. This was probably due to thermal expansion of air within the graphite as gamma heating increased the temperature of the graphite.

72 Figure 22. Two views of four graphite slabs.

73 Figure 25. Three graphite slabs positioned against FNR core......:''f~ ""''"*':'z:,::, ii~-:,:,,,:,.,:.,,:,,,.,,.,,,,,,,,,,,.,.,,

74 2. Reactor Core Modification Unfortunately the reactivity of the graphite slabs positioned directly against the fuel elements on the south core face exceeded the maximum reactivity allowed an experiment by the USAEC license for the FNR. Thus, in order to decouple the slabs and core, a row of graphite reflector elements was added on the south core face. The resulting core configuration is shown in Figure 18. It should be noted that this configuration introduces a 2-cm water gap between the graphite reflector elements and the zero collimator position. Hence, the source spectrum for the graphite measurements differs from that of the water measurements in that the former includes the effect of an additional 10-cm penetration through the row of graphite reflector elements and the water gap. The volume fractions for the graphite reflector elements are: 85.1% graphite (1.65 grams/cm3),7.9% aluminum, and 7.0% water. In order to keep the source spectrum constant, the water gap was maintained during all graphite measurements. 3. Normalization and Reactor Power These measurements were normalized to reactor power as in the water measurements except the aluminum wires were located differently during activation. They were positioned on a 36-cm diameter circle within the water gap. No perturbation in the wire activation due to the collimator position was observed. Except for the measurements of the source spectrum, the reactor was operated at 2 megawatts. The source spectrum was measured at power levels

75 of 0.5 and 1,0 megawatt using the thick detector and thin detector, respectively. 4. Counting Times and Statistics The graphite measurements were made during a three-week period. The counting times varied from three 20-minute foreground counts and three 10minute background counts for the thin detector-thin radiator case with 0 slabs of graphite to five 10-hour foreground counts and five 5-hour background counts for the thick detector-thick radiator case with 3 slabs of graphite. As for the water measurements, the foreground and background counts were alternated. At the higher neutron energies, the counting statistics were slightly poorer than those of the water data. At 10 Mev, one sigma ranged from 4.1% to 7.7%, and at 12 Mev it varied from 9.5% to 23.3%o 5. Measured Spectra and Experimental Uncertainties A machine plot of the measured spectra of FNR leakage neutrons which penetrated 0, 1, 2, and 5 slabs of graphite is shown in Figure 24, The structure is the energy averaged effect of the elastic scattering cross section of carbon. Again, the scatter of data points at the higher energies is due to statistical fluctuations. The errors are the same as those of the water measurements except for those associated with counting statistics, aluminum activation, shield thickness and shield density, These are noted in Table 7, The measured spectra in both water and graphite are tabulated in Appendix C.

76 1012 lol2I lI I I lI lI lI E'""h.LS NEUTRON PENETRATION IN GRAPHITE zt< ~ |I^~ I~ l NORMAL TO REACTOR CORE cO ]^. ~- -NIOBE 76 GROUP CALCULATION <: + EXPERIMENTAL POINTS 109 cu 105 I I I I I I I, I 0 2.0 4.0 6.0 8.0 0.0 12.0 14.0 W 1010 U) NEUTRON ENERGY (MEV) Figure 24. Neutron penetration in graphite. w I ( ^'b' I 0 ___-)\ ^ S ~1"_ W I \O% ^\^ U) ~* *''^" w ^ Figulre 24. Neutron penetration in graphite.

CHAPTER IV COMPARISON WITH CALCULATIONS AND CONCLUSIONS A, NIOBE CALCULATIONS The calculated spectra shown in Figures 21 and 24 were obtained with the NIOBE (Numerical Integration of Boltzmann Equation) code. This code was developed by Nuclear Development Corp. (now United Nuclear Corpo) beginning with the work of Certaine and Mittelman(l04) in 1955 and culminating in codes for the IBM 704 in 1960(12) and for the IBM 7090 in 1961(13)o NIOBE was selected because of its ability to calculate angular fluxes at deep penetrations through multilayered configurations, its capacity for many energy groups, and its exactness. It has two important restrictionsonly spherical configurations are allowed, and any inelastic scattering cross sections used are treated as isotropic in the laboratory system, 1o Neutron Transport Equation NIOBE solves the following steady state, multienergy, neutron transport equation for a finite, multilayered, spherical configuration, T * VF(r,uE) + EZ (r,E)F(r,v,E) = S(r,k,E) + Iel(F;r,i,E) + Iin(F;r,),E) WhereF(r,i,E) is the angular flux, i.e., the number of neutrons with energy E} per second, per unit energy, per steradian, which move in directions - -- - ----------- (103) *All NIOBE calculations were performed by Go G. Sherwood using the IBM-7094 at the Institute for Defense Analysis, Washington, D. Co 77

78 making an angle whose cosine is >t with the radius vector crossing unit area normal to the neutron direction, at distance r measured from the origin. S(r,u,E) is the number of neutrons produced by true sources per second, with energy E, which move in directions making an angle whose cosine is lp with the radius vector, per unit volume, per unit energy, per steradian, at distance r, Iel (F;r,lL,E) is the number of neutrons produced per second, with energy E, which move in directions making an angle whose cosine is t with the radius vector, per unit volume, per unit energy, per steradian, as a result of elastic scattering by all nuclei present at distance r, when the angular flux is F(r,k,E). Iin(F;r,p,E) is defined similarly for inelastic scattering. i ~- = pa +( )a; or r a Zt(r,E) = Ni(r)ti(E); N. (r) is the number of atoms per unit volume of isotope i at distance r, at(E) is the total cross section per atom of isotope i at ti energy Eo The required boundary condition is that the flux at the outer boundary of the configuration be specified; (i.e., that F(A,p,E) be given for i < 0 where A is the outer radius).

79 In order to reduce this equation to terms suitable for numerical integration, it is assumed that the angular dependence of F(r,i,E) can be represented by a finite Legendre series expansion. Accordingly, L F(r,,E) = Z 2+ F(rE)P L < 12 ~ F~(r,E)P~(kt) =0 4t Since Legendre polynomials satisfy the orthogonality relation 2~+1 J1 P'(4)pm(1t)d = 5m Ll, ~m 2 -1 1m ~ mthe scalar flux terms are given by F (r,E) = 2T F(r,pE)P (t)dI The Gaussian quadrature rule is used to evaluate the above integral. This scheme requires the selection of a discrete set of p. which are the zeros of the Legendre polynomial of degree 2Q,-where Q is an integer, This set of tq are the rays of the angular mesho The selection of discrete angular rays so as to facilitate integration is generally referred to as the discrete ordinate method, 2, Source Terms The source terms represent the total neutron gains per second per unit volume per unit energy per steradian due to true sources such as fission neutrons and slowing down sources consisting of elastically and inelastically scattered neutrons, The true source in the reactor core region is the fission source,

80 It was assumed to be separable; i.e. S(r,p,E) = W(i)V(r)g(E). Also, the angular distribution was assumed to be isotropic in the laboratory system, Thus, W(k) = 1/4t. The radial distribution, V(r), was approximated by (36) the measured radial thermal flux distribution for the ORNL BSR-I. Subsequent NIOBE calculations were made to test the sensitivity of the spectra to this V(r)o A flat radial distribution produced no significant change in the core leakage spectrum. Hence, it was concluded the form of V(r) used was satisfactory. The source energy distribution was represented by a normalized Maxwellian distribution, g(E) = (2//5)El/2e-E/T. The Maxwellian spectrum was chosen because it agrees with measured U235 fission spectra as well or better than Watt(105) or Cranberg(106) spectra(107-110) its analytical form is simple, and it requires only one parameter, T. NIOBE calculations were carried out for several values of T to obtain a best fit to the FNR leakage spectrum (O cm water). The calculated spectra were sufficiently sensitive to the choice of T that it could apparently be inferred to within +0o010 Mev. The best fit was for T=1.285 Mev. This compares well with T=130+0,03 Mev given by Terrell(l08) and the average T=1.30 Mev for the eight measurements reviewed by Conde and During(ll) All of these T values refer to U235 fission induced by thermal neutrons. For the region outside the core, both the internal source distribution and the incoming flux at the outer radius were specified to be zero The elastic scattering source term, Iel(F;r,kL,E), is evaluated by representing the angular dependence of the elastic scattering cross sec

