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A two-dimensional Doppler broadened technique in positron annihilation
N U C L E A R I N S T R U M E N T S AND METHODS 153 (1978)
189-194 ; ~)
N O R T H - H O L L A N D PUBLISHING CO.
A TWO-DIMENSIONAL DOPPLER BROADENED TECHNIQUE IN POSITRON ANNIHILATION JACK R. MacDONALD*
Bell Laboratories, Murray Hill, New Jersey 07974, U.S.A. K. G, LYNN**
Brookhaven National Laboratory, Upton, New York 11973, U.S.A. R. A. BOlE and M. F. R.OBBINS
Bell Laboratories, Murray Hill, New Jersey 07974, U.S.A. Received 11 November 1977 A new two-dimensional positron annihilation technique has been developed which is capable of measuring positrons annihilating with deeply bound electrons. The technique features extremely low background and provides a v'2 improvement in resolution over standard Doppler broadening systems. A basic description of the system is given and preliminary results are shown.
1. Introduction The fate of positrons introduced into condensed matter and the variety of techniques used in the study of positron annihilation is well documented (see ref. 1 and references contained therein). In particular, observation of the Doppler shift of annihilation gamma rays from thermalized positrons provides detailed information about electron momentum distributions in materials. If positronium is formed, the information is of chemical interest. If a bound state is not formed and the positron comes into thermal equilibrium with the lattice, information is obtained about electron momenta both in the bulk and at defect sites2). The significant fraction of positrons introduced into a defect-free metal annihilate with conduction electrons. Inasmuch as positrons are strongly repelled by nuclei, the probability of annihilation with tightly bound (core) electrons is very small. The present system, with its low background feature, is particularly well suited to study annihilation with core electrons, both to investigate the fundamental annihilation processes and to gain quantitative information about defects in metals2). The following sections describe the technique and give illustrative results for positron annihilation in Cu, Be and AI as well as in benzene, where some of the positrons form positronium. A more complete de* Present address: Department of Physics, Universiiy of Guelph, Guelph, Ontario N1G 2WI, Canada. ** Research supported by the U.S. Department of Energy under Contract No. EY-76-C-02-0016,
scription of the results in AI, including theoretical estimates for the probability of annihilation for each electron shell, has been published elsewhere3).
2. The principle of the technique The essence of the present technique is to use two Ge(Li) detectors in colinear geometry to observe, in time coincidence, both quanta from an annihilation event. Given individual photon energies E1 and E2, the sum energy E T = E t + E 2 is equal to the total energy of the electron-positron system prior to annihilation; that is, E T : 2m 0 c 2 - E B , where m 0 is the electron rest mass, c the velocity of light and EB the binding energy of the electron and positron to the solid. In cases for which the positron binding energy is negligible, EB is simply the electron binding energy and the sum energy E~ is a signature of the electron state. The energy difference AE: E2-Et, is, for pc~Ev, given by AE~-e.p where p is the electron-positron momentum in the laboratory system and e is the velocity of the photon with energy E2. Thus a simultaneous measurement of E~ and E2 (or equivalent ET and AE) can provide information about the binding energy EB and momentum p of the electron-positron system. Fig. 1 illustrates, in pictorial fashion, an idealized projection in ET and AE of events for positrons annihilating in metals. At approximately ET= 2 m0c 2 and A E = 0 there is a sharp and intense central peak corresponding to annihilations
190
J.R. MACDONALD et al. +12
caused by incomplete charge collection in one of the two detectors. Compton events occur at a lower sum energy than is shown on this figure.
