MOLECULAR BEAM METHODS FOR MEASUREMENT OF METASTABLE STATE LIFETIMES by David Edward Kaslow A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Physics) in the University of Michigan 1971 Doctoral Committee: Professor Jens C. Zorn, Chairman Assistant Professor Harvey A. Gould Associate Professor Andrew F. Nagy Assistant Professor James J. Reidy Professor IT. Michael Sanders

ACKNOWLEDGMENTS I am most grateful to Professor Jens C. Zorn for proposing this study, and for his generous advice, encouragement, and assistance during the experiment and the writing of this thesis. I am indebted to Dr. Robert S. Freund for several helpful conversations concerning the experiment. I would like to thank the AEC High Energy Physics Computing Center staff for the generous use of.their facilities. I would also like to thank Jack Hegenauer for his help with Fortran IV. I am grateful to Russell Pichlik for his assistance in the initial construction of the apparatus. I thank my wife, Diane, for typing this manuscript and for her encouragement throughout my studies. I wish to thank Mr. Leslie Thurston for his work on several of the figures contained in this thesis. The support of this research by the Atomic Energy Commission and National Aeronautics and Space Administration is also acknowledged. ii

TABLE OF CONTENTS Page ACKNOWLEDGMENTS........................................ ii LIST OF FIGURES...............e........................... v AB3 STRACT........................ o.o...*................. viii CHAPTER 1 AN INTRODUCTION TO LIFETIME MEASUREMENTS............. 1 1.1 An Introduction............................. 1 1.2 Spatial Decay....................... 3 1.3 Time-of-Flight................................. 5 2 THE THEORY OF A LIFETIME MEASUREMENT................. 9 2.1 A Lifetime Measurement from Spatial Decay Data....,....................... 9 2.2 A Lifetime Measurement from Time-of-Flight Data,..,..,..,,,,,,,,,,,,. 14 2.2.1 Scaling of the Time Axes................ 15 2.2.2 Scaling of the Amplitude Axes........... 15 2.2.3 Measurement of the Lifetime.........,.., 17 2.3 An Alternate Method for Measuring a Lifetime from Time-of-Flight Data............... 22 3 COMPUTER PROGRAMS AND SIMULATED BEAMS................ 26 3.1 Generation of the Simulated Beams............... 26 3.2 Computer Programs...*...................*...*... 27 3.3 Analysis of the Simulated Spatial Decay Data.................................... 28 3,4 Analysis of the Simulated Time-of-Flight Data...................,...,,,,. 30 4 EXPERIMENT.,........................................ 33 4,1 Apparatus...........l....le..............3.... 33 4.2 Excitation Functions.......................... 36 4,3 Acquisition of Spatial Decay and Time-of-Flight Data.......................... 40 4.4 Analysis of the Argon Data.,..................... 41 iii

TABLE OF CONTENTS (con't) Chapter Page 4 4.4.1 Spatial Decay........................ 41 4.4,2 Scaling of the Time-of-Flight Spectra................................. 44 4,4.3 Determination of the Velocity Distribution........................... 45 5 ANALYSIS OF THE NITROGEN DATA..................... 49 5,1 A Summary of Analytic Techniques,............... 49 5.2 Data............................................ 50 5.2.1 Spatial Decay at 22 eV................,. 51 5.2.2 Time-of-Flight at 22 eV................ 52 5.2.3 Time-of-Flight at 10 eV,................ 56 6 DISCUSSION OF EXPERIMENTAL RESULTS................. 62 6.1 Other Experiments...................... 62 6.2 Present Experiment.............................. 64 6.2.1 Data......*...................... 64 6.2.2 Errors and Difficulties.............. 64 6.3 Summary.... *..*.*.....*...,,.*........ 66 Appendix A ANALYSIS OF A THREE COMPONENT BEAM................... 67 LIST OF REFERENCES.........*........................ *.. 71:iv

LIST OF FIGURES Figure Page 1.1 (a) Apparatus that could be used for taking spatial decay data.................. 4 (b) A typical spatial decay................. 4 1.2 (a) Apparatus that could be used for taking time-of-flight data................. 7 (b) Typical time-of-flight distributions for a decaying and non-decaying metastable beam.*.*......... *....*.............. 7 2.1 (a) Spatial decay of a two-component metastable beam..................*......... 11 (b) Differentiation of the two-component decay with respect to distance.............. 11 2.2 Time-of-flight spectra for a non-decaying metastable beam o............................... 16 (a) Time-of-flight distributions at three distances.......................... 16 (b) The spectra after scaling of the time axes................... 16 (c) The distributions after scaling of the time and amplitude axes.............. 16 2.3 Time-of-flight distributions for a two-component metastable beam................... 19 (a) Time-of-flight spectra at three distances............o.......... 19 (b) The distributions after scaling of the time and amplitude axes..................... 19 3.1 Spatial decay for a two-component, computersimulated metastable beam..................... 29 (a) A least squares fit of the spatial decay data....................... 29 V

LIST OF FIGURES (con't) Figure Page 3.1 (b) The lifetime of the short-lived component as found from the spatial decay........................ 29 3.2 Dependence of the spatial decay lifetime calculation on the value of n, where vn exp(-mv2/2kT) is the velocity distribution.... 31 3.3 Time-of-flight distributions for a twocomponent, computer-simulated metastable beam.,... 32 (a) A least squares fit to the time and amplitude scaled distributions......... 32 (b) The lifetime of the short-lived component as found from the time-of-flight distributions............................ 32 4*1 Experimental Apparatus.**...***.....**.***....... 34 4.2 Excitation Functions....8.................. 38 (a) Helium............................. 38 (b) Argon............*..................... 38 4.3 (a) Energy level diagram for N2. ***..**.**..... 39 (b) Excitation function for N2...........0...... 39 4.4 Least Squares Fitting to the Timeof-Flight Distributions.................., 42 4.5 Spatial decay taken with 22 eV electrons......... 43 (a) Least squares fit to Ar and N2 spatial decay.o............................ 43 (b) The lifetime as calculated from the corrected N2 data.................... 43 4.6 Argon time-of-flight distributions at three distances after scaling of the time and amplitude axes.......................... 46 4.7 Determination of the argon velocity distribution........~........................ 47 vi

LIST OF FIGURES (con't) Figure Page 5.1 A histogram displaying the lifetimes found from all the N2 spatial decay taken with 22 eV electrons................... 53 5.2 N2 time-of-flight spectra taken with 22 eV electrons........................... ~54 (a) A least squares fit of the time and amplitude scaled distributions.............. 54 (b) The lifetime as calculated from the time-of-flight spectra.,................ 54 5.3 Histograms displaying the lifetimes found from all the N2 time-of-flight data.............. 55 (a) Lifetimes found from data taken with 22 eV electrons............................. 55 (b) Lifetimes found from data taken with 10 eV electrons........................... 55 5.4 N2 time-of-flight spectra taken with 22 eV electrons........................,. 57 (a) A least squares fit to the data at 13.5 cm................................. 57 (b) Predicted distributions using the & least squares fit and assumed popu(c) lations and lifetimes for the metastable beam.............................. 57 5.5 N2 time-of-flight spectra taken with 10 eY electrons........................... 58 (a) A least squares fit to the time and amplitude scaled distributions,............ 58 (b) The lifetime as calculated from the time-of-flight spectra.................. 58 5.6 N2 time-of-flight spectra taken with 10 eV electronsV....................... 60 (a) A least squares fit to the data at 13.5 cm.................................. 60 (b) Predicted distributions using the & least squares fit and assumed popu(c) lations and lifetimes for the metastable beam............................. 60 vii

ABSTRACT This thesis presents several methods for measuring a lifetime of a metastable state using spatial decay and timeof-flight data. The experimental apparatus consists of a gas source, an electron gun, and a movable detector. Spatial decay data are accumulated by operating the electron gun in a DC mode and translating the detector along the molecular beam. Time-of-flight data are obtained by pulsing the electron gun and leaving the detector stationary. The spatial decay analysis assumes that i) the metastable beam consists of two components, with one component having a very long lifetime and ii) the velocity distribution can be approximated by vn exp(-mv2/2kT) where a value for n is estimated by fitting a non-decaying time-of-flight spectrum (n is not a critical parameter). The time-of-flight analysis is the main analytic technique and makes only one assumption: the metastable beam consists of two components, with one component having a very long lifetime. The time-of-flight analysis may be generalized to a beam consisting of more than two components. The TOF method was developed to overcome difficulties present in other methods for measuring lifetimes: it does not require quenching one of the metastable states, it does not require a knowledge of the metastable velocity distribution, and it does not require the long-lived metastable state to be individually excited. These techniques were tested on a two-component, computer-simulated metastable beam and on an experiment with molecular nitrogen. The lifetime of the a11 g state was found to be (106 + 35) usec, in good agreement with recent measurements made by other workers using different methods, viii

CHAPTER 1 AN INTRODUCTION TO LIFETIME MEASUREMENTS 1.1 An Introduction This work began as part of a program to develop a series of satellite-borne experiments to measure molecular nitrogen temperatures and to study the accommodation of molecular nitrogen on surfaces in the space environment. Since it was necessary to develop an analysis of N2 time-of-flight (TOF) spectra, this experiment was initiated. N2 has three primary metastable states excited by electron impact (Freund, 1969b): the A31+ state at 6.16 eV, the a1TT state at 8.54 eV, and the E3E + at 11.87 eV. At the g g time this experiment began, the lifetime of the A3 state was known to be on the order of seconds (see Shemansky, 1969a for a recent measurement and a review of other work) and the lifetime of the aln state had been measured by Lichten (1957) and by Olmsted, Newton, and Street (1965). Lichten found a lifetime of (170 + 30) usec by measuring the spatial decay of a metastable N2 beam. Olmsted, Newton, and Street observed the time-of-flight and excitation function of N2 at two electron gun-detector separations and estimated the lifetime to be (120 + 50) gsec. After this experiment began, additional results were published. Preund (1969a) measured the prompt and delayed emission spectra and TOP spectra of N2, estimating 1