81 tion in the center-of-mass system by a finite Legendre series expansion. Then the scattering integral is evaluated using a scattering model appropriate to the mass of the scattering nuclei. NIOBE includes models for hydrogeneous, infinitely heavy, and intermediate weight scatterers, The scattering model for hydrogen treats the scattering as isotropic in the center-of-mass system. The inelastic scattering source term, Iin(F;r,p,E), is evaluated by treating the scattering as isotropic in the laboratory system. When inelastic scattering data is available, the energy distribution of the neutrons emitted per inelastic scattering at energy E, G(E,E'), is tabulated as a function of E and Eto In summary, the energy dependent cross section data required for each element consists of (1) the total cross section, (2) the elastic scattering cross section and Legendre coefficients, and (3) the inelastic scattering cross section and the energy distribution of inelastically scattered neutrons, 3o Energy Groups In addition to the use of an angular mesh and a radial mesh, an energy mesh, which divides the energy region of interest into equal intervals of in E, is used, The introduction of the energy mesh allows the transport equation to be reduced to a set of coupled equations in which the slowing down and transport terms can be treated separately. These equations are solved in two steps. First, using assumed solutions, the slow

82 ing down source is calculated for each energy group. The true source is then added to the slowing down source to get the total source for each energy group. The second step is to solve the resulting set of "one velocity" transport equations which have these source terms. The solutions are then compared with the initially assumed solutions and the process is repeated until two successive iterations agree within a specified toleranceo * Examination of the cross sections of interest showed that 4% energy intervals retained most of the differential energy detail, More importantly, 4% energy widths clearly retain more structure than is visible within the limits of the spectrometer resolution (> 12%). Use of 4% energy intervals required 76 energy groups for the energy range from 0.90 to 18o02 Mev, Sherwood's 76 group P7 NIOBE calculations (16 angular rays and 105 radial points) required about 1 hour on the IBM-7094 computer, 4~ Geometry For the water calculations, the FNR core was represented as a sphere of approximately equal volume (29 cm radius, 58% H 0 and 42% aluminum) and the pool water was represented as a spherical.shell (80 cm thick, 100% H20) about this central region. The same central region was used for the graphite calculations. Here it was surrounded by two regions: (1) a 10 cm thick shell representing the row of graphite reflector elements and the water gap (volume *The convergence criterion used was 0.001.

83 fractions: 68.9% graphite (1.65 grams/cm3), 24.7% water, and 6.4% aluminum) and (2) an 80 cm thick graphite shell (volume fractions: 93.7% graphite (1.74 grams/cm3) and 6.3% aluminum). 5. Cross Sections Cross section data was required for hydrogen, carbon, oxygen, and aluminum. For hydrogen, the total and elastic scattering cross sections are the same. The scattering model for hydrogen which treats elastic scattering as isotropic in the center-of-mass system and the theoretical (112) total cross section curve reported in BNL-525 were used. KAPL total and elastic scattering cross sections and Legendre coefficients were used for carbon(13) and oxygen.(114) Since this data extended only up to 15 Mev, the values at 15 Mev were assumed constant to 18 Mev. Due to the unavailability of inelastic scattering data for carbon and oxygen, it was omitted in the slowing down source terms. For aluminum, GA(15) cross section data, including inelastic, was used. 6. Comparison With Measurements Because the use of 76 energy groups permitted the calculations to show considerably more energy detail than the measurements, comparisons between NIOBE calculations and measured spectra were difficult to evaluate. In order to simplify the comparison, the energy dependent spectrometer response function was convoluted with the NIOBE calculations. The response function was assumed to be a Gaussian distribution function with its FWHM

84 given as a function of neutron energy by the curves shown in Figure 17. * The resulting spectra were normalized with the measured spectra at a single point (7.5 Mev at 0 cm) and machine plotted with them as shown in Figures 21 and 24. A quantitative comparison is given in Table 8 which shows the average and maximum ratios of the calculated flux to the measured flux. TABLE 8 RATIOS OF CALCULATED FLUX TO MEASURED FLUX Shield Thickness Average Ratio Maximum Ratio 0 cm H20 1.00 0.90 at 4.3 Mev 20.0 cm H20 0.92 0.36 at 3.J Mev 40.0 cm H20 0.95 0.80 at 2.5 Mev 60.0 cm H20 0.99 1.50 at 8.5 Mev 0 cm Graphite 1.00 0.32 at 2.2 Mev 20.2 cm Graphite 0.95 0.74 at 4. 2 Mev 40.4 cm Graphite 0.96 0.67 at 4.5 Mev 60.6 cm Graphite 0.98 0.67 at 4.9 Mev The comparison shows surprisingly good agreement, particularly with the water data, in view of the assumptions made in the NIOBE calculations. *A smooth line between the thin radiator curve at 4 Mev and the thick radiator curve at 6 Mev was used for the 4 to 6 Mev region.

These include (1) all regions are homogeneous and spherically symmetrical, (2) there is no inelastic scattering by carbon and oxygen in the slowing down source terms, (3) hydrogen scattering is isotropic in the center-ofmass system, (4) inelastic scattering by aluminum is isotropic in the laboratory system, and (5) carbon and oxygen cross sections and Legendre coefficients are constant from 15 Mev to 18 Mevo With regard to the graphite calculations, much better agreement was obtained by the questionable procedure of mixing cross sections and Legendre coefficients from different libraries, In convoluting the spectrometer response function with the NIOBE calculations, an important bias is introduced. As demonstrated analytically in Chapter II, the convolution process introduces a tilt in exponential spectra. Thus, the inference of the Maxwellian T characteristic of the U235 fission spectrum from the comparison of the measured core leakage spectrum with smoothed spectra calculated for different values of T requires the response function to be sufficiently well known so as to introduce little or negligible uncertainty in finding To The greatest uncertainty in the response function is that associated with the radial distribution function, F(rm). From Table 6, this uncertainty is estimated to be +lO0o Equation 14 shows that a +10 uncertainty in AE/E introduces < +05%o uncertainty in the slope of smoothed spectra. Since the uncertainty in T associated with matching the measured and calculated core

86 leakage spectra is +O.C10 Mev, the total* uncertainty in T is < + [0.010 Mev + 0.005 (1.285 Mev)] or < +0.016 Mev. Most measurements(108,111) of this T have reported uncertainties of +0.030 or +0.040 Mev. B. CONCLUSIONS A relatively simple, moderate resolution (12%), low efficiency (10-6), differential proton-recoil, fast neutron spectrometer has been developed to measure directed neutron fluxes in the presence of high intensity fission gamma fields (107 to 108 roentgens/hour). It has been used to measure the energy distributions (2 to 12 Mev) of normally directed neutrons which leaked from the Ford Nuclear Reactor core and penetrated several thicknesses of two common reactor materials, H20 and graphite. In contrast to Clifford et al.'s(49) recent spectrum measurements of uncollided reactor neutrons,these measured spectra are dominated by scattered neutrons. For example, the ratio of scattered neutrons to unscattered neutrons ranges from 100 at 2 Mev to 1 at 12 Mev for neutrons which penetrated 60 cm of H20. Although measurements of uncollided neutrons test the total cross sections very well, these measurements test both the total cross sections and the slowing down sources. In contrast with other measurements dominated by scattered neutrons and compared with detailed calculations (such as Verbinski's(3 spectra in H20 and Profio's(33) spectra in CH ), the agreement between these measured and *This does not include effects of uncertainties in the energy calibration of the spectrometer or in the cross sections used in the NIOBE calculation of the core leakage spectrum..

87 calculated spectra is excellent. In summary, because of the relatively high accuracy (+10% relative intensity and +20% absolute intensity, +2% energy) and the deep penetration (up to 60 cm), these measurements are the most useful that have been reported for testing detailed calculations of fast neutron spectra in bulk media. C. SUGGESTED FUTURE WORK Opportunities for extending the present work lie in two directions. One is in the choice of experiments and the other is in the modification and improvement of the spectrometer. However, except for modifications which give a general reduction in background (as for example might result from reducing the ID of the beam trap or reshaping the collimator throat), the important changes in the spectrometer system will probably reflect the choice of experiment. The following experiments are fairly direct extensions of the present work. 1. Spectrum measurements in H 0 at oblique angles. 2. Spectrum measurements at higher energies( ) 3. Spectrum measurements in other bulk materials (e.g. materials with relatively high and well known inelastic scattering cross sections such as iron). 4. Spectrum measurements of fission sources and (a,n) sources. 5. Measurement of angular distributions of n-p scattering using multiple detectors or a single movable detector in the detector chamber.

