Volume 24B, number 6 P H Y S I C S L E T T E R S 20 March 1967

T H E D O P P L E R B R O A D E N I N G O F A N N I H I L A T I O N R A D I A T I O N

G. MURRAY Physics Department. Manchester University, England

Received 10 February 1967

The Doppler broadening of annihilation radiation has been observed using a Ge(Li) detector. It is pointed out that detailed information on the motion of the annihilating positron-electron pairs may readily be ob- tained using such detectors.

The object of this note is to point out that the c e n t r e - o f - m a s s motion of an annihilat ing p o s i - t r o n - e l e c t r o n pa i r may be studied eas i ly and di- r ec t ly by using a Ge(Li) de tec to r to m e a s u r e the Doppler broadening of the emi t t ed annihilat ion radiat ion. The Doppler broadening of annihilat ion radia t ion had p rev ious ly been obse rved in a high p r e c i s i o n curved c r y s t a l s p e c t r o m e t e r [1], and i n /3 - r ay s p e c t r o m e t e r s [2, 3] through the study of ex te rna l conver s ion e l ec t rons produced by the annihilat ion quanta. However , mos t of the in fo r - mat ion on the c e n t r e - o f - m a s s motion of the anni- hilating p o s i t r o n - e l e c t r o n sys tem has been de- duced f rom studies of the angular c o r r e l a t i o n of the emi t t ed annihi lat ion quanta [4, 5]. This work has been r ev i ewed by Wal lace [6] and by Green [7]. In genera l the co l lec t ion of data in such ex- p e r i m e n t s is somewhat t i m e - c o n s u m i n g and r e - qu i re s r e l a t i ve ly h igh -p rec i s i on apparatus . Here we p r e sen t data which indicate that comparab le r e su l t s can, in many ca se s , be obtained using Ge(Li) de tec to rs .

In an expe r imen t [8] to m e a s u r e the r e l a t i ve in tens i t i e s of the 720 and 1022 keV 7 r ays fol - lowing the pos i t ron decay of 10C the ef f ic iency of the 20 cm 3 Ge(Li) d e t e c t o r * used was m e a s u r e d as a function of energy using pa i r s of ~ r ays of known r e l a t i ve in tens i t ies . P u l s e s f r o m the de- t e c to r were ampl i f ied using a r o o m - t e m p e r a t u r e opera ted F E T p r e a m p l i f i e r des igned by J. H. Howes at Harwel l and a TC 200 Tennelec ampl i - f i e r , and r e c o r d e d using a Harwel l ana logue- to - digi tal conve r t e r coupled to a PDP 8 data p r o - c e s so r . The l ine widths of the 7 rays (f. w. h. m.) a re plot ted as a function of energy in fig. I. Val- ues obtained for 7 rays f rom long- l ived rad io -

* Supplied by Princeton Gamma Tech. Inc., Princeton, U.S.A.

268

4

3 0 (

' I ' I ' I ' I ' I " I

I , I i , I , i I I 5(30 700 90(3 1100 1300 1500

~" -Im.~y ENERGY (keV),

Fig. 1. Plot of peak width (f. w. h. m.) versus 7 ray energy The line is a least-squares fit to the data omit-

ting the anomalous annihilation radiation point. • Radioactive source x (p.n.} reaction

ac t ive sou rces (60Co, 22Na and 46Sc) a re shown as c i r c l e s and those obtained for 7 r ays , fol low- ing the pos i t ron decay of 10C, produced by a (p ,n ) reac t ion using the Harwel l tandem a c c e l e r a t o r , as c r o s s e s . The plot ted values of the l ine widths a re ave rages of eight separa te runs and the a t - t r ibuted e r r o r s were deduced f rom the sca t t e r of the individual runs about the means. Hollander [9] has sugges ted that the roughly l inea r dependence of the l ine width on energy indica tes the s t a t i s t i - cal na ture of the detect ion p rocess .