2 the lifetime of the E3Z state to be (270 + 100) jsec (by assuming the lifetime of the a3n state of CO to be 60 msec). Borst and Zipf (1971) measured the lifetimes of the alI and E31 states to be (115 + 20) usec and (190 + 30) usec, respectively. Borst and Zipf measured these lifetimes by comparing the TOF spectra for the al and E3 states with a TOP spectrum for just the A3Z state (a long-lived state). The lifetime of the aTI state has also been found from laboratory analyses of the optical Lyman-Birge-Hopfield transition (al - x~ ) that is of considerable aeronomical g g importance: Jeunehomme (1967) obtained 10 Usec, Holland (1969) found 80 asec, and Shemansky (1969b) measured lifetimes ranging from 140 jsec for the first vibrational level to 160 usec for the eighth vibrational level. It should be noted that the metastable states of helium (Van Dyck, Johnson, and Shugart, 1970; A. S. Pearl, 1970) and molecular hydrogen (Johnson, 1971) have recently been studied with TOF methods. The lifetime measurements on the 21S state of helium performed by Van Dyck, Johnson, and Shugart yield results that agree with the calculations of Drake, Victor and Dalgarno (1969), but sharply disagree with the results of A. S. Pearl. Since helium is one of the few cases where a theoretical calculation can be made, it is seen that a good understanding of TOF lifetime measurements is essential. We have been speaking of metastable states. By "metastable" we mean that the excited state of an atom or molecule is forbidden to decay to the ground state by the usual

3 dipole selection rules. However, the state may decay by emitting magnetic dipole or electric quadrupole radiation, resulting in lifetime on the order of 10-4 seconds or longer. This brief presentation of several lifetime measurements in He and N2 demonstrates that additional measurements using different techniques are needed. This thesis presents several methods for measuring lifetime from spatial decay and TOP data. These methods apply to a two-component metastable beam, with one component having a very long lifetime, and overcomes some of the difficulties of earlier experiments. The organization of this thesis is as follows. The analysis of.spatial decay and TOP data is introduced (chapter 1) by outlining several basic techniques. However, these introductory methods are very limited and several main techniques are developed. These main techniques are the primary development of this thesis and are tested on a computer simulated metastable beam (chapter 3) and on the a Tl state of N2 (chapter 5), with the results being discussed and compared to the results found by other experimenters (chapter 6). The experimental apparatus is described and tested on a non-decaying metastable argon beam in chapter 4. Appendix A contains a generalization of the TOF technique to a beam containing more than two metastable components. 1,2 Spatial Decay One method of measuring lifetimes involves the spatial decay of a metastable beam. Figure l.la is a schematic of

4 SPATIAL DECAY APPARATUS., POSITION TO HEIGHT CONVERTER MULTICHANNEL ANALYZER AMPLIFIER GAS m I _ SOURCE ELECTRON MOVABLE GUN; DETECTOR COLLIMATOR (a) SPATIAL DECAY -.r, I.I I... I ELECTRON GUN- DETECTOR SEPARATION (b) Figure 1.1 (a) Apparatus that could be used for taking spatial decay data. (b) A typical spatial decay.

5 the apparatus that might be used to record the spatial decay. Gas effuses from a source into an interaction region where a small fraction of the ground state molecules are excited by electron bombardment. The molecules then pass through collimating slits and strike a detector that translates along the axis of the beam. Because these molecules have a thermal distribution of speeds (approximately 104 cm/ sec) only those molecules in metastable states live long enough to travel the several centimeters to be detected. The detector position is encoded on the detector pulses by the position-to-height converter, and these pulses are sorted and stored according to height by the multichannel analyzer. A typical spatial decay is shown in figure l.lb. The lifetime of the metastable state may be obtained from these data. One method of analyzing the spatial decay to obtain lifetimes is to assume a single-component beam and to replace the distribution of velocities by a single velocity. Then the intensity of the beam is written as I(Xa) -(X-X)/v I(Xb) where X is the electron gun-detector separation, v is the velocity, and T is the lifetime. This equation may be solved for (Xb-Xa)/v __ |&Xa)/ (1.1) n (Xb) Since all the quantities in the right side of equation 1.1

6 can be measured, the lifetime can calculated. If a Maxwellian velocity distribution is assumed, the intensity of the metastable beam is written as an integral over all velocities: (x) 2 -mv2/2kT -x/vT I(x) =No e e dv where m is the mass of the molecule, k is Boltzmann's constant, and T is the temperature. The lifetimes can now be measured in the manner detailed by Lichten (1957). However, the velocity distribution is generally not Maxwellian and, therefore, a method for measuring lifetimes under more general conditions is needed. Such a method is described in section 2.1. 1.3 Time-of-Fliht Another approach to measuring lifetimes involves the TOP distribution of the metastable beam. Figure 1.2a is a schematic of apparatus that might be used to record the TOF spectrum. The electron gun is pulsed and the detector is stationary. Since the metastable molecules have a distribution of speeds, they will have a distribution of times-of-arrival at the detector. The time-of-arrival is encoded on the detector pulses by the time-to-height conversion, and these pulses are sorted and stored according to height by the multichannel analyzer. A typical TOF spectrum is shown in figure 1.2b (solid curve). The first peak in the TOP spectrum is due to the arrival of photons. These photons are from the rapid decay of the non-metastable states and are used to mark zero

7 TIME OF FLIGHT APPARATUS.....'.. PULSE TIME TO HEIGHT GENERATOR CONVERTER MULTl_' —----- CHANNEL ANALYZER | DETECTOR GAS.. I D =' AMPLIFIER GAS SOURCE ELECTRON GUN' COLLIMATOR (a) I,'' TIME-OF-FLIGHT DISTRIBUTION Im''.. -I \' | -'/ \: a NON-DECAYING BEAM E / | \ DECAYING BEAM PHOTONS TIME-OF-FLIGHT (b) Figure 1.2 (a) Apparatus that could be used for taking time-of-flight data. (b) Typical time-of-flight distributions for a decaying and non-decaying metastable beam. The arrival of the photons from the rapid decay of the non-metastable states is used to mark zero time.

8 time. The second peak is due to the arrival of the metastable molecules. The lifetime of the metastable state may be measured from these data. One method of analyzing these TOF data to obtain lifetimes is to assume a single-component beam that has a certain TOF distribution in the absence of any decay (dashed curve in figure 1.2b). By multiplying this initial distribution by e t/ one gets the solid curve in figure 1.2b. Then the lifetime is found by adjusting T to give a good fit to the experimental data. The first problem to arise is the determination of the initial velocity distribution. J. C. Pearl (1970) developed a theory to predict the molecular velocity distribution after electron impact. However, his theory requires knowledge of the electron energy and the collimation of the incoming and outgoing molecular beam, and is not easily applied to lifetime measurements. Another problem often arises from the presence of more than one metastable component. In the case of He, the 21S component can be quenched (Fry and Williams, 1969) and this was done in the lifetime measurements performed by A. S. Pearl (1970) and by Van Dyck, Johnson, and Shugart (1970). But these quenching techniques do not apply to N2. A method for measuring lifetimes that does not depend on knowledge of the velocity distributions, and that accounts for the presence of more than one component,is presented in section 2.2.

CHAPTER 2 THE THEORY OF A LIFETIME MEASUREMENT The spatial decay and TOF techniques discussed in sections 1.2 and 1.3 have the drawbacks that they do not consider the proper velocity distribution and they do not apply to a beam including more than one metastable component. The methods for measuring lifetimes presented below do apply to a beam consisting of more than one component and either use a measured approximation to the velocity distribution (spatial decay method) or do not depend on the velocity distribution at all (TOP method). 2.1 A Lifetime Measurement from Spatial Decay Data The spatial decay analysis generalizes the approach of Lichten (1957) and assumes the following: i) The metastable beam consists of two components: one component has an initial population N1 and a lifetime T, and the other component has an initial population N2 with an infinite lifetime. By "infinite lifetime" we mean that the state does not measurable decay from the time of creation to the time of detection. ii) The velocity distribution of the molecules after electron impact is described by the 9

10 function v exp(-mv2/2kT) where a value for n is assigned by fitting a non-decaying TOF distribution (section 4.4.3). Figure 2.la shows the spatial decay for a two-component metastable beam. Since the intensity of the longlived state is not a function of x, examine the short-lived state's behavior by taking the derivative of the intensity with respect to x (figure 2.1b). Take the ratio of the derivatives at two points X and Xb to give a db dI Gexpt (2.1) di dxlXb The notation "expt" is to remind us that this is an experimental quantity. G et is used to measure the lifetime as follows. expt Since it is assumed that the velocity distribution of the two-component beam is known, the intensity of the beam is written as an integral over all velocities: 2 I(x) = "vn e-mv /2kT.(Nl.e-x/vT + N2) dv. (2.2) The constant C with any number of primes is a normalization constant. It is convenient to express the velocity and

A TWO-COMPONENT S^ N\METASTABLE BEAM (a) ELECTRON GUN - DETECTOR SEPARATION Xa Xb >.. I,'..,' i —-' i I dI, dx Xba 0. ii - -dI:: a. g rQ^~~ DIFFERENTIATION OF THE 2g ABOVE SPATIAL DECAY o L W.R.T. DISTANCE (b) Figure 2.1 (a) Spatial decay of a two-component metastable beam. One component has a very long lifetime. (b) Differentiation of the two-component decay with respect to distance. This differentiation eliminates the longlived component since its intensity is not a function of distance. The lifetime of the short-lived component is found from the ratio of the derivatives of the intensity at two points Xa and Xb.

