A simple and efficient yet accurate calculation of the double-differential Compton cross section within the impulse approximation

It is shown that with proper values of the effective charge, the hydrogen-like (HL) wave functions are almost as good as the more sophisticated Hatree-Fock (HF) wave functions in calculations of the double-differential cross section of Compton scattering within the nonrelativistic impulse approximation (IA). Only a single value of the optimized effective charge for a given subshell of an atom is required for an accurate description of Compton spectra in a wide range of experimental conditions under which IA is a good approximation. That is demonstrated by results obtained for the K-shell of several atoms and for higher subshells in germanium. It has been found that a constant value of the optimal effective charge can be used as a criterion for the validity of IA, which is explained within the existing knowledge of IA. Simple analytical expressions for HL-Compton profiles have a compact form and are a much faster way to calculate the cross sections than using extensive tabulations of HF Compton profiles. These features can be useful in very extensive numerical calculations of Compton scattering in radiation physics, biomedicine, industry and in other practical applications

Jednostavno i učinkovito a ipak točno računanje dvostrukih diferencijalnih Comptonovih udarnih presjeka u impulsnoj aproksimaciji

It is shown that with proper values of the effective charge, the hydrogen-like (HL) wave functions are almost as good as the more sophisticated Hatree-Fock (HF) wave functions in calculations of the double-differential cross section of Compton scattering within the nonrelativistic impulse approximation (IA). Only a single value of the optimized effective charge for a given subshell of an atom is required for an accurate description of Compton spectra in a wide range of experimental conditions under which IA is a good approximation. That is demonstrated by results obtained for the K-shell of several atoms and for higher subshells in germanium. It has been found that a constant value of the optimal effective charge can be used as a criterion for the validity of IA, which is explained within the existing knowledge of IA. Simple analytical expressions for HL-Compton profiles have a compact form and are a much faster way to calculate the cross sections than using extensive tabulations of HF Compton profiles. These features can be useful in very extensive numerical calculations of Compton scattering in radiation physics, biomedicine, industry and in other practical applications.Pokazuje se kako se s određenim vrijednostima efektivnog naboja i vodikovih (H) valnih funkcija postižu dvostruko-diferencijalni presjeci za Comptonovo raspršenje u nerelativističkoj impulsnoj aproksimaciji (IA) koji su gotovo jednako dobri kao s profinjenim Hartree-Fockovim (HF) valnim funkcijama. Potrebna je samo jedna povoljna vrijednost efektivnog naboja za danu podljusku za točan opis Comptonovih spektara u širokom području eksperimentalnih uvjeta za koje vrijedi IA. To se prikazuje rezultatima za K-ljuske više atoma i za više podljuske germanija. Rezultati pokazuju da se stalnost povoljnog efektivnog naboja može uzeti kao uvjet punovažnosti IA, što se obrazlaže na osnovi poznavanja IA. Jednostavni analitički izrazi za H-Comptonove profile su sažeti i brži su način računanja udarnih presjeka nego upotreba velikih tablica za HF-Comptonove profile u tablicama F. Biggsa i dr., a dobivaju se pouzdani rezultati. Te su odlike pogodne u opsežnim numeričkim računima Comptonovog raspršenja