88 60 Measurements of spectrometer efficiency and resolution using D(d,n)He3 and T(d,n)He4 neutron sources of known intensity and energy width, 7o Collimator studies(ll6-122) to measure the influence of (a) wall and liner material, (b) shape, and (c) length.

APPENDIX A EFFECT OF CARBON RECOILS Fast neutrons,incident on CH2 radiators scatter carbon ions as well as protons. Although many of the carbon ions are stopped within the radiator, those which do escape the radiator and reach the detector are indistinguishable from protons of the same energy. The necessary condition for the background counts due to carbon recoils to be negligible compared to the proton recoil counts is that 5 (g5 lgEC OF Dr, 5 Ao R6x ey where C(E ) is the count rate for protons with energy Ep, and C(EC) is the count rate for carbon ions with energy ECo To find the ratio of carbon recoil counts to proton recoil counts, first note that from Equations 2 and 6, C(6 < (6) ) atRG rust,p(E) )(FV l (15) where G - ( l The expression for the total efficiency, e(E), was derived with the assumptions that n-p scattering is isotropic in the center-of-mass system and that all protons which are scattered toward the detector escape the radiator with some mean energy loss $E, where 5Ep ~ Epo Both of these assumptions are invalid for carbon ions because n-C scattering is not 89

90 isotropic in the center-of-mass system and the carbon ion energy losses in the radiator are so large that most of the ions do not escape the radiator with energies above 1 5 Mev. The energy of the carbon ions before losing any energy is related to the energy of the incident neutrons by EC- = (A -I, C 2IP6 (16) With A = 12 and cos2. = 0.85, EC = 0.236E' An expression for C(Ec) which includes the carbon ion energy losses in the radiator is developed as follows c P ( (17) where Co(E)dEC is defined as C(EC)dEc except that carbon ion energy losses in the radiator are assumed to be zero, P(E',Ec)dEC is the probability that carbon ions, which would be counted with energies in dEI about EC if energy C C losses in the radiator were zero, are counted with energies in dEC about EC. E" = 0O236Emax C max From its definition, Co / — ( g A) l (') where e(Ev) is the total efficiency for counting carbon ions with energy Ev = 00236E'o It is evaluated as before for n-p scattering except that C the carbon ions are assumed to be scattered isotropically in the laboratory system. This assumption requires that

91 -.c (F e- _-At This is equivalent to replacing (l/:) cnp(E) cost by (1/4it) anc(E) in the previous expression for c(E) so that Co (~Co C 1. [s N R & C \E' (18) Thus, El Ec Hence, the ratio of count rates is C(E h "-( } )A ^ J ) CEP(EC~cFsTo(+946c}) R+16-1 For a CH2 radiator, (NC/NH) = 1/2. Here cost = 0.91, (dE/dE )' (l/cos2t) = 1o20, and (dE'/dE') = L24. Using these values, the ratio becomes C (FM(?6 CI~ pl \ c~r R iE~I) o ( Ep) r (6; ~(g In order to evaluate the integral, OnOQ(E) and cp(E) must be specifiedo For example, choose L D So E > Ems? where (EC)min = (Ep)min = (Emin cos2t - Ep) = 1.5 Mev and 4.24 (E)mi = 6536 Mev Since n _Q(E) = 1.5 + 0o8 barns for 6356 Mev < E < 20 Mev, choose

92 For this example, - PE0, ) To evaluate the integral, assume where C R cH(e -R c or 0 rC( < ewHa t > Rc L(Ee" Rc(CEc) is the range of carbon ions with energy EC in CH2 t = t sec* = 1.38 milligrams/cm2 R Thus, c RC, (Ea KCHEA - ____ rgL) I R' ^7 Using this result, to S5R (20) C (E) |- - (E) 6/6- where EC = Ep = E cos2-bEp and EC = 0236 Emaxo A range-energy curve for carbon ions in CH2 is not available. An approximate one can be obtained using the following relationship(l12) C (L&/i4 ) K (g I I/H) EM _ With MH = 1 amu and MC = 12 amu, C4 (ECIIX) s l2- RC (CCIIR) r^ (EC/il) = EH R(4H hL'

95 where EH and (EC/12) are the energies of the hydrogen and carbon ions, respectively, expressed in Mev/amu, A range-energy curve for protons in carbon for the proton energies of interest (01o to 0.5 Mev) is not available, Hence, the ratio of ranges of protons in CH2 and carbon is estimated by assuming that both of the ranges can be represented by R(E) = AEB so that R. W (p W-S. R% r ) () fl The constants are evaluated using the ranges of protons in CH2 and carbon at E = 2 Mev and EH = 4 Mev as calculated by Barkas and Berger' Using this procedure, the ratio is found to vary from,0 7 to 0 75 as EH increases from 0ol to 0 5 Mev, Using these results and a range-energy curve(123) for carbon ions in carbon, an approximate range-energy curve for carbon ions in CH2 is obtained. From this curve, which is shown in Figure 25, and the values for np(E) which are tabulated by Gammell(100) the ratio of count rates is calculated for Ema = 14 Mev and Ema = 18 Mev. The results are shown in Figure 26 as a function of the incident neutron energy, It is noted that this example generally overestimates the background due to carbon recoils for the spectrum measurements reported here, Even so, as shown in Figure 26, the effect of carbon recoils is small.

7 6 / w5 z C) z 4 0 z 0 3 -) 0 Figure 25. Range of carbon Ions in polyethylene. Figure 25. Range of carbon ions in polyethylene.

0.07 Ec = Ep = E cos2V- 8Ep 0.06 (E) 0 <E<6.36 MEV 9(E) =,6.36 MEV<E<_EMAX 0, E > EMAX 0.05 0.04 E:,= 18 ME/ C(Ec) MAX C(Ep) 0.03 ~ r0.02 X' \ 0.01 0.0 2 3 4 5 6 7 NEUTRON ENERGY IN MEV Figure 26. Ratio of carbon recoil counts to proton recoil counts.

APPENDIX B COLLIMATOR EFFECTS To zeroth order approximation, the neutron beam which exits the collimator consists only of neutrons which entered the source end of the collimator and traveled to the exit end without being scattered or attenuatedo Let these neutrons be designated FE. Three corrections must be considered. First, a fraction of the neutrons are absorbed or scattered by the gas in the collimator, For long, air-filled collimators this fraction can be significant. Here, it is negligible because the collimator is evacuatedo Secondly, some of the neutrons in the exiting beam entered the collimator through the source end, but were scattered in the collimator wall before reaching the exito These neutrons are degraded in energy, although for long collimators the most probable scattering angles may be so small that the energy degradation is negligible. Even so, these scattered neutrons were not directed toward the exit when they entered the collimator so that the exiting neutrons have an additional component which is designated FEW Thirdly, some of the neutrons in the exiting beam entered the collimator initially through the wall rather than through the source endo Let this additional component be designated FWo Both FEW and FW depend on the angular dependence of the source and on the geometry of the source and the collimator. There are no general 96

97 expressions available which can be used to evaluate these terms. However, they can be roughly estimated for long, cylindrical and long, conical collimators used with isotropic sources. Here "long" implies that the length of the collimator is much larger than its largest diameter. Simon and Clifford(ll6) have estimated (FEW/FE) for the case where a point, isotropic source is located on the axis of a long, cylindrical collimator. Their calculation considers only single scattering in the collimator walls and depends on the assumptions that the scattering is isotropic in the laboratory system and that the energy degradation is negligibleo Their result is FEW N=Tr. (FEW - ~~ 2 t (2-) ~(21) where 5 is the radius of the cylinder I is the length of the cylinder Ls andZb are the macroscopic scattering and total cross sections, respectively, for the wall of the cylinder. If the collimator wall is hydrogeneous, it is a good approximation to assume the scattering is isotropic in the center-of-mass system. This assumption can be incorporated into the above results by replacing Zs by 4 ZEs I, where L is the average cosine of the scattering angles associated with FEWo Since for long collimators, most of the neutrons which contribute to FEW are scattered through relatively small angles, | is approximately unityo Thus, for long, cylindrical collimators with hydrogeneous walls,