12 distance using variables m x m = v 2k W = T (2.3) Then equation 2.2 is n-u 2 I(x) = C' u.e"e- (Nl.e -/+ N2) du (2.4) Take the derivative of equation 2.4 with respect to x to eliminate the long-lived component. Remember that W is a function of x. di C-N1 n- -u -W/u = -- u * e u eW/U du (2.5) Given an n, the integral in equation 2.5 is a function of W and may be evaluated numerically. Now take the ratio of the derivatives at two points Xa and Xb: n-1 u W(Xa) u aa 0 X ~-s fX~. -un-l. eW(X du dxA. IA- b

13 But equation 2.3 gives Xb W(Xb) = - W(Xa) o (2.7) a Substitution of equation 2.7 into equation 2.6 gives dII 2 dIx Xa un1. e exp [- W(Xa)/u] du ox X ctn"le ~ e. xp - W(Xa)/u du But the left side of equation 2.8 may be replaced by the left side of equation 2.1: ~o un-1 e-U2 J un-l.e exp [-W(Xa)/U] du ^a (2.9) e un le u2 exp bW(Xa)/u du The left side of equation 2.9 is an experimental number while the right side is a theoretical expression. Since n, Xa, and Xb are known, the right side of equation 2.9 can be evaluated for various W(Xa) until the equality a is satisfied. Once W(Xa) is determined, equation 2.3 gives Xa m/2k (2.10) W(Xa)

14 Given the two assumptions at the beginning of this section, we now have a method for measuring lifetimes from spatial decay data. This technique is used as follows: i) Estimate n by fitting a non-decaying TOP spectrum with vn exp(-mv2/2kT), where n is varied to give a best fit. ii) Take the ratio of the derivatives of the spatial decay at two points Xa and Xb, forming Gexpt. iii) Use equation 2.9 to find W(Xa)o This is done a by evaluating the right-hand side for various W(X ) until the equality is satisfied. a iv) Once W(Xa) is found, the lifetime of the shortlived component is given by equation 2.10. This series of steps is carried out for various X and Xb, generating a series of values for the lifetime. Since these numbers should all be the same, an average can be taken. This method of measuring lifetimes will be applied to a computer-simulated metastable beam (section 3.3) and to an experiment on metastable molecular nitrogen (chapter 5). 2.2 A Lifetime Measurement from Time-of-Flight Data It is first necessary to develop a method of scaling time and amplitude so that TOP spectra can be compared on a common set of axes. The principles of this scaling are

15 conveniently illustrated by a non-decaying beam (argon for example). Figure 2.2a displays non-decaying TOF spectra at 13, 17, and 21 cm. 2.2.1 Scaling of the Time Axes Consider TOF distributions at distances Xa and Xb. A group of metastable molecules having a velocity V, has an amplitude Fa(Ta = Xa/V) at the distance Xa. By "amplitude" we mean the number of particles per unit time. This same group has an amplitude Fb(Tb = Xb/V = Ta-Xb/X ) at the distance Xb. If these two TOF distributions are to be displayed on a common time axes so that Fa and Fb have the same time coordinate, then the time a b scale of the second TOF spectrum must be multiplied by Xa/Xb. Figure 2.2b shows the results of scaling the time axes of the TOP spectra at 17 and 21 cm by multiplying by 13/17 and 13/21, respectively. The TOP spectra still do not overlap because a scaling of the amplitude axes is necessary. 2.2.2 Scaling of the Amplitude Axes Again consider TOF spectra taken at distances Xa and Xb (the time axes are not scaled). Consider a group of molecules at Xa that has times-of-arrival between Ta a a and Ta. The time spread is ATa = Ta - T. Note that a* ia a a this group has velocities between V = Xa/Ta and V' = Xa/T'. This same group has times-of-arrival at

16 TIME-OF- FLIGHT., 13cm DISTRIBUTIONS OF LU / A Kul7cm A NON-DECAYING X / 21cm METASTABLE BEAM Ch. TIME-OF-FLIGHT (a) t -13cm AFTER SCALING OF " - 1/<f7Cm THE TIME AXES 17cm 21 cm. I I SCALED TIME-OF-FLIGHT (b) w "~ A/~ ~AFTER SCALING OF'~ -- u \ ~ THE TIME AND _~ X/ \ ~AMPLITUDE AXES a:: - 13,17,21cm LUI.-J _ E SCALED TIME-OF-FLIGHT (c) Figure 2.2 Time-of-flight spectra for a non-decaying metastable beam. (a) Time-of-flight distributions at three distances. (b) The spectra after scaling of the time axes (section 2.2.1). (c) The distributions after scaling of the time and amplitude axes (section 2.2.2). The spectra overlap as they should.

17 X of T = Xb/V = Tab/Xa and T Xb/V = b/Xa This group now has a time spread of &Tb = T- - T = TXb/Xa - TXb/xa = AT aXb /Xa Note that the time spreads of this group at the two distances are related as &Ta = Tb.Xa/Xb. Since the number of particles does not change from Xa to Xb and since the time spread does increase at Xb, the amplitude (number of particles per unit time) must decrease, It must decrease by the ratio of the distances. If these two TOP spectra are to be displayed on a common amplitude axis so that this spreading of the particles is corrected, the amplitude scale of the second TOF spectrum must be multiplied by Xb/Xa. Figure 2.2c shows the results of scaling the amplitude axes (the time axes are also scaled) of the TOF spectra at 17 and 21 cm by multiplying by 17/13 and 21/13, respectively. The three TOP distributions now overlap, as they should. 2.2.3 Measurement of the Lifetime Only one assumption is needed to obtain lifetimes of metastable states from time-of-flight data: the, beam consists of only two metastable states, with one state having a very long lifetime, The description of the two-component metastable beam requires the knowledge of three unknowns: the initial populations of the long-lived state (N2), the initial population of the short-lived state (N1), and

18 the lifetime of the short-lived state (T). Since there are three unknowns, three equations are needed if a solution is to be found. These three equations may de derived from three TOF distributions as measured at different electron gun-detector separations (distances). Figure 2.3a shows TOP spectra for a two-component metastable beam at the distances Xa Xb = Xa + AX, and Xc = Xa + 2. X. (2.11) Figure 2.3b shows the same spectra after time and amplitude scaling. How does this change in shape of TOF spectra relate to the decay of the short-lived metastable state? Construct a perpendicular line on the scaled time axis at T' (dotted line in figure 2.3b). The intersections of this line with the three TOF distributions gives the amplitudes of a group of molecules having a velocity V = X /T' at the distances Xa, Xb, and Xc. Label the coordinates of the intersections (Fa, T)(, (F T), and (F', T'). The prime denotes a scaled quantity. Since we assume a two-component beam, the initial populations are designated Nl(V) and N2(V), with N2 having the infinite lifetime. This dependence of the initial populations on V is simply the distribution of velocities. The amplitudes of this group of metastable molecules

19 TIME - OF- FLIGHT DISTRIBUTIONS OF A TWO-COMPONENT METASTABLE BEAM::L / \ yXa NI=95 Tl=100lsec aE= Xa N2=5 T2= oo -,Xb /, b TIME-OF-FLIGHT (a) -- AFTER SCALING OF THE TIME AND wo ~ / \ AAMPLITUDE AXES Fg -Fb Fc T SCALED TIME-OF-FLIGHT (b) Figure 2.3 Time-of-flight distributions for a two-component metastable beam (N1=95, N2=5, Tl=100 usec, and'2=0o). (a) Time-of-flight spectra at three distances. (b) The distributions after scaling of the time and amplitude axes (sections 2.2.1 and 2.2.2). The lifetime of the short-lived state is found from the three amplitudes F', F', and F', at the time T'. t' b' ~

20 at the three points are written as F' = Nl(V).eX a/V + N2(V) V = X/T' (2.12) F = Nl(V). eXb/V' + N2(V) (2.13) Fc = N(V) e Xc/V. + N2(V). (2.14) Since this theory should apply directly to experimental data equations 2.12, 2.13, and 2.14 are written in terms of unscaled time and amplitude as F (T) = Nl.e-Ta/ + N2 Ta = X/V (2.15) (Xb/Xa).Fb(Tb) = Nl- e-b/ + N2 Tb X/V (2.16) (Xc/Xa)Fc(Tc) = Nl.eTc/T + N2 Tc = X/V. (2.17) Equation 2.11 implies Tb = Ta + AT, Tc = Tb + AT, and aT = tX/V.(2.18) Subtracting pairs of equations to eliminate N2 and substituting from equation 2.18, equations 2.15, 2.16, and 2.17 become

21 Fa(Ta) - X Fb(Tb) = N1 e a/ ~ (1 - e bT/T ) (2.19) Fb(Tb - c(T) = Nlee- b/T (1 - e- T/ ).(2.20) a a Now divide equation 2.19 by equation 2.20 to eliminate N1 and solve for the lifetime: r' _- Tb - Ta (2.21) Fa (Ta) (Xb/Xa )-Fb(Tb) n (Xb/Xa)-Fb(Tb) - (Xc/Xa) Fc(Tc)] ~ Equation 2.21 is written in terms of scaled qianitities as T'(Xb/Xa - 1) (2.22) [I(T') - F(T ) In LFi(Tt) - FP(T')J Given the one assumption at the beginning of this section, we now have a method for measuring lifetimes from TOF data. This technique is used as follows: i) Take TOF distributions at three distances Xa, b = Xa + Ax, and Xc = Xa + 2.'X. ii) Time and amplitude scale these spectra.