+10 +8 +6
3. Experimental
ET + 4 (keV) +2 2mOcZ -2 -4 -6 -8 -I0 -12
40 30 20
10 0 10 20 30 40 AE (keY)
Fig. 1. Schematic representation of a two dimensional ET vs A E spectrum. The elliptical area at E T = 2 m0 c2 centered at
AE= 0 represents annihilation events with conduction electrons. The hatched area (marked 1) illustrate where events would be found for annihilation with electrons bound by ~ 5 keV. The hatched area (marked 2) depicts annihilation with high momentum conduction electrons.
with conduction electrons4). The elliptical shape depicts the momentum distribution of the conduction electrons. The " h a t c h e d " area (marked 1), centered at ET = 2 mo c 2 - 5 keV, indicates what might be expected when positrons annihilate with electrons bound by 5 keV. The distribution of these events along the zlE axis is related to the momentum distribution of these bound electrons. The area (marked 2) at Ex = 2 mo c2 , which extends to large values of 3E, depicts annihilation with high momentum conduction electrons. These contributions are mainly attributable to deviations of the electron and positron wavefunctions from simple plane waves ~) which give rise to high momentum wavefunction components (HMC's) and corresponding events at ET = 2 mo c 2 extending to high momenta (large ,JE). In principle, the present technique permits the separation of high momentum events due to HMC and core electrons. The inherent energy resolution of the system does, however, cause a smearing in the spectra which makes this separation difficult. Finally, the "Vshaped" curve which extends above JET = 2 mo c 2 is due to a "piled-up" event in one detector in coincidence with a full energy (nominally 511 keV) event in the other detector. Similarly, the inverted "V-shaped" curve below E T = 2 mo c2 is largely
Annihilation gamma rays were observed with two Ge(Li) detectors with efficiencies of 10% and energy resolutions of approximately 1.15 keV for the 514 keV gamma ray of 85Sr. The electronic system (see block diagram of fig. 2) included a standard fast/slow coincidence system, pile-up rejection and gain stabilization on each detector channel, and pulse-height analysis and storage of individual and coincident (two-dimensional) energy spectra. Fast timing signals from each detector were obtained from timing filter amplifiers, processed by constant fraction discriminators and sent to a time to amplitude converter (TAC) to establish fast coincidences. Separate timing filter amplifier outputs were sent through low level discriminators to an event counting pile-up inspector which rejects the majority of those events contaminated by pulse pile-up. Single channel analysers (SCA) fed by amplified energy signals from each detector were used to establish individual energy windows from 400 keV to 600 keV and a third SCA fed by the TAC output selected real coincidences. Gated singles spectra were recorded for each detector and gains were digitally stabilized on the centroids of the 511 keV peaks. In addition, the sum energy E T and difference energy A E was formed digitally from the output of the ADC's and stored in a two-dimensional array of 128 by 256 channels. Samples were prepared by depositing approximately 50/~Ci of 68Ge as a thin film on one of the inside surfaces of a sandwich of well-annealed metal, an arrangement which minimized annihilation in the source itself. For the benzene sample, 68GEC14 w a s dissolved and the liquid was held in a plastic container. In all cases singles count rates were maintained at a low value of a few thousand counts per second to insure optimum energy resolution and spectral purity. Photopeak coincidence rates were approximately 100 events per second and total data accumulation times were typically 60-8O h. The energy response of the system was determined by a pseudo-coincidence technique using 514 keV gamma rays from a 85Sr source. Singles events in each detector were treated in pairs as though they were a coincidence event and the
T W O - D I M E N S I O N A L DOPPLER BROADENED T E C H N I Q U E
191
SAMPLE AND SOURCE (68 Ge)
Timing Filter Amp
Timing Filter
Pile-up Inspector
Const. Fraction Discriminator
Const. Fraction I
' ~ AMPLIFIER r : 3Fsec delay
"r
~
Discriminator
Amp
Discriminator
-~ Discriminator
I P.e-up I inspector
Stop
= O,Sp.sec
r
Bipolar
Slo
I
i
GATE
= O,Sp.sec Bipolar
r
= ~,Fsec
delay
C]
r
I ABOR_RT__ _L_LL
STAB'L'ZERI Comp°tori.01STA"IL' I ZERJADCLMCA "1 21 Fig. 2. Block diagram of the electronic configuration.