98 (FEW) =2(0 ) 2t (2(j\) (22) where: hs = l/s and t = 1/Zt Extension of the analysis of Simon and Clifford to long, conical collimators gives the same result except that (s + be) - 1 where: 5 is the radius of the source end and s b is the radius of the exit end (FW/FE) can be crudely estimated for the case of a plane, isotropic source at the end of a long, cylindrical collimator. If only the uncollided neutrons are considered, it can be shown that F 2 (25) FE Extension of the same analysis to long, conical collimators gives (FC2) (24) From the above two expressions, it is noted that (1) For long collimators, (FW/FE) depends on (Xt/~), not (5&/); (2) When using a long, corical collimator with a plane source, it is advantageous to use the large end of the collimator as the source end so that (5 /e ) < 1. Also, it is noted that the above expressions for (FW/FE) do not include neutrons which enter the collimator through the wall and then

99 reenter the wall to be scattered to the collimator exito This contribution is expected to be small compared to (FEW/FE), at least when (Se/ s) < lo (FEW/FE) and (FW/FE) can now be evaluated for the collimator used with this spectrometer. The cross section of the collimator is actually dodecagonal rather than circular, but the difference is neglected herec The wall of the collimator is 0532 cm thick aluminum surrounded by watero Since the aluminum is very thin relative to the mean free path of Mev neutrons in aluminum, the collimator wall is represented by a water wall, Hence, these ratios are evaluated for a long, evacuated, conical collimator with water walls and the following dimensions: I = 305 cm, 5 =) 5o10 cm, and be = 0~95 cmo For 10 Mev neutrons in water, At = 9 6 cm and s 1 = 12 o- cmo Using these values, FEW\ A, So, \H2 \ Et w e = o.048 3 (25) FE/ H\xH20/K \ f^- 2(/t ) = 0.017 (26) Thus, (FEW/FE) + (FW/F) = 6o50o This small percentage, although only a rough estimate, indicates the collimator effects are relatively small.

APPENDIX C TABULATION OF MEASURED SPECTRA The measured spectra are tabulated on the following four pages. The neutron energy.12030E+02 is read 12.03 Mev. The flux.19700E+09 is read 1.97 x 108 neutrons sec-1 cm-2 Mev-! steradian-1 megawatt-1o It was measured normal to the reactor core. The phrase 0 CM WATER refers to the thickness (0 cm) of material (water) between the Ford Nuclear Reactor core and the source end of the spectrometer collimator. 100

101 NEUTRON FLUX FLUX FLUX FLUX ENERGY 0 CM 20.0 CM 40.0 CM 60.0 CM IN MEV WATER WATER WATER WATER.12030E+02.19700E+09.38700E+08.56200E+07.81100E+06.11910E+02.20800E+09 42400 8.70200E+07.89500E+06.11790E+02.23500E+09.44300E+08.68700E+07.95200E+06.11670E+02.25200E+09.51100E+08.72700E+07.92800E+06.11550E+02.32400E+09.51800E+08.87500E+07.11800E+07.11430E+02.30000E+09.55000E+08.88900E+07.12800E+07.11310E+02.34500E+09.65200E+08.89500E+07.10300E+07.11190E+02.38300E+09.68400E+08.99600E+07.13400E+07.11070E+02.40700E+09.83000E+08.95400E+07.14400E+07.10950E+02.39300E+09.78400E+08.11400E+08.15000E+07.10830E+02.48800E+09.86700E+08.12700E+08.20300E+07.10710E+02.48300E+09.90500E+08.13400E+08.21000E+07.10590E+02.50900E+09.99200E+08.14100E+08.21400E+07.10470E+02.55000E+09.11800E+09.16100E+08.21200E+07.10350E+02.65900E+09.11900E+09.18200E+08.22400E+07.10230E+02.74200E+09.12400E+09.16400E+08.28000E+07.10110E+02.77900E+09.13400E+09.21600E+08.26800E+07.99900E+01.86200E+09.14600E+09.22600E+08.30300E+07.98800E+01.92500E+09.16100E+09.21200E+08.29400E+07.97600E+01.98300E+09.17600E+09.25500E+08.32600E+07.96400E+01.10200E+10.18600E+09.25100E+08.32400E+07:95200E+01.11800E+10.20500E+09.26900E+08.37900E+07.94000E+01.13300E+10.22600E+09.32200E+08.36000E+07.92800E+01.13600E+10.22700E+09.32000E+08.46800E+07.91600E+01.14600E+10.24800E+09.33400E+08.44500E+07.90400E+01.16100E+10.27700E+09.35900E+08.49700E+07.89200E+01.17100E+10.29800E+09.38000E+08.49800E+07.88000E+01.19100E+10.30600E+09.41700E+08.48700E+07.86800E+01.19200E+10.32700E+09.39000E+08.52100E+07.85600E+01.22200E+10.35000E+09.45100E+08.53600E+07.84500E+01.24400E+10.39100E+09.44500E+08.48400E+07.83300E+01.25800E+10.39400E+09.47200E+08.55500E+07.82100E+01.28600E+10.42900E+09.52000E+08.63800E+07.80900E+01.30900E+10.45800E+09.56400E+08.62000E+07.79700E+01.34300E+10.49600E+09.61900E+08.60400E+07.78500E+01.36400E+10.52700E+09.64400E+08.63000E+07.77300E+01.38800E+10.56100E+09.67700E+08.65800E+07 76200E+01.42100E+10.62700E+09.71900E+08.75500E+07.75000E+01.47800E+10.67400E+09.74900E+08.74300E+07.73800E+01.50700E+10.71700E+09.83100E+08.83300E+07.72600E+01.54500E+10.77900E+09.88200E+08.90700E+07.71400E+01.58700E+10.85600E+09.96800E+08.10200E+08.70200E+01.66400E+10.91400E+09.10500E+09.10600E+08

102 NEUTRON FLUX FLUX FLUX FLUX ENERGY 0 CM 20.0 CM 40.0 CM 60.0 CM IN MEV WATER WATER WATER WATER.69100E+01.71300E+10.99600E+09.11100E+09.11800E+08.67900E+01.77300E+10.10900E+10.12000E+09.12400E+08.66700E+01.84400E+10.11400E+10.12900E+09.12900E+08.65500E+01.90600E+10.12500E+10.13400E+09.14000E+08.64400E+01.98000E+10.13200E+10.14000E+09.13600E+08.63200E+01.10900E+11.14000E+10.14700E+09.14000E+08.62000E+01.11600E+11.14700E+10.15400E+09.13500E+08.60800E+01.12500E+l1.15500E+10.15400E+09.13900E+08.59600E+01.13700E+11.16300E+10.15100E+09.13300E+08.58500E+01.15000E+11.17300E+10.15300E+09.13900E+08.57300E+01.16100E+11.18200E+10.15600E+09.13900E+08.56100E+01.18000E+11.19100E+10.15900E+09.14300E+08.55000E+01.19500E+11.20200E+10.16400E+09.13500E+08.53800E+01.20800E+11.21100E+10.16900E+09.12800E+08.52600E+01.22800E+11.22400E+10.17500E+09.14100E+08.51400E+01.25000E+11.23600E+10.17600E+09.13500E+08.50300E+01.27100E+11.24400E+10.18200E+09.14400E+08.49100E+01.28900E+11.25400E+10.18500E+09.14000E+08.47900E+01.31000E+11.26400E+10.18800E+09.13400E+08.46700E+01.33300E+11.26500E+10.18600E+09.13300E+08.45500E+01.35600E+11.27000E+10.17600E+09.12900E+08.44300E+01.36900E+11.27400E+10.17300E+09.11500E+08.43100E+01.39400E+11.28500E+10.17200E+09.10600E+08.42000E+01.41800E+11.28600E+10.16200E+09.10200E+08.40800E+01.43900E+11.28500E+10.15700E+09.92600E+07.39600E+01.46200E+11.27600E+10.14200E+09.87400E+07.38400E+01.48100E+11.26500E+10.12400E+09.74900E+07.37300E+01.50800E+11.25800E+10.11800E+09.60400E+07.36100E+01.54500E+11.25800E+10.10400E+09.62600E+07.34900E+01.58800E+11.26700E+10.10500E+09.53600E+07.33700E+01.65700E+11.30300E+10.11300E+09.62000E+07.32600E+01.71700E+11.35600E+10.13600E+09.66600E+07.31400E+01.78800E+11.41700E+10.16100E+09.80400E+07.30200E+01.85100E+11.47300E+10.18300E+09.92500E+07.29100E+01.90100E+11.51600E+10.20400E+09.95900E+07.27900E+01.95200E+11.55700E+10.21300E+09.89100E+07.26700E+01.10400E+12.58600E+10.23500E+09.94300E+07.25600E+01.11600E+12.64000E+10.24800E+09.10200E+08.24400E+01.12800E+12.68200E+10.26900E+09.11100E+08.23300E+01.13800E+12.69800E+10.28400E+09.22200E+01.14500E+12.67700E+10.25600E+09.21000E+01.15300E+12.64600E+10.23300E+09.19900E+01.16200E+12.62000E+10