22 iii) Pick a scaled time T' and find the corresponding amplitudes FPa FB, and F'. iv) Then the lifetime of the short-lived component is given by equation 2.22. This series of steps is carried out for various T', generating a series of values for the lifetime. Since these'-numbers should all be the same, an average can be taken. Note that equation 2.22 does not require a knowledge of the initial populations or their velocity distributions. This method of measuring lifetimes will be applied to a computer-simulated metastable beam (section 3.4) and to an experiment on metastable molecular nitrogen (chapter 5). 2.3 An Alternate Method for Measuring a Lifetime from Time-of-Flight Data The theory of the previous section applies only to a two-component metastable beam. The following theory may be applied to a three-component beam. Suppose the first component has an initial population Nl(V) and a lifetime Tl, the second component has an initial population N2(V) and a lifetime T2, and the third component has an initial population N3(V) and an infinite lifetime. It is assumed that the initial

23 populations have the same velocity distributions; the relative populations N1/N3 and N2/N3 are velocity independent. If the appearance potentials of the three states are such that just N1 and N3 are excited with low voltage electrons then the TOF theory for a two-component beam (section 2.2) gives the lifetime Tl Now increase the energy of the electrons until all three states are excited. We now have four unknowns: N1, N2, N3, and T 2 ( T 1 has just been measured). By using TOF spectra at four distances, the theory of section 2.2 may be generalized to measure T 2 (appendix A), However, the range of detector movement may not permit TOF data to be taken with sufficient separation for the spectra to be distinct and allow unambigious measurements. Or it may not be possible to separately excite the metastable states. It is, therefore, desirable to have a second method for calculating lifetimes from TOF data. Suppose TOP spectra are taken at distances Xa and Xb, and time and amplitude scaled. It should be possible to use the spectrum at Xa and calculate the spectrum at Xb, using assumed population ratios and lifetimes. Then if the experimental and calculated distributions compare favorably, the assumed population ratios and lifetimes are correct. As in the previous sections, we examine a group of

24 molecules that has a velocity V. At the distance Xa, this group has a time-of-flight T, = X /V and an ama a plitude (number of particles per unit time) F (Ta). a a The amplitude is written as F (Ta) = Nl(V).e-Ta/1 + N2(V) eTa/2 + N3(V).(2.23) Since the relative population ratios are assumed to be known from other considerations, divide equation 2.23 by N3(V): a(Ta) N1(V) -~a/T1 T(VT -Ta N V) T Fa(Ta) = e= aT + T e Ta/T + 1. (2.24) N3(V) 3 v Equation 2.24 is solved for Fa(Ta) N3(V) a (2.25) (tl/N3)e Ta/l + (N2/N3)-eTa/ 2 + 1. The right-hand side of equation 2.25 contains only known quantities: Fa(Ta) (experimental data), N1/N3, a a N2/N3, T1, and T2. The left-hand side of equation 2.25 is the initial population of molecules in the longlived state having a velocity V. The initial populations of the other two states are found from equation 2.25 and the assumed relative population ratios:

25 N1(V) = (N1/N3)-N3(V) (2.26) N2(V) =(N2/N3)-N3(V) (2.27) Equations 2.25, 2.26, and 2.27 give the initial populations of molecules having a velocity V. At Xb, this same group of molecules has a time-ofarrival of Tb = Xb/V. Since the time-of-flight, the initial populations, and the lifetimes are known, the amplitude at Xb is found from Fb(Tb) = Nl(V).e- b/ 1 + N2(V).eTb/ T 2 + N3(V).(2.28) The superscript p denotes Fb(Tb) to be a predicted amplitude. The predicted amplitude can be compared with the experimental amplitude, and if the two compare favorably,, the assumed population ratios and lifetimes are correct. As an example, 1 might be known from a previous measurement and N1/N3 and N2/N3 could be estimated from cross-section measurements. Then various values of T 2 are assumed and the TOF spectra at Xaare used to predict the spectra at Xb ising the above theory). By comparing the predicted and experimental spectra, the best value of T2 is picked.

CHAPTER 3 COMPUTER PROGRAMS AND SIMULATED BEAMS 3.1 Generation of the Simulated Beams The preceding analysis of the spatial decay and TOP data is best performed by a computer. The computer programs and the analysis are tested by generating a set of simulated data (spatial decay and TOP data) with assumed populations and lifetimes. Then this set of simulated data is treated as "real data" and analyzed by the computer, The computer routines should return the assumed lifetimes. The simulated data are generated with the following assumptions: i) The metastable beam has two components. One state has an initial population N1 and a lifetime T. The other state has an initial population N2 and an infinite lifetime. ii) The velocity distribution of metastable molecules is given by the function v3 exp(-mv2/2kT). k is Boltzmann's constant, m is the molecular weight of molecular nitrogen, and the temperature T is taken as 300 K. The simulated spatial decay [intensity (I) versus 26

27 distance (x)] and TOF data [amplitude (F) versus time-offlight (t) at a distance (x)] are generated with the following functions: 4o 2 i) I(x)= J. v-m /2kT(Nle-x/v+ N2) dv ii) F(t) e-mv/2k(Nl t/ + 2) t5 These functions are calculated as follows: i) Assume N1 = 90%, N2 = 10%, and T= 100 usec. ii) Evaluate the spatial decay function from x = 13 cm to x = 27 cm in 0.2 cm intervals. ii) Evaluate the TOF function from t = 50.sec to t = 500 )asec in 10 usec intervals, at the distances x = 13, 17, and 21 cm. It should now be possible to analyze these computersimulated metastable beams and retrieve the assumed lifetime of 100 jisec. 3.2 Computer Programs All the computer programs contain a subroutine that fits the data with a least squares curve. The fitting technique is detailed in Mathews and Walker (1965) and is based on a computer program written by Mr. George Schofield of this laboratory. The spatial decay intensity is fitted with the function: Co + cl-(x-13) +... + c4.(x-13)4 (3.1) where 13 cm is the distance of closest approach.

28 The natural logarithm of the TOF amplitude is fitted with the function: cO + c1 in + c3.~ + c4.t [t is in jsec] (3.2) The coefficients ci are computed by the least squares subroutine and the fitted curves are returned to the main program for the lifetime calculation. These two functions are sufficiently general so that they do not bias the data. The spatial decay program uses the theory of section 2.1. The data arefitted with a least squares curve and the slope is found at distances Xa and Xb (=R-Xa). Then equations 2.1 and 2.9 are used to find W(Xa), with equation 2.10 giving the lifetime. A series of lifetime values is calculated by fixing Xa and incrementing R, or fixing R and incrementing Xa. The TOF program uses the theory of section 2.2. TOP distributions at three distances are time and amplitude scaled and fitted with a least squares curve. A time T' is picked and equation 2.22 gives the lifetime. T' is incremented between two limits, generating a series of values for the lifetime. 3.3 Analysis of the Simulated Spatial Decay Data The data points in figure 3.la are the spatial decay

29 SPATIAL DECAY OF A TWO- COMPONENT METASTABLE BEAM > 1.0 N1 = 90 T1 = 100 usec c z N2 = 10 T2 = o: Z.8..6 ELECTRON GUN - DETECTOR SEPARATION (CM) (a) n lo 110 LIFETIME OF THE SHORT-LIVED COMPONENT 100 ~ ~. H 90 13 15 17 DISTANCE Xa (CM) (Xb = 1.5 Xa) (b) Figure 3.1 Spatial decay for a two-component computer-simulated metarivative of the intensity at two points X and X stablECTRO beam - DETE 1(=R-X00 ). a d a (a) ~ 90 le. qae t(oi uv)t h pta ea (dtapint)

30 generated according to section 3.1. The solid curve is the least squares fit using function 3.1. Since the simulated data is assumed to have a velocity distribution v3 exp(-mv2/ 2kT), the data is analyzed with n = 3. Figure 3.lb shows the results of analyzing this simulated data with the theory of section 2.1. As expected, T= 100 Asec with only a small scatter (~ l1 sec) in values. Since the value of n in a real experiment is generally not known with any certainty, the simulated spatial decay data are analyzed allowing n to assume values of 2.50, 2.75, 3.00, 3.25, and 3.50. Figure 3.2 shows that the value used for n is not very critical: a 17% error in n results in only a 5% error in the lifetime. 3.4 Analysis of the Simulated Time-of-Flight Data The data points in figure 3.3a are the three TOP spectra (after time and amplitude scaling) generated according to section 3.1. The solid curve is the least square fit using function 3.2. Figure 3.3b shows the results of analyzing this simulated data with the theory of section 2.2. As expected, T = 100 %sec, with only a small scatter (+ 2 usec) in values. The slight oscillatory behavior of the lifetime values is a result of the least squares fit to the data. If the form of the fitting function is changed, the oscillations change. However, the average lifetime is always (100 ~ 2) isec, regardless of the particular form of the fitting function.

31 110 LIFETIME FOUND FROM A TWO-COMPONENT 100'..SPATIAL DECAY 90 90...., n =3.50 110 VELOCITY DISTRIBUTION n -mv2/2kT 100 v e 2kT'* **I.. *..*' I S V A R I E D 90n = 3.25 Cs r.X 110 U3 100 L.... E-4 90 <>-,,~, n 3. 00 (CORRECT VALUE) H 110 100 90. 90_.. n = 2.75 110 100 90 n =2.50 13 15 17 DISTANCE X (CM) a (Xb 1.5 X ) b a Figure 3.2 Dependence of the spatial decay lifetime calculation on the value of n, where vn exp(-mv2/2kT) is the velocity distribution. The correct value of n is 3.0 for the two component, simulated spatial decay. A 17% error in n results in only a 5% error in the lifetime.

