Theoretical and experimental Compton scattering cross sections at 1.12 MeV in the case of strongly bound K-shell electrons

Abstract

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...

Compton Shifting with Scattering Angle and Masses of Order 10-31kg To 1-0-27kg

“…Compton scattering energy photon ranges up to a few MeV; therefore, it is one of the best studies for firmly bound atomic K-shell electrons, and some experimental data range between 0.279 to 1.0002 more detail in [9]. The interaction of matter and energy of X-rays (less than 1MeV) has different types of scattering like coherent (Rayleigh) scattering, incoherent (Compton) scattering, and photoelectric absorption [10].…”