103 NEUTRON FLUX FLUX FLUX FLUX ENERGY 0 CM 20.2 CM 40.4 CM 60.6 CM IN MEV GRAPHITE GRAPHITE GRAPHITE GRAPHITE.12030E+02.91700E+08.17000E+08.24000E+07.24000E+06.11910E+02.11200E+09.17500E+08.19900E+07.29900E+06.11790E+02.11500E+09.16500E+08.27500E07 33700E+06.11670E+02.97100E+08.21400E+08.20800E+07.25400E+06.11550E+02.14600E+09.20300E+08.32200E+07.35100E+06.11430E+02.11200E+09.26200E+08.37600E+07.39700E+06.11310E+02.14200E+09.22300E+08.34800E+07.46300E+06.11190E+02.15100E+09.27400E+08.55000E+07.58400E+06.11070E+02.20700E+09.31200E+08.50300E+07.47400E+06.10950E+02.19600E+09.33600E+08.54600E+07.72600E+06.10830E+02.21900E+09.38200E+08.63400E+07.97800E+06.10710E+02.23800E+09.46500E+08.66900E+07.94900E+06.10590E+02.27300E+09.42000E+08.64700E+07.91400E+06 ~10470E+02.28000E+09.53400E+08.67900E+07.12800E+07.10350E+02.28700E+09.55300E+08.99300E+07.12700E+07.10230E+02.36300E+09.61300E+08.94500E+07.15600E+07.10110E+02.34300E+09.71600E+08.10500E+08.13900E+07.99900E+01.40700E+09.71000E+08.11600E+08.17400E+07.98800E+01.46300E+09.79600E+08.12300E+08.20200E+07.97600E+01.44600E+09.84400E+08.12900E+08.20200E+07.96400E+01.52100E+09.87500E+08.12800E+08.21800E+07.95200E+01.53500E+09.10800E+09.16300E+08.28200E+07.94000E+01.57100E+09.11300E+09.18900E+08.28700E+07.92800E+01.66300E+09.12800E+09.19600E+08.31300E+07,91600E+01.71200E+09.13700E+09.21000E+08.38200E+07.90400E+01.81700E+09.14900E+09.24100E+08.45000E+07.89200E+01.86300E+09.15900E+09.26500E+08.46000E+07.88000E+01.93300E+09.16800E+09.27300E+08.51800E+07.86800E+01.98700E+09.18200E+09.30600E+08.58100E+07.85600E+01.10700E+10.19100E+09.33400E+08.57900E+07.84500E+01.10800E+10.18600E+09.29900E+08.54200E+07.83300E+01.12400E+10.19300E+09.31600E+08.54400E+07.82100E+01.12700E+10.19500E+09.30700E+08.49300E+07.80900E+01.13900E+10.20700E+09.29700E+08.48000E+07.79700E+01.14600E+10.22900E+09.31400E+08.54100E+07.78500E+01.17500E+10.25800E+09.36100E+08.71000E+07.77300E+01.18400E+10.32600E+09.56900E+08.12100E+08.76200E+01.20900E+10.39400E+09.80200E+08.19100E+08.75000E+01.24900E+10.49500E+09.10700E+09.27600E+08.73800E+01.27900E+10.61700E+09.13400E+09.35900E+08.72600E+01.31800E+10.76100E+09.17800E+09.46200E+08.71400E+01.35800E+10.88100E+09.21900E+09.55600E+08.70200E+01.39500E+10.97400E+09.24600E+09.62600E+08

104 NEUTRON FLUX FLUX FLUX FLUX ENERGY 0 CM 20.2 CM 40.4 CM 60.6 CM IN MEV GRAPHITE GRAPHITE GRAPHITE GRAPHITE.69100E+01.42500E+10.10500E+10.26300E+09.66300E+08.67900E+01.45800E+10.10900E+10.27400E+09.67200E+08.66700E+01.48700E+10.11500E+10.27200E+09.63800E+08.65500E+01.52500E+10.11600E+10.26000E+09.60000E+08.64400E+01.56300E+10.11700E+10.25600E+09.54400E+08.63200E+01.59300E+10.12100E+10.24600E+09.50100E+08.62000E+01.63800E+10.12500E+10.24400E+09.46600E+08.60800E+01.68900E+10.13400E+10.24300E+09.44000E+08.59600E+01.72600E+10.14500E+10.25900E+09.44800E+08.58500E+01.80200E+10.15500E+10.27800E+09.45600E+08.57300E+01.86400E+10.16500E+10.30000E+09.47000E+08.56100E+01.91600E+10.17800E+10.31800E+09.50500E+08.55000E+01.99300E+10.19400E+10.34600E+09.54200E+08.53800E+01.10500E+11.20500E+10.35700E+09.54600E+08.52600E+01.11600E+11.21600E+10.37800E+09.57400E+08.51400E+01.12200E+11.22300E+10.37500E+09.62200E+08.50300E+01.13100E+11.23300E+10.38300E+09.64700E+08.49100E+01.13800E+11.23400E+10.40000E+09.62200E+08.47900E+01.14400E+11.22900E+10.37800E+09.55900E+08.46700E+01.15000E+11.22600E+10.34500E+09.47300E+08.45500E+01.15300E+11.21300E+10.30900E+09.41300E+08.44300E+01.16000E+11.20400E+10.26900E+09.35700E+08.43100E+01.16600E+11.19500E+10.24000E+09.27800E+08.42000E+01.17500E+11.19200E+10.21800E+09.26400E+08.40800E+01.17800E+11.18300E+10.18800E+09.20900E+08.39600E+01.17600E+11.16600E+10.17100E+09.19500E+08.38400E+01.17300E+11.14600E+10.14800E+09.16900E+08.37300E+01.17400E+11.13500E+10.13000E+09.14800E+08.36100E+01.18100E+11.13100E+10.11200E+09.12000E+08.34900E+01.19500E+lI.15000E+10.12000E+09.14600E+08.33700E+01.22300E+11.19500E+10.16800E+09.18600E+08.32600E+01.25300E+11.24900E+10.23700E+09.26200E+08.31400E+01.28900E+11.29000E+10.29900E+09.32800E+08.30200E+01.31200E+11.31900E+10.32500E+09.38800E+08.29100E+01.34600E+11.33800E+10.32700E+09.36100E+08.27900E+01.39600E+11.38700E+10.34500E+09.38000E+08.26700E+01.45600E+11.46100E+10.39400E+09.43100E+08.25600E+01.52200E+11.55300E+10.48200E+09.51900E+08.24400E+01.57600E+11.63100E+10.57500E+09.60800E+08.23300E+01.60000E+11.68200E+10.65900E+09.68500E+08.22200E+01.61400E+11.71400E+10.71200E+09.71600E+08.21000E+01.63400E+11.75100E+10.75800E+09.74100E+08.19900E+01.66500E+11.79100E+10.81300E+09