sum and difference energies were stored in a twodimensional array. The peak energy width in both sum and difference energy coordinates is a factor of ,/2 larger than that exhibited by either detector for 511 keV gamma rays, as the pseudo-coincidence events are uncorrelated. The gamma rays from a positron annihilation event, however, have Doppler shifts which are equal in magnitude but of opposite sign. Thus the observed Doppler effect is twice that obtained in a single Ge(Li) detector system and the effective energy (momentum) resolution is a factor of x/2 better in the two-detector system. In the standard one-detector system, counts due to either incomplete charge collection, ? rays, or piled-up events contribute a significant background which obscures Doppler-shifted data in regions a few keV below or above the dominant annihilation peak at 511 keV. Typically, the ratio of peak height to background level is of order 103 to 1 for a single detector and a 68Ge positron source. In the two-detector system, a peak to background ratio of better than 106 to 1 is obtained in the equivalent difference energy spectra. The magnitude and shape of the background are calculable
from individual detector responses and agree with the measured background from the pseudo-coincidence runs. The background varies slowly with the sum energy, being slightly higher at sum energies <2 m0c 2 than at sum energies > 2 m0c 2. (The use of a NaI detector in coincidence with a Ge(Li) detector will also give partially reduced backgroundS), but of course, does not give improved energy resolution or simultaneous total energy information.) The present technique using matched Ge(Li) detectors offers the further advantage over a single detector because the photopeaks are intrinsically symmetrical about ,dE= 0 in the difference energy spectra, thus permitting analysis and comparison of data on each side of ,dE = O. 4. Results and discussion
Fig. 3 is a photograph of an E T vs AE computer display for well-annealed Be. The vertical scale is the logarithm of the number of counts per channel, the energy dispersion in each coordinate is 0.4 keV/channel and the total number of counts is approximately 30 million. The dominant features illustrated in fig. 1 are clearly seen, particularly the intense central peak centered near ET-----2mo c2
192
J.R.
MACDONALD
et al.
>
2MOC2 I--
I.d
I
0
AE (keV) Fig. 3. Fhotograph of a two d i m e n s i o n a l logarithmic display o f tains approximately 30 million counts.
and " w i n g s " extending to values of AE~-20 keV. In order to easily extract momentum information from two-detector data, it is convenient to project such data as are seen in fig. 3 onto the d E axis, for a range of sum energies ET appropriate to the electron binding energies of a given material. For example, fig. 4 shows such projections for annihilation of positrons in Cu, Be, AI and benzene and for pseudo-coincidence data using aSSSr source. The range of Ev for Be, 85Sr and benzene is (2 mo c 2 - 1 keV)
E T vs AE for positron annihilation in Be. The s p e c t r u m con-
dE = 1 keY - dO = 1.96 mrad. The raw data of fig. 4 for Cu, Be, AI and benzene are included to show the response of the system for different momentum distributions and the sensitivity at large momenta. The effect of deconvo!uting the Doppler shift data for AI using the measured response function is shown in fig. 5 together with the angular correlation data obtained by Haut@irvi 6) with an angular resolution of 1 mrad. Only positive values of AE are shown as an equivalent angular scale. An iterative deconvolution procedure, similar to that of van Cittert 7) and WertheimS), was applied without smoothing and without assuming a functional form for either spectrum. These results have previously been compared to theoretical calculations of annihilation probabilities with electrons in specific inner shells3). As previously mentioned in this paper and as illustrated in fig. 1, annihilation with inner shell
TWO-DIMENSIONAL
DOPPLER
BROADENED
193
TECItNIQUE
Conclusion The technique described in this paper offers unique possibilities for exploring positron annihilation at high center-of-mass momentum, largely due to the absence of background events in energy regions of interestg). The improved energy resolution, relative to the standard one-dimensional Doppler broadening technique, might be of particular interest in selected circumstances although a price is clearly paid in data accumulation rates. It should be noted that count rates in the experiments described herein have been purposely maintained at extremely low values in order to demonstrate the feasibility of ;he technique under optimum conditions. In subsequent experiments, coincident photopeak rates of 10 3 per second have 5.
L [71
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o
A + X
1 ff N < 0
z
.< r.l
10'-
b.. Z 0 ~
10:'
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+
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.....................
107 _
I
~,
~
I
I
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ANNEALED
-30
-20
-I0
0
10
20
iO ( = -
Fig. 4. Projections of data onto the ,dE axis for events whose sum energy lies close to 2 mo C2 (see text), for annihilation in Cu Be, AI and benzene. A pseudo-coincidence 85Sr spectrum is shown to illustrate the system response. These one-dimensional spectra have been shifted in the vertical scale for ease of comparison.