32,1~.~0 TIME-OF-FLIGHT DISTRIBUTION OF A TWO-COMPONENT METASTABLE BEAM.8 N1 = 90 T1 = 100 Psec g IU~ \\;~ CN2 = 10 t2 = c.6 - I- \V -13 cm a., |J \t\Z —17 cm 100 200 300 400 500 SCALED TIME-OF-FLIGHT (UJSEC) (a) LIFETIME -OF THE U 110 SHORT-LIVED COMPONENT * —-— 21 cm C-l 0 90 H1!0 100 200 300 400 500 SCALED TIME TF (USEC) (b) Figure 3,3 Time-of-flight spectra for a two-component, computer-simulated metastable beam (N1=90, N2=10, T1=100 Psec, and T2=o) (a) A least squares fit (solid curve) to the time and amplitude scaled distributions (data points). (b) The lifetime of the short-lived component as found from the above spectra. The lifetime is found at a time T' from the corresponding amplitudes of the three spectral from the corresponding amplitudes of the three spectra.

CHAPTER 4 EXPERIMENT 4.1 Apparatus Figure 4.1 is a schematic of the experimental apparatus. The vacuum chamber is divided by a bulkhead into a source chamber and a detector chamber. Each section contains a cold trap and is evacuated by an oil diffusion pump equipped with a baffle to prevent backstreaming of pump oil. The diffusion pumps exhaust into a common foreline that is backed by a rotary forepump, Pressures in each section are monitored by ionization gauges. Base pressures, with liquid nitrogen in the cold traps, are approximately 1x10'7 torr. Operating pressures in the source chamber are typically in the 10-6 torr range. The gas to be studied is emitted into the source chamber through a long copper pipe. The gas reservoir is a balloon. The gas flow of about.1 micron-liter/sec is controlled by a Nupro very fine needle valve. The electron gun has four elements: an indirectly heated cathode, two accelerating grids, and an enclosed anode. At an anode-cathode potential difference of +30 volts, the anode typically draws 100 vamps. The electron energy spread is estimated to be (section 4.2) +1 eV, 33

34 EXPERIMENTAL APPARATUS BULKHEAD DIVIDING THE CHAMBER ION GAS INLET TRAPS PIPE LJ': II - -i. — COLLIMATORS __ MOVABLE ELECTRON DETECTOR GUN Figure 4.1 Experimental Apparatus

35 An electromagnet of approximately 100 gauss is used to focus the electron beam and to confine charged particles to the interaction region. The collimators are holes approximately 1 mm in diameter, in a.003 inch thick metal plate. The charged particle traps are two metal plates approximately 2 cm apart. These plates are typically biased at +100 volts. The detector is a Bendix "Channeltron" continuous dynode electron multiplier (Donnelly et al,, 1969). Upon striking the detector surface, ultraviolet photons and metastable molecules eject electrons (with an efficiency of a few percent) by the photoelectric and Auger process, respectively. These electrons are cascaded by the continuous dynode structure into a detector pulse. The detector is enclosed in an aluminum box to reduce the background counts, and is- mounted on a movable carriage that translates along the beam axis. The detector has a range of movement of approximately 17 cm and has a distance of closest approach to the electron gun of 12.7 cm. As outlined in chapter 1, this apparatus may be used to observe spatial decay of TOF spectra. The time-to-height conversion takes place as follows. When the pulse generator supplies a voltage pulse to the anode it also initiates a linear voltage ramp. The detector pulses, generated by the metastable molecules created during the electron gun pulse, are passed through

36 a preamplifier, an amplifier, and to the input of a linear gate. This linear gate is operated in a coincidence mode with the linear ramp. Thus, the output of the linear gate is a series of pulses, with the height of each pulse being proportional to the transit time of the metastable molecules. These pulses are sorted according to height and stored by the multichannel analyzer. The distancea4-o-height conversion follows the same series of steps as the time-to-height conversion, except that th eelectron gun is in a DC mode and the linear ramp is generated by a battery and a multi-turn potentiometer connected to the detector drive. 4.2 Excitation Functions The techniques presented in sections 2.2 and 2.3 for measuring lifetimes assume a two-component metastable beam, with one component having a very long lifetime. The A3E and a lT states of N2 satisfy these criteria with the A31 having a lifetime on the order of seconds (Shemansky, 1969a). Before a lifetime measurement can be made, it must be determined that these two states can be excited while the E 3 state is excluded. The excitation function measurements described below confirm that the E3Z state is not excited if the energy of the electrons is below 12.0 eV. The anode voltage of the electron gun is calibrated using the known appearance potentials for the metastable

37 states of He and Ar. Figures 4.2a and 4.2b show the plots of normalized detector signal versus anode voltage (the excitation function) for He and Ar (since the anode current increased with the anode voltage, the detector signal is normalized by dividing with the anode current). It is seen from the excitation functions that the initial increase in normalized signal has a portion that is linear with anode voltage. The extrapolation of this linear portion back to the zero or background level gives the appearance potential of the state that is being excited. Figure 4.2a and 4.2b show that the He appearance potentials (known to be 19.82 eV) is measured to be 28.0 eV, while the Ar appearance potential (known to be 11.55 eV) is measured to be 19.5 eV. The discrepancy of approximately 8 eV is not fully understood, but it is not unusual when compared to the results of other workers in this laboratory. Since this 8 eV discrepancy was measured on a number of occasions, it is reasonable to assume that the difference between the actual and measured anode voltage is 8 eV for all excitation functions. The electron energy spread is estimated from the He excitation function (Fox, et al. 1955) to be +1 eV. Figure 4.3a is an energy level diagram for N2 showing the lower lying states, and figure 4.3b is the excitation function measured in this experiment. Freund (1969b), reported that the metastable excitation function is mainly due to the A35, al1, and E3E states. The mall p^eak at 6 eV

38 3 _.."9 HELIUM -"! * EXCITATION FUNCTION H ^_ w Z 2 O H 3:2.ARGON H 1 Q {, / 0 _: o9 17 22 27 ELECTRON ENERGY (EV) 25 3 0 35 ANODE VOLTAGE (a) 3 - I. *EEXCITATION FUNCTION Q ~......... Cg M < N'- - 3.1 1 _ / 7 12 17 22 ELECTRON ENERGY (EV) 15 20 25 30 ANODE VOLTAGE(b) Figure 4.2 Excitation Functions (a) Helium (b).Argon

59 LOWER ENERGY LEVELS OF N2 13 C31 D3+ U 1+ a"1 --- " g 3. —-- -E+ E. C3 ~= w L ~9. -u-____ L -, g B'tU a a TT R3 ~9 _ _B,WI O an 3 E -U --- B. n W.& u 7 g M ___ A3 + o 1+ _ _ _ _ _ _ _ _ N2 EXCITATION FUNCTION z CD; E-4 4, ~ 2 Q H / 0 5 10 15 20 25 ELECTRON ENERGY (EV) (b) Figure 4.3 (a) Energy level diagram for N2 showing lower lying states (after Dressler, 1969). (b) Exeitation function for N2. <c p (b) Exettation function for No.

40 is assigned to the A3F state. The linear rise that gives an 8.5 eV appearance potential is due to the alTI state, and the break in the excitation function at 12.5 eV is assigned to the E3Z state. Thus, if we are to use a two component beam, the electron energy must be below 12.0 eV. 4.3 Acquisition of Spatial Decay and Time-of-Flight Data The spatial decay data were taken by connecting the detector drive to a motor and making four passes over the range of interest. The data were checked for drifts of the beam intensity and for binding of the detector drive by requiring that data taken with the same electron energy and source pressure overlapped (when plotted on the same graph). Ar and N2 spatial decay data were taken for a variety of voltages and pressures. However, problems with the beam stability and uniformity of the detector drive were severe enough that only 22 eV data were retained for final analysis. Since the superior TOF techniques were developed while the spatial decay measurements were going on, the spatial decay experiment was not carried to competion except for the 22 eV data. Since the beam intensity should remain constant during. a series of TOF measurements, electron gun current and source chamber pressure were monitored. The source pressure always remained constant, but occasionally the electron current would drift. The anode current was not monitored, but the second grid current was recorded at both the beginning and

41 end of each single TOF distribution acquisition. After a series of these distributions were taken, each spectrum was normalized to correct for any current drift. As a further check on beam stability, the first and last TOF distributions in a series were taken at the same distance. If these two spectra did not overlap after current normalization, the series was rejected. Only the TOF data taken with 10 and 22 eV electrons survived this test. The TOF distributions are fitted with a least squares curve before lifetimes are calculated. Figure 4.4 gives examples of fits to data with large and small scatter. These spectra as well as all other spectra used function 3.2 as a fitting function. The remaining TOP distributions are presented only as fitted curves. 4.4 Analysis of the Argon Data Since the two metastable states of argon (3P0 and 3P) have very long lifetimes (Muschlitz, 1968), they do not decay while travelling from the electron gun to the detector. Thus Ar data is used to i) investigate instrumental effects in spatial decay and TOF data, ii) verify the time and amplitude scaling as outlined in sections 2.2.1 and 2.2.2, and iii) determine the velocity distribution in the absence of any decay. 4.4.1 Spatial Decay The data in figure 4.5a is Ar spatial decay taken

