Me asure me nt s a re re po rt ed for th e diffe re ntial c ross sec tion s for Co mpt o n sca tt e rin g of 1.12 Me V ga mma rays by th e K-s he ll e lec tro ns of tin , tantalum, gold, and th o rium . A few di screpa nc ies be t ween approxim ate th eo reti ca l ca lc u lation s and th e ex perim e ntal res ult s for diffe re nt e ne rgies are point e d ou t. Th e nee d for an e xact re lati vis ti c ca lc ul a ti o n is indi ca te d.Key word s : Co mpton sca tt e rin g; diffe re nti a l c ross section ; e lectro n bindin g; ga mma rays; K-s he ll ; photon s .Th e Compton scatte rin g of ga mma rays by s tron gly bound atomic K-shell ele ctron s has bee n studi ed experimentally a t 0. [12]. W e hav e give n preliminary reports on similar measurements mad e with a zinc-65 so urce at an e ne rgy of 1.12 MeV [13J.Motz and Mi ssoni [3J s ugges ted that th e res ults for large momentum transfers ca n be unders tood within the fram e work of an impuls e approximation. Recentl y, a jus tifi cation [14] of thi s approximation within th e framework of nonrelativi sti c quantum mechani cs has been given. If the target elec tron momentum p mak es angles a and a' with the mom e nta TI and TI' of the incide nt a nd th e scattered ph otons respectively, the e ne rgy k of the photon scatter ed through a n angle () is giv en by eq (1).where ko is the incid e nt photon e nergy, f3 is the ratio of the initial electron velocity to the veloci t y of light and E is the sum of the res t e nergy and the kinetic e ne rgy T of the targe t electron. In view of the virial th eore m , a convenient measure of T is taken 2 to be the bindin g energy of th e elec tron. Unfortu nately , in th e work of lau c h and R o hrl;~h [15], there was a *Wnrk s upported in pari by a g ra nt from tli e Na tiona l Bureau of S ta nd ards. W as hin g ton . D.C. undf!rt he I'L-480 p r-u~rallllll e. ** Presc nt address: Ph ysics Department. Indian I nstit ute ufT ec h nulogy, Pow ai. Bomha y-76. In dia.1 Fi gures in bracke ts ind ica te th e lit era ture referen ces at th e e nd of this paper.t At:curdin g tu the virial th eorem , the a verage ki ne ti c c ncrgy of an e lec t run bou nd by t he attrac ti ve Co ulomb pot e nti al in a n a tom turn s ou t to be e qu a l 10 the negative of half th e average p(Iten ti a l ('nergy. The rrfo rc. the average kine tic e nergy is the nega t ive uf th e su m of th e po te ntial and th e kin e ti c ene rgies. Thus. t he kin e tic c nc '·gy ma y be put e qual t o t he bind ing en ergy o f 1he e lectron. mi s prinl SO that a appeared in th e de nominator instead of a'. Th e final resu lt for th e cross section ( du K ) is obtained in te rm s of an average , as in eq. dO tmp .(2).( du K)where cf> is th e angle bet wee n th e planes formed by th e pairs of vectors (TI , p ) and (TI ', p ) a nd th e relativi s ti c expression for du/ dO in th e case of a free but fast electron has been giv e n by l a uc h and Rohrli c h.In th e calc ulation of Motz and Misso ni for 0.662 MeV , th e misprinted formula with Ct in ste'ld o...
A study has been made of the Compton scattering of 1,12-MeV gamma rays by K-shell electrons of tin, tantalum, gold, lead, and thorium. K x rays of target atoms were detected in coincidence with the scattered gamma rays. A careful investigation of false coincidences has been carried out. The ratio der~/do. F of the Kshell electron cross section to the Compton cross section for a free electron at rest was determined at serveral angles between 25' and 120'. The cross-section ratio in the case of gold and thorium is less than 1 at 25', larger than 1 in the neighborhood of 90', and
II. EXPERIMENTAL DETAILSIn the present experiment, a fast-slow coincidence system was used with resolving times of 30 nsec and 2 p, sec, respectively. Pulse-height analysis of anode pulses from the y detector was made with the help of a 20-channel analyzer gated by the output of the coincidence circuit. The linearity of pulse height was checked not only through the singles spectra of the y rays of different energies but also through the spectra obtained in the coincidence mode. Annihilation quanta from a Na source, and 1.17-and 1.33-MeV y rays from a~Co source were used for the spectral measurements in the coincidence mode. The photopeaks obtained in the coincidence mode agreed 'with the positions of the corresponding peaks in the singles spectra. Therefore, useful linearity and gain stability checks could be made more frequently in the singles mode than would have been possible in the coincidence mode. If a check showed a pulseheight shift of more than 2%, the corresponding data were discarded.Pulse-height distributions of the scattered y rays were studied at 60' and 100' scattering angles.In each case, the pulse-height distribution of false events was determined and subtracted from the measured distribution in order to obtain the "true" distribution. In all cases, the chance coineidenee rate was less than 1% of the total rate and was considered negligible. figure. With the help of the response function of the detector, it is necessary to deconvolute the pulse-height distribution in order to obtain the energy distr ibution. The deconvolution procedure is outlined in the Appendix.
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