I
AI
o DECONVOLUTED DOPPLER BROADENING DATA • ANGULAR CORRELATION DATA (RESOLUTION=[.O0 mred)
30
DIFERENCE ENERGY (KEY)
I
E
o --
_ 105
o
0
\
o
o
electrons is characterized by a sum energy ET = 2 m0 c 2 decreased by an amount equal to the binding energy of the electrons4). This effect is best observed by projecting the two-dimensional ET vs AE data onto the ET axis for a given range of dE. For example, fig. 6 shows a spectrum of counts vs Es for well-annealed copper for all events with AE between 19 and 23 keV. This range of AE largely excludes annihilations with conduction and d-band electrons but should include annihilations with 2s, 2p, 3s and 3p core electrons with binding energies of approximately 1.10, 0.94, 0.12 and 0.07 keV respectively. The data indicated by open circles exhibit an energy centroid of (210+_30)eV less than 2mo c2. The solid curve of fig. 6 shows a projection from the Cu data for AE= 8 keV (for this value of AE the sum energy should be 2 m0 c2). Core annihilation is in clear evidence as indicated by the observed deficit in total energy.
%
%
5~ 104
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oo oo
N
%
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%
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O
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102 e ODD
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io
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I 20
I
~
50 40 8 (tared)
I
?
50
60
70
Fig. 5. A comparison of angular correlation and deconvoluted Doppler broadening data for AI. The Doppler data is a AE projection (AE= 1 keV is equivalent to ,dO= 1.96 mrad) which has been deconvoluted using the measured 85Sr response. The angular correlation data is from Haut@irvi6).
194
J.R. MACDONALD et al. [
I
i
i
I
¢~Cu 19 k e V ~ A E ~<2 3 keY 800
600 Iz
o
400
'--
200
annihilation, this aspect of the technique has not yet been fully exploited. A full two-dimensional deconvolution procedure is presently being implemented, although in many cases, the data as taken establish reasonable limits on annihilation rates with core electrons. Indeed, if detailed total energy information is not required, the technique can be appreciably simplified by storing only the one-dimensional AE spectra for a range of sum energy ET which can be determined by simple logic circuitry. Such a procedure, presently being developed, eliminates the need for storage of large twodimensional arrays while preserving the low background and good energy resolution features of the system. The authors wish to thank W. L. Brown for his many contributions to this work.
-4
-7'
2m0c2
+2
+4
E T (keV) Fig. 6. A projection of two dimensional data for Cu onto the E T axis for events with AE in the range 19 to 23 keV. The energy centroid of the peak is found to be (210_+ 30)eV below 2 m 0 c 2 as a result of annihilation with core electrons. The solid curve is a similar projection for zJE= 8 keV for which the sum energy centroid is at 2 m 0 (.2. This curve has been shifted down in energy by 210 eV and normalized to the peak height.
been achieved without significant energy resolution or pulse pile-up Although shifts in total energy served and can be unequivocally
deterioration of effects. have been obrelated to core
References l) R. N. West, Adv. Phys. 22 (1973) 263. 2) A. Seeger, J. Phys. F 3 (1973) 248. 3) K. G. Lynn, J. R. MacDonald, R. A. Boie, L. C. Feldman, J. D. Gabbe, M. F. Robbins, E. Bonderup and J. Golovchenko, Phys. Rev. Lett. 38 (1977) 241 ; see also, J. R. MacDonald, R. A. Boie, L. C. Feldman, M. F. Robbins, P. Mauger and K. G. Lynn, Bull. Am. Phys. Soc. 20 (1975) 580; and R. Douglas, private communication. 4) The difference between the positron and electron work function can usually be neglected. 5) K. G. Lynn and A. N. Goland, Sol. St. Comm. 18 (1976) 1599. 6) P. Hautoj/irvi, Sol. St. Commun. 11 (1972) 1049. 7) P. H. van Cittert, Z. Physik 69 (1931) 239. s) G. K. Wertheim, J. Electron Spectrosc. 6 (1975) 239. 9) W. L. Brown, M. F. Robbins, R, A. Boie and K, G. Lynn, Bull. Am. Phys. Soc. 22 (1977) 440.