REFERENCES o1 Fo Co Maienschein, "Methods of Fast-Neutron Spectroscopy for Reactor Shielding," Shielding Division Report ANS-SD-2, ppol-9, American Nuclear Society (1965). 2, E. P. Blizard and P. S. Mittelman, "Recent Advances in Reactor Shielding in the United States," Proco Third United Nations Intero Conf. on Peaceful Uses of Atomic Energy, Volo 4, 348 (1964)o 3. M. Grotenhuis, P. S. Mittelman, and E. P. Blizard, "Reactor Shielding in the United States of America," Reactor Shielding, Technical Reports Series No. 34, pp. 98-107, International Atomic Energy Agency (1964). 4. Yu. A. Egorov, "Some Problems of Biological Shielding in Reactors," Reactor Shielding, Technical Reports Series No. 34, pp. 108-134, International Atomic Energy Agency (1964). 5o A. Do Kantz, "Average Neutron Energy of Reactor Spectra and Its Influence on Displacement Damage," J. Appl. PhySo, 34, 1944 (1963)0 60 Ao Do Rossin, "Dosimetry for Radiation Damage Studies," ANL-6826, Argonne National Laboratory (1964). 70 Ro E. Dahl and H. H. Yoshikawa, "Neutron-Exposure Correlation for Radiation-Damage Studies," Nuclo Sci. Engo, 21, 312 (1965). 80 Fo Storrer, "Pulsed Neutron Experiments on Fast and Intermediate Systems," Pulsed Neutron Research, Volo II, pp. 317-33555 International Atomic Energy Agency (1965). 90 W. Yo Kato et al, "Fast-Reactor Physics Parameters from a Pulsed Source," Pulsed Neutron Research, Vol, II, ppo 373-396, International Atomic Energy Agency (1965), 10o H. Borgwaldt et alo, "SUAK, A Fast Subcritical Facility for Pulsed Neutron Measurements," Pulsed Neutron Research, Vol. II, ppo 399-415, International Atomic Energy Agency (1965), 11o Jo Lo Russell, Jro and Ao Eo Profio, "Adequacy of Fast and Intermediate Cross Section Data from Measurement of Neutron Spectra in Bulk Media," Neutron Cross Section Technology, CONF-660303, ppo 782-795 ( 966)o 105

106 REFERENCES (Continued) 12. S. Preiser, G. Rabinowitz, and E. deDufour, "A Program for the Numerical Integration of the Boltzmann Transport Equation-NIOBE," ARL Technical Report 60-314, Nuclear Development Corp. (1960). Also reprinted as UNUCOR-632, United Nuclear Corp. (1963). 13. D. Yetman, B. Eisenman, and G. Rabinowitz, "Description of Input Preparation and Operating Procedures for 9-NIOBE, an IBM-7090 Code," NDA 2143-18, United Nuclear Corp. (1961). Also reprinted as UNUCOR631, United Nuclear Corp. (1963). 14. S. Preiser, "9-NIOBE (UNC-90-2) Computer Code Abstract," Nucl. Sci. Eng., 12, 447 (1962). 15. K. D. Lathrop, "DTF-IV, a FORTRAN-IV Program for Solving the Multigroup Transport Equation with Anisotropic Scattering," LA-3373, Los Alamos Scientific Laboratory (1965). 16. D. C. Irving et al., "05R, A General-Purpose Monte Carlo Neutron Transport Code," ORNL-3622, Oak Ridge National Laboratory (1965). 17. J. Butler et al., "Methods for Calculating Radiation Attenuation in Shields," Reactor Shielding, Technical Reports Series No. 34, pp. 146151, International Atomic Energy Agency (1964). 18. "Neutron Attenuation in Optically Thick Shields," Shielding Division Report ANS-SD-1, American Nuclear Society (1964). 19. B. Murray, "Methods of Fast-Neutron Spectroscopy," WADC Technical Note 57-298, Part I, pp. 151-171, Wright Air Development Center, Wright-Patterson Air Force Base, Ohio (1958). 20. B. V. Rybakov and V. A. Sidorov, Fast-Neutron Spectroscopy, Consultants Bureau, New York (1960). 21. "Measurement of Neutron Flux and Spectra for Physical and Biological Applications," National Bureau of Standards Handbook 72 (1960). 22. L. Cranberg and L. Rosen, "Measurement of Fast Neutron Spectra," in Nuclear Spectroscopy, Part A, F. Ajzenberg-Selove, ed., pp. 358398, Academic Press, New York (1960).

107 REFERENCES (Continued) 23. J. M. Calvert and A. A. Jaffe, "Neutron Spectroscopy," in Fast Neutron Physics, Part II: Experiments and Theory,J. B. Marion and J. L. Fowler, eds., pp. 1907-1952, Interscience Publishers, New York (1963). 24. R. Wallace, "Four-Pi Fast-Neutron Spectrometers for Detection and Dosimetry," Neutron Dosimetry, Vol. I, pp. 575-587, International Atomic Energy Agency (1963). 25. R. A. Coombe, "Neutron Energy Spectra - Its Measurement in the Energy Range 0.5 to 15 Mev," Nucl. Power, 8, pp. 47-50 (Jan. 1963), pp. 4648 (Feb. 1965), and pp. 54-56 (April 1963). 26. K. H. Beckurts and K. Wirtz, Neutron Physics, trans. L. Dresner, pp. 286-296, Springer Verlag, New York (1964). 27. G. Di Cola and A. Rota, "Calculation of Differential Fast-Neutron Spectra from Threshold-Foil Activation Data by Least-Squares Series Expansion Methods," Nucl. Sci. Eng., 23, 344 (1965). 28. W. N. McElroy, S. Berg, and G. Gigas, "Neutron-Flux Spectral Determination by Fol Activation," Nucl. Sci. Eng., 27, 533 (1967). 29. S. H. Levine and R. E. Fortney, "Effect of Threshold Cross Section on the Derivation of Fast-Neutron Spectra," Neutron Cross Section Technology, CONF-660303, pp. 660-674 (1966). 30. J. L. Russell, Jr. et al., "Determination of Neutron Spectra in Bulk Media by Time-of-Flight," Pulsed Neutron Research, Vol. II, pp. 445459, International Atomic Energy Agency (1965). 31. D. B. Gayther and P. D. Goode, "Measurements of Fast Neutron Spectra in Reactor Materials," Pulsed Neutron Research, Vol. II,pp. 435-443, International Atomic Energy Agency (1965). 32. W. J. Paterson, W. B. McCormick, and J. W. Weale, "Some Measurements of Fast Reactor Spectra by the Time-of-Flight Technique Using a Pulsed Neutron Source," Pulsed Neutron Research, Vol. II, pp. 417-433, International Atomic Energy Agency (1965). 33. A. E. Profio, "Verification of Analytical Techniques (GAPLSN-Transport Theory and 05R-Monte Carlo Theory) by Utilization of Measured Fast Neutron Spectra in Infinite Paraffin and Spherical Paraffin Shields," GA-6765, General Atomic (1966). Also designated AFWL-TR-65-193, Air Force Weapons Laboratory, Kirtland Air Force Base, New Mexico (1966).

108 REFERENCES (Continued) 34. A. E. Profio, J. U. Koppel, and A. Adamantiades, "Measurements and Calculations of the Slowing-Down and Migration Time," Pulsed Neutron Research, Vol. I, pp. 123-138, International Atomic Energy Agency (1965). 35. R. J. Huber, "In-Core Experiments with a Li6'Sandwich' Fast Neutron Spectrometer," Shielding Division Report ANS-SD-2, pp. 25-38, American Nuclear Society (1965). 36. V. V. Verbinski and M. S. Bokhari, "Measurements and Calculations of Energy and Angular Details of Fast Neutron Flux in Water from a Pool-Type Reactor," Shielding Division Report ANS-SD-2, pp. 71-111, American Nuclear Society (1965). 37. V. V. Verbinski et al., "Measurements and Calculations of the Spectral and Spatial Details of the Fast-Neutron Flux in Water Shields," Nucl. Sci. Eng., 27, 283 (1967). 38. A. W. Manning et al., "He3 - Spectrometer Characteristics and Applications," Nucleonics, 23, No.4, 69 (1965). 39. T. R. Jeter and M. C. Kennison, "Recent Improvements in Helium-3 Solid State Neutron Spectrometry," IEEE Trans. Nucl. Sci., NS-14, No. 1, 422 (1967). 40. A. Sayres, "3He Fast Neutron Spectrometer with Extended Energy Range," Shielding Division Report ANS-SD-2, pp. 136-140, American Nuclear Society (1965). 41. W. A. Bair, "An Improved 3He Neutron Spectrometer," UCRL-16595, University of California Lawrence Radiation Laboratory (1966). 42. R. B. Murray, "Use of 6LiI(Eu) as a Scintillation Detector and Spectrometer for Fast Neutrons," Nucl. Instrum. Methods,2, 237 (1958). 43. N. Hartmann and G. R. Hopkins, "Fast Neutron Penetration Through Reactor Shields,"' WAPD-T-783, Westinghouse Atomic Power Division (1959). 44. H. W. Broek and C. E. Anderson, "The Stilbene Scintillation Crystal as a Spectrometer for Continuous Fast-Neutron Spectra," Rev. Sci. Instrum., 31, 1063 (1960).