42 LEAST SQUARES FIT TO THE TIME-OF-FLIGHT DISTRIBUTIONS M 61 -\6 Q I \ " H -.\ STATISTICAL E* \ UNCERTAINTY < 4 AT THE PEAK H PAT T ~~- 2 0. ~-s 0 100 300 500 TIME-OF-FLIGHT (JJSEC) F-i H - - \ STATISTICAL 1 6 1 | \ UNCERTAINTY HZ 4 1 F \ AT THE PEAK ~. N S3 F ~ * \, ~ 2 \ 0 O O 0 100 300 500 TIME-OF-FLIGHT (JSEC) Figure 4.4 Least Squares Fitting to the Time-of-Flight Distributions

43 SPATIAL DECAY 22 EV ELECTRONS 1.0 X-~~~~ An~r H.9.8 E>^, ok. C< N2 CORRECTED z wc ~.^-^, WITH Ar DISTANCE X (CM) (b) N2 S 13.5 - 17.5 21.5 25.5 ELECTRON GUN - DETECTOR SEPARATION (a) u 170 LIFETIME FOUND FROM a THE ABOVE CORRECTED ~ 160 _ --.pro Na SPATIAL DECAY - 150.. t c * d. 13.5 16.5 DISTANCE Xa (CM) (b) Figure 4.5 Spatial decay taken with 22 eV electrons. (a) Ar and N2 spatial decay (data points) are fitted with a least squares curve (solid line). The Ar fitted curve provides a correction to the N2 data points (the dashed curve is the least squares fit to the corrected N2 data). (b) The lifetime as calculated (according:to technique I) from the corrected N2 data. The lifetime is found from the derivative of the intensity at two points Xa and Xb (=R.Xa). The lifetime is assigned to a composite of the altr and E3. states.

44 with 22 eV electrons. The solid curve is the least squares fit using cO + c1.(x-13.5) + c2.(x-13.5)2 as a fitting function. Only three terms are used so that the scatter in the data is averaged out. Since metastable Ar does not decay, this spatial variation in intensity is due to effects such as atoms scattering out of the beam, geometrical spread of the beam, and spatial dependence of the detector efficiency (due to stray magnetic fields). The Ar spatial decay provides a correction to the N2 spatial decay as follows. The Ar data is fitted with the three term fitting function and the percentage change is found at each point along the fitted curve. This percentage change is applied as a correction to the N2 data. Then the corrected N2 spatial decay is fitted with a least squares curve. The Ar spatial decay in figure 4.5a is used as the correction for all the N2 spatial decay data. Since the electron gun is operated in a DC mode for spatial decay data, this data includes photons as well as metastable molecules. However, these photons contribute only a small percentage to the total signal, and do not present a problem. 4.4.2 Scaling of the Time-of Flight Distributions Non-decaying TOP distributions taken at different

45 distances should overlap after time and amplitude scaling. This is found to be true for all the Ar spectra, with the distributions in figure 4.6 being typical. These three TOP spectra overlap to within the statistical uncertainty of the data (defined as plus or minus the square root of the number of counts). Since the Ar spatial decay is fairly constant over the region from 13.5 to 21.5 cm, it is not necessary to provide a correction to the TOP data. Thus, if N2 TOF distributions taken at different distances do not overlap after scaling, a decay of the metastable states is observed, 4.4.3 Determination of the Velocity Distribution The theory of lifetime measurements from spatial decay data (section 2.1) assumes that the metastable velocity distribution is described by f(v) dv = vn.e-mv /2k dv This distribution converts to a TOP distribution f(t) dt = xn+ e-(m/2kT)2/t2 dt The parameter n is found b ffitting Ar TOP spectra with the above distribution and varying n to give a best fit. The data points in figure 4.7 show an Ar TOP spectrum

46 TIME AND AMPLITUDE SCALING OF ARGON TIME-OF-FLIGHT DISTRIBUTIONS D 6 STATISTICAL;/,\ iUNCERTAINTY 3CQm~ *~ / \~ AT THE PEAK 4. ia 2^ — 13.5 cm --— 17.5 cm Q. — 21.5 cm 0 O 100 300 500 SCALED TIME-OF-FLIGHT (jJSEC) Figure 4.6 Argon time-of-flight distributions at three distances after scaling of the time and amplitude axes.

47 A FITTING OF ARGON DATA TO DETERMINE THE VELOCITY DISTRIBUTION 1.0.n+l xn2 exp(-mv /2kT) Z / \,8. n =2.7 ~ 1 \ / \.6 H \ Q N 4'.2 ~. 2' *.. z 0 L 0 100 300 500 TIME-OF-FLIGHT (UJSEC) Figure 4.7 Determination of the argon velocity distribution. An argon time-of-flight distribution is fitted with-the function xn+l/tn+2 exp(-mv2/2kT). n is varied to give a best fit. The solid curve is calculated with n=2.7.

48 taken with 22 eV electrons at 13.5 cm from the electron gun. The solid curve is the fit using the above distribution with n = 2.7. This value of n is consistent with the remaining Ar data and is used in the analysis of all the N2 spatial decay. It has been observed that the velocity distribution depends on many parameters, including the source pressure, the electron energy, and the molecular mass. Thus, the velocity distribution that describes Ar might not apply to N2. However, it has been shown (section 3.3) that the exact value of n is not needed for an accurate lifetime measurement.

CHAPTER 5 ANALYSIS OF THE NITROGEN DATA In chapter 4 we described the calibration of the electron gun and showed that the Ar spatial decay and TOP spectra behaved as expected. We may nowi.use the techniques of chapter 2 on N2 spatial decay and TOF data to obtain a value for the lifetime of the alT~ state. 5.1 A Summary of Analytic Techniques We have three methods for analyzing the N2 data. These techniques and some comments: I) The first technique (section 2.1) is applied to spatial decay data. It assumes a two-component beam, with one component having a very long lifetime. It also assumes that the N2 velocity distribution can be approximated by the Ar velocity distribution. This method is limited since it requires some knowledge of the velocity distribution and is not easily generalized to more than a twocomponent beam. We found that the data were hard to obtain cleanly and reproducibly since this method relies upon the long term beam stability and the uniformity of the detector drive. II) The second technique (section 2.3) is.applied to 49

50 TOP spectra. It assumes a two or three-component beam, with one component having a very long lifetime. It also assumes that the relative populations are independent of velocity. This method is limited by the ability to judge the "goodness" of a theoretical fit to experimental data. It is included as a technique for investigation and is not intended as an accurate measurement technique. III) The third technique (section 2.2) is the main analytic tool to be applied to TOP spectra. It assumes a two-component beam, but does not make any assumption concerning the velocity distribution. TOP distributions are taken at three equally spaced distances and time and amplitude scaled (sections 2.2.1 and 2.2.2). Then a time T' is picked and equation 2.21 gives the lifetime. Lifetimes are calculated for a series of T' and an average is taken. Method III is an accurate technique of handling a two-component beam as seen from the analysis of a computer-simulated metastable beam (section 3.4). This technique can be generalized to the analysis of a more than two-component beam (appendix A). 5.2 Data The data consists of i) spatial decay taken with 22 eV electrons, ii) TOF spectra taken with 22 eV electrons,

51 and iii) TOP spectra taken with 10 eV electrons. Before this data is analyzed, recall that (section 4.2) if 10 eV electrons are used, the A3E and the aln states are excited. If 22 eV electrons are used, the A3E, aT, and EE states are excited. 5.2.1 Spatial Decay at 22 eV Seven sets of data pass the stability tests and are retained for final analysis. Figure 4.5a shows the spatial decay for one of these runs. The solid curve is the least square fit with co + cl.(x-13.5) +... + c4-(x-13.5)4 used as a fitting function. Figure 4.5a also shows the N2 data after the Ar correction (section 4.4.1) is applied. The slight break in the corrected data in the 23 to 24 cm region occurs in all the N2 spatial decay. Because this break cannot be explained, calculations are limited to data in the 13.5 to 22.5 cm region. Technique I is used to calculate the lifetime from corrected and fitted N2 spatial decay. The derivative of the intensity at points X and Xb, and the approximate velocity distribution (section 4.4.3) are needed for the calculation. R (=Xb/Xa) is fixed at 1.26 and Xa is incremented from 13.5 to 16.5 cm in intervals of 0.5 cm. Figure 4.5b is a display of the lifetime found from the single spatial decay in figure 4.5a. Figure 5.1 is a

52 histogram disp ying the lifetimes found from all seven runs. The apparent lifetime is 154 uasec. Since we are applying a two-component theory to a three-component beam, the 154 jsec refers to a composite lifetime of the a l and E3 - states. 5.2.2 Time-of-Flight at 22 eV The data from seven runs at distances of 13.5, 17.5, and 21.5 cm pass the stability tests (section 4.3) and are therefore retained for the final calculations. Figure 5.2a shows one set of 22 eV TOF distributions. Technique III is used to calculate the lifetime from the scaled and fitted spectra. The scaled time T' is incremented from 200 to 400 usec in 10 usec intervals and equation 2.22 is used to calculate the lifetime. Figure 5.2b is a display of the lifetime found from the single set of TOF spectra in figure 5.2a. Figure 5.3a is a histogram displaying the lifetimes found from all the combinations of distances. The apparent lifetime is 161 Asec. Since we have again applied a two-component theory to a three-component beam, the 161 usec refers to a composite lifetime of the al' and E T states. Note that this lifetime agrees very well with the spatial decay data taken with 22 eV electrons (154 xjsec) where we also analyzed a two-component beam with a three-component theory.