189-194 ; ~)
N O R T H - H O L L A N D PUBLISHING CO.
A TWO-DIMENSIONAL DOPPLER BROADENED TECHNIQUE IN POSITRON ANNIHILATION JACK R. MacDONALD*
Bell Laboratories, Murray Hill, New Jersey 07974, U.S.A. K. G, LYNN**
Brookhaven National Laboratory, Upton, New York 11973, U.S.A. R. A. BOlE and M. F. R.OBBINS
Bell Laboratories, Murray Hill, New Jersey 07974, U.S.A. Received 11 November 1977 A new two-dimensional positron annihilation technique has been developed which is capable of measuring positrons annihilating with deeply bound electrons. The technique features extremely low background and provides a v'2 improvement in resolution over standard Doppler broadening systems. A basic description of the system is given and preliminary results are shown.
1. Introduction The fate of positrons introduced into condensed matter and the variety of techniques used in the study of positron annihilation is well documented (see ref. 1 and references contained therein). In particular, observation of the Doppler shift of annihilation gamma rays from thermalized positrons provides detailed information about electron momentum distributions in materials. If positronium is formed, the information is of chemical interest. If a bound state is not formed and the positron comes into thermal equilibrium with the lattice, information is obtained about electron momenta both in the bulk and at defect sites2). The significant fraction of positrons introduced into a defect-free metal annihilate with conduction electrons. Inasmuch as positrons are strongly repelled by nuclei, the probability of annihilation with tightly bound (core) electrons is very small. The present system, with its low background feature, is particularly well suited to study annihilation with core electrons, both to investigate the fundamental annihilation processes and to gain quantitative information about defects in metals2). The following sections describe the technique and give illustrative results for positron annihilation in Cu, Be and AI as well as in benzene, where some of the positrons form positronium. A more complete de* Present address: Department of Physics, Universiiy of Guelph, Guelph, Ontario N1G 2WI, Canada. ** Research supported by the U.S. Department of Energy under Contract No. EY-76-C-02-0016,
scription of the results in AI, including theoretical estimates for the probability of annihilation for each electron shell, has been published elsewhere3).
2. The principle of the technique The essence of the present technique is to use two Ge(Li) detectors in colinear geometry to observe, in time coincidence, both quanta from an annihilation event. Given individual photon energies E1 and E2, the sum energy E T = E t + E 2 is equal to the total energy of the electron-positron system prior to annihilation; that is, E T : 2m 0 c 2 - E B , where m 0 is the electron rest mass, c the velocity of light and EB the binding energy of the electron and positron to the solid. In cases for which the positron binding energy is negligible, EB is simply the electron binding energy and the sum energy E~ is a signature of the electron state. The energy difference AE: E2-Et, is, for pc~Ev, given by AE~-e.p where p is the electron-positron momentum in the laboratory system and e is the velocity of the photon with energy E2. Thus a simultaneous measurement of E~ and E2 (or equivalent ET and AE) can provide information about the binding energy EB and momentum p of the electron-positron system. Fig. 1 illustrates, in pictorial fashion, an idealized projection in ET and AE of events for positrons annihilating in metals. At approximately ET= 2 m0c 2 and A E = 0 there is a sharp and intense central peak corresponding to annihilations
190
J.R. MACDONALD et al. +12
caused by incomplete charge collection in one of the two detectors. Compton events occur at a lower sum energy than is shown on this figure.