109 REFERENCES (Continued) 45. G, G. Doroshenko, V. G. Zolotukhin, and B. A. Efimenko, "Matrix Analysis of Data Obtained by Means of a Single-Crystal Fast-Neutron Scintillation Spectrometer, Atomnaya Energiya, 19, 51 (1965). 46. V. G. Zolotukhin, G. G, Doroshenko, and B. A, Efimenko, "Analysis of Systematic Error in Differentiating Apparatus Spectra Measured by Means of a Single-Crystal Fast-Neutron Spectrometer," Atomnaya Energiya, 19, 56 (1965). 470 Wo R, Burrus and V. V. Verbinski, "Recent Developments in the Proton-Recoil Scintillation Neutron Spectrometer," Shielding Division Report ANS-SD-2, pp. 148-185, American Nuclear Society (1965), 48. V. V. Verbinski et al,, "The Response of Some Organic Scintillators to Fast Neutrons," Shielding Division Report ANS-SD-2, pp. 189-228, American Nuclear Society (1965). 49. Co E. Clifford et al,, "Measurements of the Spectra of Uncollided Fission Neutrons Transmitted Through Thick Samples of Nitrogen, Oxygen, Carbon, and Lead: Investigation of the Minima in Total Cross Sections," Nuclo Scio Eng., 27, 299 (1967). 50. E. F. Bennett, "Fast Neutron Spectroscopy by Proton-Recoil Proportional Counting," Nucl. Sci. Eng., 27, 16 (1967), 51. E. Fo Bennett, "Neutron Spectrum Measurement in a Fast Critical Assembly," Nuclo Sci, Engo, 27_, 28 (1967), 52. Eo Fo Bennett, "Neutron Spectra in a Depleted Uranium Block," Transo Am, Nuclo Soc., 9, 234 (1966). 530 CO H. Johnson, "Recoil Telescope Detectors," in Fast Neutron Physics, Part I: Techniques, Jo B, Marion and Jo L. Fowler, eds,, pp, 247295, Interscience Publishers, New York (1960). 54. So B. Herdade et al,, "Simplified Proton-Recoil'Telescope' for Reactor-Beam Fast-Neutron Spectrometry," Neutron Dosimetry, Vol. I, ppo 409-415, International Atomic Energy Agency (1963), 55. Ao Ko Furr and R. So Runyon, "A Fast Neutron Spectrometer for Reactor Flux Measurements," Nucl, Instrunm Methods, 27, 292 (1964),

110 REFERENCES (Continued) 56. E. R. Flynn and H. C. Bryant, "High Efficiency Solid State Neutron Telescope for 15-35 Mev Neutrons," Rev. Sci. Instrum., 37, 215 (1966). 57. L. Harris, Jr., G. Sherwood, and J. S. King, "Fast-Neutron Spectra in Water and Graphite," Nucl. Sci. Eng., 26, 571 (1966). 58. C. M. Cialella, "Design and Calibration of a Broad Range Magnetic Neutron Spectrometer," IEEE Trans. Nucl. Sci., NS-12,No.1,400 (1965). 59. C. M. Cialella, "A Broad Range Magnetic Neutron Spectrometer," BRL MR 1753, U. S. Army Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland (1966). 60. R. G. Cochran and K. M. Henry, "Fast Neutron Spectra of the BSF Reactor," AECD-3720, Oak Ridge National Laboratory (1953). 61. R. G. Cochran et al., "Reactor Radiations Through Slabs of Graphite," CF-54-7-105, Oak Ridge National Laboratory (1954). 62. V. V. Verbinski, "Fast-Neutron Transport in LiH," Trans. Am. Nucl. Soc., 6, 190 (1963). 63. G. D. Trimble, G. K. Houghton, and J. H. Audas, "Measurement of Neutron Spectra in Liquid Hydrogen," GA-5750, General Atomic (1964). Also assigned NASA-CR-54230, National Aeronautics and Space Administration (1964). 64. G. D. Trimble et al., "Fast-Neutron Spectra in Liquid Hydrogen," Trans. Am. Nucl. Soc., 8, 465 (1965). 65. A. E. Profio and J. Kirkbride, "Measurement of Fast Neutron Spectra in an Infinite Medium of CH2," GA-5973, General Atomic (1964). Also assigned WL-TR-64-180, Air Force Weapons Laboratory, Kirtland Air Force Base, New Mexico (1964). 66. A. E. Profio, "Fast-Neutron Spectra in Paraffin Shields," Trans. Am. Nucl. Soc., 8, 464 (1965). 67. A. E. Profio, H. M. Antunez, and J. L. Russell, Jr., "Time-ofFlight Measurements of the Neutron Angular-Flux Spectrum in Graphite," Trans. Am. Nucl. Soc., 9, 351 (1966). 68. V. N. Avaev et al., "Spectra of Fast Pile Neutrons in Passage through Polyethylene," Atomnaya ~nergiya, 15, 20 (1963).

111 REFERENCES (Continued) 69. A. P. Veselkin et al,, "Spectra of Fast Reactor Neutrons after Passing through Graphite, Lead, and Iron," Atomnaya Energiya, 16, 32 (1964). 70. G, A. Vasil'ev et al,, "The Attenuation of Reactor Radiation by Means of Serpentine Concrete," Atomnaya Energiya, 18, 121 (1965). 71. G. Go Doroshenko and Io V. Filyushkin, "The Spectra of Fast Neutrons from a Po-Be Source Which Have Passed through Water Shielding" Atomnaya Energiya, 16, 152 (1964)o 72, G. Go Doroshenko, V. A. Fedorov, and Eo So Leonov, "Changes in FastNeutron Spectra after Penetrating Aluminum, Paraffin, and Water," Atomnaya Energiya, 19, 460 (1965)0 735 Go During, R. Jansson, and No Starfelt, "Experimental Fast-Neutron Spectra in Aluminum and Iron," Neutron Dosimetry, Vol. I, ppo 359367, International Atomic Energy Agency (1963). 74, So Passe, "Measurement of Fast-Neutron Spectra by Means of Nuclear Emulsions," Neutron Dosimetry, Vol, I, ppo 481-499, International Atomic Energy Agency (1963). In Frencho 75. E. Tochilin, "Flux and Spectral Measurements of Primary and Moderated Neutron Sources," Neutron Dosimetry, Volo I, ppo 553-563, International Atomic Energy Agency (1963). 76. G. Ben-David, E, Nardi, and M. Pasternak, "Fast-Neutron Spectroscopy in a Pool-Type Reactor with Activation Detectors," Nucl, Scio En 20, 281 (1964)o 77. E. Aalto, Ro Fraeki, and R, Sandlin, "Measured and Predicted Variations in Fast Neutron Spectrum in Massive Shields of Water and Concrete," Nucl. Structo Engo, 2, 233 (1965). 78. Jo Ro Stehn et al,, "Neutron Cross Sections, Volume I, Z=1 to 20," BNL 325, 2nd edo, Supplement Noo 2, Brookhaven National Laboratory (1964). 790 J. 00 Hirschfelder and J. L, Magee, "Range-Energy Relations for Protons in Substances Containing C, H, 0, A, and Xe," Phys. Revo, 73, 207 (1948).