53 HISTOGRAM OF THE LIFETIMES FOUND FROM N2 SPATIAL DECAY 22 EV ELECTRONS Cn z 0 gz< ZC) 100 150 200 LIFETIME (UJSEC) Figure 5.1 A histogram displaying the lifetimes (calculated according to technique I) found from all the N2 spatial decay taken with 22 eV electrons. Each spatial decay contributes seven points to the histogram. The lifetime (154 isec) is assigned to a composite of the aln and E3T states.

54 1.0 N2 TIME-OF-FLIGHT DISTRIBUTIONS E.8 / \ z \ 22 EV ELECTRONS <1.6 - -13.5 cm g~ \ \ \_L~.-17.5 cm E4 \\\ —\-21 5 cm.2 0 ____,_,___________________________, 0 100 300 500 SCALED TIME-OF-FLIGHT (JJSEC) (a) LIFETIME FOUND FROM THE ABOVE DISTRIBUTIONS w 180 6 0 160.. 14Q'e tM I H.] 0 100 300 500 SCALED TIME T' (OJSEC) (b) Figure 5.2 N2 time-of-flight spectra taken with 22 eV electrons. (a) A least squares fit of the time and amplitude scaled distributions. (b) The lifetime as calculated (according to technique III) from the above spectra. The lifetime is found at a time T', from the corresponding amplitudes of the three spectra. The lifetime is assigned to a composite of the al3 and E3z states.

55 HISTOGRAMS OF THE LIFETIMES FOUND FROM N2 TIME-OF-FLIGHT DATA cO X 2-22 EV ELECTRONS 2 20 0. 10 - z 0 A 100 150 200 LIFETIME (iJSEC) (a) 30. -- 10 EV ELECTRONS 20 o 0 100 150 200 LIFETIME (USEC) (b) Figure 5.3 Histograms displaying the lifetimes (calculated according to technique III) found from all the N2 time-of-flight data. (a) Lifetimes found from data taken with 22 eV electrons. This lifetime (161 nsec) is assigned to a composite of the a~T and E3Z states. (b) Lifetimes found from data taken with 10 eV electrons. This lifetime (106 Dsec) is assigned to the a state. This lifetime (106 usec) is assigned to the a 1^ state.

56 Now we will analyze this data as a three-component beam according to technique II, Figures 5.4a, 5.4b and 5.4c show the TOF spectra at 13.5, 17.5, and 21.5 cm. The solid curve in figure 5.4a is a least squares fit using function 3.2. The solid curves in figures 5*4b and 5.4c are the TOF spectra predicted using i) the least squares fit of figure 5.4a, ii) lifetimes of T1 = 105 usec and T2 = 210 jisec (section 2.3), and iii) adjusting the populations to give a best fit (N1 = 30, N2 = 70, and N3 = 12 is displayed). Because we have a three-component beam, the 105 usec refers to the al state and the 210 jsec refers to the E3' state. Altogether, it would be better to work at low enough electron energies so that only two states are excited. This approach is described in the next section. 5.2.3 Time-of-Flight at 10 eV The data from seven runs at distances of 12.9, 14.9, 16.9, 18.9, 20.9, and 22.9 cm pass the stability tests (section 4.3) and are therefore retained for final calculations. Figure 5.5a shows one set of 10 eV TOF distributions. Technique III is used to find the lifetime from the scaled and fitted spectra. The scaled time T' is incremented from 200 to 350 usec in 10 ysec intervals and equation 2.22 is used to calculate the lifetime. Figure 5.5b is

57 C\J 0 $ - C)/ > 0 C'q I ~J (dLL E — P C" - C - laH * c o) HoCO r4- r,, m'40 LO -, Q ) HO CY) u / r'-~ H t fr~H C3 0 o4 1 t IS~~~~~~~~~~~ g Uo/o~~~c - 2 0,i O L O On t0 $ k 4-P -H 0 g -*.^^ U3 ) *d O, (D( _~ o::) rd *C 4-)H *H rH Hr ~ ~ ~ ~ ~~~~~ - *f c 3.H 0 iI ~ 0 e +. Hw O~0~4 s 4I -^ *S ^* * 0 ) 0 0(3) Ul) _ o O Q) G 0H H. <. p ro p' Cil r-S C I 0 0 ^F -PH IO / CH H4 ~- o I 0o 0 0 o oo (.o - oU 0) c.-4 SsI~n * sue) sansI Idwe Ir-4'8{).GHIUNVrdcG~ o 0 (S*% -a ) - 0~~~~~ ~ ~ ~ 004 U)~ (N * ~ ~ ~ ~ ~ ~ ~ ~ r 9, 9 9'-'r (SLI~~fl a~IV) aanL~~t~awv ~IflV3S

58 1.0 N2 TIME-OF-FLIGHT DISTRIBUTIONS H 8. m 3 1 \ 10 EV ELECTRONS.6 X 12 0 \ FOUD-12.9 cm ~ /7 \\ V^.~~ —17.9 cm -21.9 cm E 84 Q=.2 9. 0 100 300 500 SCALED TIME-OF-FLIGHT (JJSEC) (a) o LIFETIME FOUND FROM w 120 THE ABOVE DISTRIBUTIONS Figure 5 5 N2 time-of-flight spectra taken with 10 eV electrons, (a) A least squares fit of the time and amplitude scaled distributions. - from the above spectra The lifetie is foud at a.. H 800 100 300 500 SCALED TIME T' (JJSEC) (b) Figure 5.5 N2 time-of-flight spectra taken with 10 eV electrons. (a) A least squares fit of the time and amplitude scaled distributions. (b) The lifetime as calculated (according to technique III) from the above spectra. The lifetime is found at a time T', from the corresponding amplitudes of the three spectra. The lifetime is assigned to the a1l state.

59 a display of the lifetime found from the single set of TOF spectra in figure 5.5a. Figure 5.3b is a histogram displaying the lifetimes found from all the appropriate combinations of distances. The calculated lifetime is 106 isec. Since we have applied a two-component theory to a two-component beam, the 106 asec refers to the a l state. The stability of the beam is checked by taking the first and last TOF spectra in a series at the same distance (section 4.5). If the two spectra do not overlap, the entire series is rejected. If the beam is stable for six of the spectra and drifts during only the last spectra, the entire series is rejected. Valid data (the first six spectra) could be lost in this manner. To check on this possibility, the rejected data is analyzed according to technique III. In every case except one, the lifetime values have extreme amounts of scatter and are entirely meaningless (the data was properly rejected). In the one case, the lifetime values have only a small amount of scatter with values very close to the 106 )sec found above (we had rejected some data that was partially okay). One final bit of analysis with technique II substantiates the 106 jssec lifetime of the all state. Figures 5.6a, 5.6b, and 5.6c show the TOF spectra at 12.9, 16.9, and 20.9 cm. The solid:curve in figure 5.6a is a least squares fit using function 3.2. The solid curves in

60 cn 4 z O 0,0 O-,C\J i o Fn uI ~ ~ fO,.I,) 4 -- ~ x LO O / ~*. 4 [-,-tW1~~~~~~~~~~ o *',_c "c02 0c.O ~ ~ 04.1 o0 oD:. () c r-( ai a? 0 O <>^^^0'p ~02 *. HH OM')0 D3 W, 4 m "P mp /. CO~~~~~~~~~~~~~Cd 0 A>m E4 * I CE HM. I<,P eO Q @ - CD h^0 ^ ~ *r1 m I -P.-4 r. _,.^H CH o. omw X=d~~~~:P~ ~ ~~' o t[~~~4 Q~C0 (1 0. Ln) *'CO O C4;^0 -P r. [4 _g_.*4I.0 > - P O H H O ) I *^^^ * (Df~~~~~~ 0 0-,- 0 W. S L. P H ^ cu 0E-e'*~~. -: a) -P0 I. ^ --- -~-. o? q-{ $> H - ES;CDv~~~~~~, I J.-1 *drt~~~~~~~~~~~~~ r- r, ~c~ q —I~ 4 -kQ tl rO i 0 o *H 0' o' - - 03 oi- I3 (c SP ) *f d I -I ~, I, 0 O0 (JOCQ < 0 ~ ~.... o,^!,. S o (S&I-r~. C' ) I ><'^*r< ChO e g o Cr *r-.d d ^^-^. O hQ 0 C H 0 Q) r

61 figures 5.6b and 5.6c are the TOF spectra predicted using i) the least squares fit of figure 5.6a, ii) a lifetime of T1 = 105 usec (section 2.3), and iii) adjusting the populations to give a best fit (N1 = 100, N2 = 0, and N3 = 17 is displayed). Because we have a two-component beam, the 105 usec refers to the al11 state.