+10 +8 +6
3. Experimental
ET + 4 (keV) +2 2mOcZ -2 -4 -6 -8 -I0 -12
40 30 20
10 0 10 20 30 40 AE (keY)
Fig. 1. Schematic representation of a two dimensional ET vs A E spectrum. The elliptical area at E T = 2 m0 c2 centered at
AE= 0 represents annihilation events with conduction electrons. The hatched area (marked 1) illustrate where events would be found for annihilation with electrons bound by ~ 5 keV. The hatched area (marked 2) depicts annihilation with high momentum conduction electrons.
with conduction electrons4). The elliptical shape depicts the momentum distribution of the conduction electrons. The " h a t c h e d " area (marked 1), centered at ET = 2 mo c 2 - 5 keV, indicates what might be expected when positrons annihilate with electrons bound by 5 keV. The distribution of these events along the zlE axis is related to the momentum distribution of these bound electrons. The area (marked 2) at Ex = 2 mo c2 , which extends to large values of 3E, depicts annihilation with high momentum conduction electrons. These contributions are mainly attributable to deviations of the electron and positron wavefunctions from simple plane waves ~) which give rise to high momentum wavefunction components (HMC's) and corresponding events at ET = 2 mo c 2 extending to high momenta (large ,JE). In principle, the present technique permits the separation of high momentum events due to HMC and core electrons. The inherent energy resolution of the system does, however, cause a smearing in the spectra which makes this separation difficult. Finally, the "Vshaped" curve which extends above JET = 2 mo c 2 is due to a "piled-up" event in one detector in coincidence with a full energy (nominally 511 keV) event in the other detector. Similarly, the inverted "V-shaped" curve below E T = 2 mo c2 is largely
Annihilation gamma rays were observed with two Ge(Li) detectors with efficiencies of 10% and energy resolutions of approximately 1.15 keV for the 514 keV gamma ray of 85Sr. The electronic system (see block diagram of fig. 2) included a standard fast/slow coincidence system, pile-up rejection and gain stabilization on each detector channel, and pulse-height analysis and storage of individual and coincident (two-dimensional) energy spectra. Fast timing signals from each detector were obtained from timing filter amplifiers, processed by constant fraction discriminators and sent to a time to amplitude converter (TAC) to establish fast coincidences. Separate timing filter amplifier outputs were sent through low level discriminators to an event counting pile-up inspector which rejects the majority of those events contaminated by pulse pile-up. Single channel analysers (SCA) fed by amplified energy signals from each detector were used to establish individual energy windows from 400 keV to 600 keV and a third SCA fed by the TAC output selected real coincidences. Gated singles spectra were recorded for each detector and gains were digitally stabilized on the centroids of the 511 keV peaks. In addition, the sum energy E T and difference energy A E was formed digitally from the output of the ADC's and stored in a two-dimensional array of 128 by 256 channels. Samples were prepared by depositing approximately 50/~Ci of 68Ge as a thin film on one of the inside surfaces of a sandwich of well-annealed metal, an arrangement which minimized annihilation in the source itself. For the benzene sample, 68GEC14 w a s dissolved and the liquid was held in a plastic container. In all cases singles count rates were maintained at a low value of a few thousand counts per second to insure optimum energy resolution and spectral purity. Photopeak coincidence rates were approximately 100 events per second and total data accumulation times were typically 60-8O h. The energy response of the system was determined by a pseudo-coincidence technique using 514 keV gamma rays from a 85Sr source. Singles events in each detector were treated in pairs as though they were a coincidence event and the
T W O - D I M E N S I O N A L DOPPLER BROADENED T E C H N I Q U E
191
SAMPLE AND SOURCE (68 Ge)
Timing Filter Amp
Timing Filter
Pile-up Inspector
Const. Fraction Discriminator
Const. Fraction I
' ~ AMPLIFIER r : 3Fsec delay
"r
~
Discriminator
Amp
Discriminator
-~ Discriminator
I P.e-up I inspector
Stop
= O,Sp.sec
r
Bipolar
Slo
I
i
GATE
= O,Sp.sec Bipolar
r
= ~,Fsec
delay
C]
r
I ABOR_RT__ _L_LL
STAB'L'ZERI Comp°tori.01STA"IL' I ZERJADCLMCA "1 21 Fig. 2. Block diagram of the electronic configuration.