112 REFERENCES (Continued) 80. J. B. Parker, P. H. White, and R. J. Webster, "The Interpretation of Recoil Proton Spectra," Nucl. Instrum. Methods, 23, 61 (1963). 81. W. H. Barkas and M. J. Berger, "Tables of Energy Losses and Ranges of Heavy Charged Particles," NAS-NRC Publication 1133, Nucl. Sci. Series Report No. 39, pp. 103-172, National Academy of Sciences - National Research Council (1964). 82. P. J. Van Heerden, "The Crystal Counter: A New Instrument in Nuclear Physics," Noord-Hollandsche Uitgevers-Mij., Amsterdam (1945). 83. K. G. McKay, "A Germanium Counter," Phys. Rev., 76, 1537 (1949). 84. Proc. Informal Conf. Semiconductor Nucl. Particle Detectors, Asheville, N. C., Sept. 28-30, 1960, J.W.T. Dabbs and F. J. Walter, eds., NASNRC Publication 871, Nucl. Sci. Series Report No. 32, National Academy of Sciences-National Research Council (1961). 85. Proc. IRE Prof. Group Nucl. Sci. Annual Meeting, Solid State Radiation Detectors, Gatlinburg, Tenn., Oct. 3-5, 1960, IRE Trans. Nucl. Sci., NS-8, No. 1 (1961). 86. W. J. Price, Nuclear Radiation Dectection, 2nd. ed., pp. 212-266, McGraw-Hill Book Co., New York (1964). 87. J. M. Taylor, Semiconductor Particle Detectors, Butterworths, London (1963). 88. G. Dearnaley and D. C. Northrop, Semiconductor Counters for Nuclear Radiation, John Wiley, New York (1963). 89. G. D. O'Kelley, "Detection and Measurement of Nuclear Radiation," NAS-NS 3105, pp. 58-75, National Academy of Sciences - National Research Council (1962). 90. W. Shockley, "Problems Related to p-n Junctions in Silicon," SolidState Electronics, 2, 35 (1961). 91. A. G. Chynoweth, "Energy Required for Electron-Hole Pair Formation in Silicon," NAS-NRC Publication 871, Nucl. Sci. Series Report No. 32, pp. 95-98, National Academy of Sciences-National Research Council (1961).

113 REFERENCES (Continued) 92, C. Bussolati, A. Fiorentini, and G. Fabri, "Energy for ElectronHole Pair Generation in Silicon by Electrons and Alpha Particles," Phys. Rev., 136, A1756 (1964), 930 Fo Eo Emery and T, Ao Rabson, "Temperature Dependence of Average Energy per Pair in Semiconductor Detectors," IEEE Trans. Nucl. Sci., NS-13, No. 1, 48 (1966). 94. So A. Baranov, V. M, Kulakov, and V. M. Shatinsky, "New Data on Am243 and Am241 Alpha Decays," Nucl. Phys., 56, 252 (1964)o 95, A. H. Wapstra, "Recalibration of Alpha Particle Energies," Nuclo Phys., 57, 48 (1964), 96. C. Mo Lederer et al., "Energy Levels of 237Np, (I). The Alpha Decay of 241Am," Nucl Phys., 84, 481 (1966), 97. P. Siffert, A. Coche, and F, Hibou, "Resolution Limitation of Solid State Radiation Detectors for Heavy Particles," IEEE Trans. Nucl, Scio, NS-13, No, 3, 225 (1966), 98. Ho DeLyser, Fo P. Ziemba, and W. Ro Van Antwerp, "A Lithium Drifted Germanium Surface Barrier Detector," IEEE Trans, Nucl, Sci,, NS-12, Noo 1, 265 (1965). 99. R. Lo Chase, Nuclear Pulse Spectrometry, pp. 39-40, McGraw-Hill Book Co,, New York (1961). 100o J. Lo Gammel, "The n-p Total and Differential Cross Sections in the Energy Range 0-40 Mev," in Fast Neutron Physics, Part II: Experiments and Theory, J. B. Marion and J. Lo Fowler, eds, ppo 2185-2226, Interscience Publishers, New York (1963), 101. J, Bo Bullock, "Absolute Power Measurements of the Ford Nuclear Reactor," Trans. Am, Nuclo Soc., 8 (Supplement), 26 (1965). 102. Eo Eo Lockett and R, Ho Thomas, "The Half-Lives of Several Radioisotopes,' Nucleonics, 11, No, 3, 14 (1953)o 103o Go Go Sherwood, University of Michigan Doctoral Thesis, in progress,

114 REFERENCES (Continued) 104, Jo.Certaine and P. S, Mittelman, "A Procedure for the Numerical Integration of the Boltzmann Transport Equation," NDA 10-161, Nuclear Development Corp. (1955). 105. B. E, Watt, "Energy Spectrum of Neutrons from Thermal Fission of U235," Physo Rev., 87, 1037 (1952)o 106, L, Cranberg et al,, "Fission Neutron Spectrum of U235," Physo Revo, 103, 662 (1956). 107. J. Terrell, "Fission Neutron Spectra and Nuclear Temperatures," Phys. Rev., 113, 527 (1959). 108, J. Terrell, "Neutron Yields from Individual Fission Fragments, Phys. Rev,, 127, 880 (1962), See Appendix I, Fission Neutron Emission Energies. 109, Jo Terrell, "Prompt Neutrons from Fission," Physics and Chemistry of Fission, Volo II, pp. 3-23, International Atomic Energy Agency (1965). 110o Eo Ko Hyde, The Nuclear Properties of the Heavy Elements, III, Fission Phenomena, pp. 237-242, Prentice-Hall, Englewood Cliffs, N. J. (1965), 111 H. Conde and Go During, "Fission Neutron Spectra of U235 Pu239 and Cf252" Physics and Chemistry of Fission, Vol. II, pp. 93-102, International Atomic Energy Agency (1965), 112. D. J. Hughes and R B. Schwartz, "Neutron Cross Sections," BNL 325, 2nd ed,, Brookhaven National Laboratory (1958), 113. Co R, Lubitz, private communication with Go G. Sherwood on unpublished C12 cross sections and Legendre coefficients (1965), 114. Eo L. Slaggie and J, To Reynolds, "016 Fast-Neutron Cross Sections and Legendre Moments Below 15,0 Mev," KAPL-M-6452, Knolls Atomic Power Laboratory (1965). 115o Go D. Joanou and C. A. Stevens, "Neutron Cross Sections for Aluminum," GA-5884, General Atomic (1964).

115 REFERENCES (Concluded) 116. A, Simon and C. E, Clifford, "The Attenuation of Neutrons by Air Ducts in Shields," Nuclo Sci, Engo, 1, 156 (1956)o 117. A, Langsdorf, Jr., "Experimental Applications of Shielding and Collimating to Neutrons from Sources Employing the Electrostatic Generators" WADC Technical Note 57-298, Part I, pp. 196-206, Wright Air Development Center, Wright-Patterson Air Force Base, Ohio (1958). 118o A. Langsdorf, Jr., "Neutron Collimation and Shielding for Experimental Purposes," in Fast Neutron Physics, Part I: Techniques, Jo B, Marion and J. L. Fowler, eds,, pp. 721-806, Interscience Publishers, New York (1960). 119o Bo Antolkovic et al., "Influence of Collimation on the Energy Spectrum of 2o7 Mev Neutrons," Glasnik mato-fizo i astr,, 16, 135 (1961)o 120, Do Co Piercey and D. Eo Bendall, "The Transmission of Fast Neutrons Along Air Filled Ducts in Water," AEEW-R-69, United Kingdom Atomic Energy Authority (1962), 121o Wo B, Green and R. S. Hubner, "Monte Carlo Analysis of NeutronCollimator Efficiency," Trans. Am. Nuclo Soc., 8, 65 (1965). 122. Eo Ao Straker and Mo Bo Emmett, "Fast Neutron Collimator Studies," Trans. Am, Nucl Soc., 9, 355 (1966), Also ORNL 3973, Vol. I, ppo 40-41, Oak Ridge National Laboratory (1966). 1235 L. Co Northcliffe, "Passage of Heavy Ions Through Matter, IIo Range-Energy Curves," NAS-NRC Publication 1133, Nucl, Scio Series Report No, 39, ppo 173-186, National Academy of Sciences-National Research Council (1964).

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