CHAPTER 6 DISCUSSION OF EXPERIMENTAL RESULTS 6.1 Other Experiments There are two common methods for measuring the lifetime of the al state of N2. One method involves the analysis of the optical transition al T - X + and yields values g g ranging from 10 to 160 isec (Jeunehomme, 1967; Holland, 1969; Shemansky, 1969b). The second method, which involves either spatial decay or TOF measurements on a beam of excited N2 molecules, has yielded results with less scatter, The spatial decay method used by Lichten (1957) gave a lifetime of (170 + 30) uisec for the al1 state, but it was necessary to assume a Maxwellian velocity distribution. However, the work of J. C. Pearl (1970) demonstrated that the velocity distribution after electron impact is often not Maxwellian. The techniques presented in this thesis overcome this difficulty: the spatial decay method uses a measured velocity distribution and the TOF method does not depend on the velocity distribution at all. On the basis of the analysis of the N2 experimental data and of the computer-simulated data, it appears that the TOF method presented here is capable of yielding more accurate results that the method employed by Olmsted, Newton 62

63 and Street (1965) in which the lifetime of (120 + 50) usec was estimated from the excitation function data taken at two distances. Borst and Zipf (1971) used a TOF method to measure the lifetime of the a l state. They recorded two TOF spectra: one spectrum was taken with low energy electrons exciting just the a ll state, while the other spectrum was taken with higher energy electrons exciting both:;the A3f and alT states. Then by assuming that the kinematics of the electron - molecule collision is the same for each TOF spectrum, they measured a lifetime of (115 ~ 20) isec by attributing the difference in shape of the two TOF spectra to the decay of the a l state. This assumption of unchanging kinematics is a good one for their particular geometry, but could be a very poor assumption in other experimental situations (see J. C. Pearl, 1970). Furthermore, their method requires that a long-lived state can be excited and the TOF spectrum recorded while the short-lived state remains unexcited, which can be difficult for an electron gun of modest energy resolution (for example, helium has metastable states separated by only.8 eV). The TOF technique presented in this thesis is not limited by the kinematical assumption and does not require that the long-lived state be individually excited.

64 6.2 Present Experiment 6.2.1 Data The analyzed data falls into two categories: i) 10 eV data involving the lifetime of the al T state and ii) 22 eV data involving the composite lifetime of the al1 and the E3' states. The 22 eV data consists of seven TOF runs and seven spatial decays. The lifetime of approximately 157 jsec as found by techniques I and III is assigned to a composite of the a TV and the E3' states on the basis of excitation function measurements. This is in good agreement with the work of Borst and Zipf (1971): they found a composite lifetime of 154 usec when 12.2 eV electrons were used to excite N2. The TOF data is also analyzed by technique II indicating a lifetime for the a lt state in the region of 105 isec. The 10 eV data consists of seven TOF runs retained for final analysis with an additional six runs supplying supportive results. The lifetime of 106 jsec as found by technique III is assigned to the al l state on the basis of excitation function measurements. The 106 usec is also confirmed by analysis with technique II. 6.2.2 Errors and Difficulties There are several experimental uncertainties. The electron gun-detector separation is uncertain (+.5 em) because of the finite lengths of the interaction region and detector

65 cone. The electron gun pulse width (10 usec) and the multichannel bin width (10 jsec) make any time calibration uncertain. In addition to these experimental uncertainties, the histogram displaying the results of the lifetime calculation (figure 5.3b) shows that there is some statistical uncertainty. A calculation of the standard deviation of the mean is very difficult because of problems such as i) weighing the result of each lifetime calculation (a TOF spectrum can be involved in more than one calculation) and ii) assigning the error resulting from the least squares fittings The standard deviation of the mean was not found, but an estimate for the limit of the error is + 35 isec. The major difficulty in this experiment was the extremely low detector signal when using 10 eV electrons. As can be seen from the excitation function for N2 (figure 4.3), the detector signal at 10 eV was more than an order of magnitude lower than the signal at 22 eV. To continue this experiment it would be desirable to have an electron gun with better energy resolution and with improved long-term stability. With better resolution it would be easier to determine which states were being excited, and with improved stability it would be possible to integrate the TOF spectra over long periods of time. Another desirable modification would be to use a detector with a larger sensitive area so that more of the excited molecules in the beam could be counted.

66 6.3 Summary This thesis has presented spatial decay and TOF techniques for measuring the lifetime of a short-lived metastable state in a two-component beam. The TOF method overcomes difficulties present in other methods for measuring lifetimes: it does not require quenching of one of the metastable components, it does not require a knowledge of the metastable velocity distribution, and it does not require the long-lived metastable state to be individually excited. A generalization of the TOF technique can be used.in the analysis of a beam consisting of more than two components, These spatial decay and TOF methods were tested on a twocomponent, computer-simulated beam and on an experiment with molecular nitrogen. The lifetime of the a 17 state of N2 was found to be (106 + 35) Asec, in good agreement with recent measurements made by other workers using different techniques.

APPENDIX A ANALYSIS OF A THREE COMPONENT BEAM Assume the three-component beam described in section 2.3. The first component has an initial population Nl(V) and a lifetime T1, the second component has an initial population N2(V) and a lifetime T2, and the third component has an initial population N3(V) and an infinite lifetime. It is assumed that 71 is known from a previous measurement and we wish to measure T2. Then we have four unknowns N1, N2, N5, and T2 and we will need TOF spectra at four distances Xa Xb Xc, and Xd, where Xb a= X +aX, X + X, and Xd = X +AX. (A 1) b a C D b d c If we are going to measure T2, assuming T1 to be known, then consider a group of metastable molecules having a velocity V. At the four distances, this group has amplitudes (number of molecules per unit time) and times-of-arrival Pa Nl-eTa/]l + N2-*eTa/ 2 + N3 T Xa/V (A.2) Fb = Nl-e-Tb/1 + N2-e-Tb/12 + N3 Tb = Xb/V (A.3) 67

68 F' = N1 eTc/ l+ N2 e-c/' 2 + N T= X /V (A.4) C c c FP = N1 e-Td/l + N2 eTd/T2 + N3 Td = Xd/V (A.5) where the prime denotes a scaled amplitude. Equation A.1 implies Tb = Ta + T, Tc = Tb + T, and Td = Tc + T (A.6) where 6T = X/V. Substituting equation A.6 into equations A,2, A.3, A,4, and A.5, and subtracting pairs of equations to eliminate N3: F - Fb = Nle-eTa/l (l - e-6T/Tl) + N2.e-Ta/T2.(l - e T/2) (A.7) F - F = Ne-l'Ta/ e-T/T l e- -T/Tl) + N2.e-Ta/I2.e-eT/T2. ( - e- T/2) (A.8) c - Fd = Nl.e Ta/ 1 e -2' lT/t.. (1 T/1 ) + N2. e-T/t.e-2^T/2(1 - eT/2). (A.9) Rearranging equations A.7, A.8, and A.9 and subtracting pairs

69 of equations to eliminate N1: (F - F) (' - F').e4T/l = (a? - PF) - (F~ - Fc).e1^1 = a b b C (A.l) (A.10) N2e-Ta/T2. (1-e-T/l2) (1-exp [-sT/t2 + QT/T1]) (Fb - F) - (FP - FA).e/ 1 = (FF - F)- - F) eT/'l 1 (A.12) (F' - Ie) - (F - Fp) e^-T/1 e-T/'72 Then equation A.12 can be solved for: AT (F - Ft) - F) - e6T/'l a- a b c (F - F) - F- e-T/ 1 where OT = X.Ta/Xa. The lifetime of the second component maybe found as follows:

70 i) Measure the lifetime of the first component in the manner suggested in section 2.3 (by exciting just the first and third component and using the theory of section 2.2). ii) Take TOF spectra at distances Xa, Xb = Xa +X, Xc= Xa + 2bX, and Xd = Xa + 3.eX. iii) Amplitude scale these spectra. iv) Pick a time Ta, and find the times Tb T, and Td by using equation A.6. v) Find the scaled amplitudes Fa, Fb, F, and F cora cb d responding to the times in iv. vi) Use equation A.13 to find the lifetime T2 (knowing the lifetime Tl). This series of steps is carried out for various T, ay generating a series of values for the lifetime T2. Since these numbers should all be the same, an average can be taken. It appears that this method of TOP spectrum analysis can be generalized to a beam that has an arbitrary number of components. It would only be necessary to have at least as many TOF spectra as there are unknowns in the problem.

LIST OF REFERENCES Walter L. Borst and Edward C. Zipf, Phys. Rev. A3, 979 (1971). Denis P. Donnelly, John C. Pearl, Richard A. Heppner and Jens C. Zorn, Rev. Sci. Instr. 40, 1242 (1969). G. W. F. Drake, G. A. Victor, and A. Dalgarno,,Phys. Rev. 180, 25 (1969). Kurt Dressier, Can. J. Phys. 47, 547 (1969). R. E. Fox, W. M. Hickam, D. J. Grove and T. Kjeldass, Jr., Rev. Sci. Instr. 26, 1101 (19555. Robert S. Freund, J. Chem. Phys. 50, 3734 (1969a); J. Chem. Phys. 51, 1979 (1969b). E. S. Fry and W. L. Williams, Rev. Sci. Instr. 40, 1141 (1969). R. F. Holland, J. Chem. Phys. 51, 3940 (1969). M. L. Jeunehomme, Air Force Weapons Lab. Rept. AFWL-TR-66-143, March 1967. C. E. Johnson, Bull. APS 16, 533 (1971). William Lichten, J. Chem. Phys. 26, 306 (1957). Jon Mathews and R. L, Walker, Mathematical Methods of Physics, W. A. Benjamin, Inc., New York (1965). E. E. Muschlitz, Jr., Science 159, 599 (1968). John Olmsted III, Amos S. Newton, and K. Street, Jr., J. Chem. Phys. 42, 2321 (1965). A. S. Pearl, Phys. Rev. Letters 24, 703 (1970). J. C. Pearl, Ph.D. dissertation, "Velocity Distributions in Beams of Metastable Atoms excited by Electron Impact", University of Michigan, 1970; available from XeroxUniversity Microfilms, Inc., Ann Arbor, Michigan; J. C. Pearl, D. P. Donnelly, and J. C. Zorn, Phys. Letters 30A, 145 (1969). D, E. Shemansky, J. Chem. Phys. 51, 689 (1969a); J. Chem. Phys. 51, 5487 (1969b). R. S. Van Dyck, Jr., C,. E. Johnson, and H. A. Shugart, Phys. Rev. Letters 25, 1403 (1970). 71