Of pa r t i cu l a r i n t e r e s t in fig. 1 is the anomo- lously high value of the l ine width of the annihi- la t ion quanta f rom both the 22Na source and the 10C source . We a t t r ibute this effect to the smear ing of the energy of the annihilat ion r ad i a - tion due to Doppler broadening a r i s ing f rom the motion of the c e n t r e - o f - m a s s of the annihilating p o s i t r o n - e l e c t r o n pair . The magnitude of the broadening of the annihilat ion peak, at half peak height, is [(5.4)2 - (4.3)21½ = 3.2 keV. It is i n t e r -

Volume 24B, number 6 P H Y S I C S L E T T E R S 20 March 1967

es t ing to compa re this value with the one ob- ta ined in the Chalk R ive r expe r imen t [3] where annihilat ion quanta w e r e ex te rna l ly conver ted in a u ran ium rad ia to r and the energy spec t rum of the conver s ion e l ec t rons studied in a f l - s p e c t r o - me te r . The obse rved l ine width of the convers ion e l ec t rons was 0.5% in momentum which is equiv- alent to 3.1 keV. The inherent reso lu t ion of the Chalk R i v e r in s t rumen t is negl ig ible in this con- text. The quali ty of a g r e e m e n t between the Chalk R i v e r work and the p r e s e n t work is probably to some extent for tu i tous s ince in the f o r m e r case the annihilat ion p r o c e s s o c c u r r e d p r inc ipa l ly in wate r and in the p r e sen t work in the gold backing of the target .

Annihilat ion takes p lace a f te r the pos i t ron has r e a c hed t he rma l ene rg i e s [10, 11] so it is the mo- tion of the par t i c ipa t ing e l ec t ron which leads to the Doppler effect. Deta i led informat ion on the e l ec t ron momenta could thus be obtained by r e - moving the contr ibut ion of the appropr ia te in- s t rumen ta l l ine shape f rom the obse rved shape of the annihilat ion radia t ion spec t rum. H e r e we have s imply made a c rude f i r s t - o r d e r ca lcula t ion of the ave rage energy of the e l ec t rons based on the half-width at half height due to Doppler broadening and obtain a value of 10.6 eV. The ca lcu la ted F e r m i energy in gold is 5.5 eV. The above value for the ave rage energy of the anni- hilat ing e l ec t rons is cons i s ten t with that deduced f rom the e l e c t r o n momentum d is t r ibu t ion in gold m e a s u r e d by S tewar t [5] and d i scussed by F e r r e l l [22].

The reso lu t ion of the p r e sen t sys tem (~ 4 keV) is comparab le in magnitude to the Doppler b road- nening of the annihi lat ion quanta and comes ma in - ly f rom e lec t ron ic noise in the p r e - a m p l i f i e r . The de tec to r and a m p l i f i e r s were chosen in this ex- p e r i m e n t to study r e l a t i ve ly high energy ~ rays (> 1 MeV) with opt imum counting ef f ic iency and not to study 511 keV ~ rays at high resolut ion. Recen t deve lopments in Ge(Li) de t ec to r s and the a s soc i a t ed e l ec t ron i c s [9, 13] sugges t that, for a spec i f ic expe r imen t such as the study of annihi-

la t ion radiat ion, an i m p r o v e m e n t in reso lu t ion of perhaps a fac tor of th ree over the p r e sen t f igure should be poss ib le . C lea r ly in some s tudies , for example the detect ion of the contr ibut ion of the pos i t ron motion to the Doppler broadening [14], the supe r io r reso lu t ion of the angular co r r e l a t i on method (eff ict ively ~ 250 eV) is s t i l l the d e t e r - mining fac tor in the choice of technique. The g rea t advantage of the use of Ge(Li) de tec to r s in this f ield is in the speed and exper imenta l ease with which s t a t i s t i ca l ly accura te data may be ob- tained. The annihilat ion radia t ion data r e p r e - sented by the c i r c l e in fig. 1 was r e c o r d e d in a total pe r iod of two hours using a weak 22Na source .

The author wishes to thank Drs . J. G. Jenkin and D. Robinson for the i r a s s i s t ance in the e x p e r - iment and Dr. J . M. F r e e m a n , P r o f e s s o r s W. E. Burcham, S. F. Edwards and J. C. Wil lmott for valuable d iscuss ions .

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