sum and difference energies were stored in a twodimensional array. The peak energy width in both sum and difference energy coordinates is a factor of ,/2 larger than that exhibited by either detector for 511 keV gamma rays, as the pseudo-coincidence events are uncorrelated. The gamma rays from a positron annihilation event, however, have Doppler shifts which are equal in magnitude but of opposite sign. Thus the observed Doppler effect is twice that obtained in a single Ge(Li) detector system and the effective energy (momentum) resolution is a factor of x/2 better in the two-detector system. In the standard one-detector system, counts due to either incomplete charge collection, ? rays, or piled-up events contribute a significant background which obscures Doppler-shifted data in regions a few keV below or above the dominant annihilation peak at 511 keV. Typically, the ratio of peak height to background level is of order 103 to 1 for a single detector and a 68Ge positron source. In the two-detector system, a peak to background ratio of better than 106 to 1 is obtained in the equivalent difference energy spectra. The magnitude and shape of the background are calculable
from individual detector responses and agree with the measured background from the pseudo-coincidence runs. The background varies slowly with the sum energy, being slightly higher at sum energies <2 m0c 2 than at sum energies > 2 m0c 2. (The use of a NaI detector in coincidence with a Ge(Li) detector will also give partially reduced backgroundS), but of course, does not give improved energy resolution or simultaneous total energy information.) The present technique using matched Ge(Li) detectors offers the further advantage over a single detector because the photopeaks are intrinsically symmetrical about ,dE= 0 in the difference energy spectra, thus permitting analysis and comparison of data on each side of ,dE = O. 4. Results and discussion
Fig. 3 is a photograph of an E T vs AE computer display for well-annealed Be. The vertical scale is the logarithm of the number of counts per channel, the energy dispersion in each coordinate is 0.4 keV/channel and the total number of counts is approximately 30 million. The dominant features illustrated in fig. 1 are clearly seen, particularly the intense central peak centered near ET-----2mo c2
192
J.R.
MACDONALD
et al.
>
2MOC2 I--
I.d
I
0
AE (keV) Fig. 3. Fhotograph of a two d i m e n s i o n a l logarithmic display o f tains approximately 30 million counts.
and " w i n g s " extending to values of AE~-20 keV. In order to easily extract momentum information from two-detector data, it is convenient to project such data as are seen in fig. 3 onto the d E axis, for a range of sum energies ET appropriate to the electron binding energies of a given material. For example, fig. 4 shows such projections for annihilation of positrons in Cu, Be, AI and benzene and for pseudo-coincidence data using aSSSr source. The range of Ev for Be, 85Sr and benzene is (2 mo c 2 - 1 keV)
E T vs AE for positron annihilation in Be. The s p e c t r u m con-
dE = 1 keY - dO = 1.96 mrad. The raw data of fig. 4 for Cu, Be, AI and benzene are included to show the response of the system for different momentum distributions and the sensitivity at large momenta. The effect of deconvo!uting the Doppler shift data for AI using the measured response function is shown in fig. 5 together with the angular correlation data obtained by Haut@irvi 6) with an angular resolution of 1 mrad. Only positive values of AE are shown as an equivalent angular scale. An iterative deconvolution procedure, similar to that of van Cittert 7) and WertheimS), was applied without smoothing and without assuming a functional form for either spectrum. These results have previously been compared to theoretical calculations of annihilation probabilities with electrons in specific inner shells3). As previously mentioned in this paper and as illustrated in fig. 1, annihilation with inner shell
TWO-DIMENSIONAL
DOPPLER
BROADENED
193
TECItNIQUE
Conclusion The technique described in this paper offers unique possibilities for exploring positron annihilation at high center-of-mass momentum, largely due to the absence of background events in energy regions of interestg). The improved energy resolution, relative to the standard one-dimensional Doppler broadening technique, might be of particular interest in selected circumstances although a price is clearly paid in data accumulation rates. It should be noted that count rates in the experiments described herein have been purposely maintained at extremely low values in order to demonstrate the feasibility of ;he technique under optimum conditions. In subsequent experiments, coincident photopeak rates of 10 3 per second have 5.
L [71
1 0"
o
A + X
1 ff N < 0
z
.< r.l
10'-
b.. Z 0 ~
10:'
r~
+
1
+
+
~<
.....................
107 _
I
~,
~
I
I
1
ANNEALED
-30
-20
-I0
0
10
20
iO ( = -
Fig. 4. Projections of data onto the ,dE axis for events whose sum energy lies close to 2 mo C2 (see text), for annihilation in Cu Be, AI and benzene. A pseudo-coincidence 85Sr spectrum is shown to illustrate the system response. These one-dimensional spectra have been shifted in the vertical scale for ease of comparison.
I
AI
o DECONVOLUTED DOPPLER BROADENING DATA • ANGULAR CORRELATION DATA (RESOLUTION=[.O0 mred)
30
DIFERENCE ENERGY (KEY)
I
E
o --
_ 105
o
0
\
o
o
electrons is characterized by a sum energy ET = 2 m0 c 2 decreased by an amount equal to the binding energy of the electrons4). This effect is best observed by projecting the two-dimensional ET vs AE data onto the ET axis for a given range of dE. For example, fig. 6 shows a spectrum of counts vs Es for well-annealed copper for all events with AE between 19 and 23 keV. This range of AE largely excludes annihilations with conduction and d-band electrons but should include annihilations with 2s, 2p, 3s and 3p core electrons with binding energies of approximately 1.10, 0.94, 0.12 and 0.07 keV respectively. The data indicated by open circles exhibit an energy centroid of (210+_30)eV less than 2mo c2. The solid curve of fig. 6 shows a projection from the Cu data for AE= 8 keV (for this value of AE the sum energy should be 2 m0 c2). Core annihilation is in clear evidence as indicated by the observed deficit in total energy.
%
%
5~ 104
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Fig. 5. A comparison of angular correlation and deconvoluted Doppler broadening data for AI. The Doppler data is a AE projection (AE= 1 keV is equivalent to ,dO= 1.96 mrad) which has been deconvoluted using the measured 85Sr response. The angular correlation data is from Haut@irvi6).
194
J.R. MACDONALD et al. [
I
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i
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¢~Cu 19 k e V ~ A E ~<2 3 keY 800
600 Iz
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annihilation, this aspect of the technique has not yet been fully exploited. A full two-dimensional deconvolution procedure is presently being implemented, although in many cases, the data as taken establish reasonable limits on annihilation rates with core electrons. Indeed, if detailed total energy information is not required, the technique can be appreciably simplified by storing only the one-dimensional AE spectra for a range of sum energy ET which can be determined by simple logic circuitry. Such a procedure, presently being developed, eliminates the need for storage of large twodimensional arrays while preserving the low background and good energy resolution features of the system. The authors wish to thank W. L. Brown for his many contributions to this work.
-4
-7'
2m0c2
+2
+4
E T (keV) Fig. 6. A projection of two dimensional data for Cu onto the E T axis for events with AE in the range 19 to 23 keV. The energy centroid of the peak is found to be (210_+ 30)eV below 2 m 0 c 2 as a result of annihilation with core electrons. The solid curve is a similar projection for zJE= 8 keV for which the sum energy centroid is at 2 m 0 (.2. This curve has been shifted down in energy by 210 eV and normalized to the peak height.
been achieved without significant energy resolution or pulse pile-up Although shifts in total energy served and can be unequivocally
deterioration of effects. have been obrelated to core
References l) R. N. West, Adv. Phys. 22 (1973) 263. 2) A. Seeger, J. Phys. F 3 (1973) 248. 3) K. G. Lynn, J. R. MacDonald, R. A. Boie, L. C. Feldman, J. D. Gabbe, M. F. Robbins, E. Bonderup and J. Golovchenko, Phys. Rev. Lett. 38 (1977) 241 ; see also, J. R. MacDonald, R. A. Boie, L. C. Feldman, M. F. Robbins, P. Mauger and K. G. Lynn, Bull. Am. Phys. Soc. 20 (1975) 580; and R. Douglas, private communication. 4) The difference between the positron and electron work function can usually be neglected. 5) K. G. Lynn and A. N. Goland, Sol. St. Comm. 18 (1976) 1599. 6) P. Hautoj/irvi, Sol. St. Commun. 11 (1972) 1049. 7) P. H. van Cittert, Z. Physik 69 (1931) 239. s) G. K. Wertheim, J. Electron Spectrosc. 6 (1975) 239. 9) W. L. Brown, M. F. Robbins, R, A. Boie and K, G. Lynn, Bull. Am. Phys. Soc. 22 (1977) 440.