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

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

Compton backscattering of Hf K X-rays in germanium

The differential cross section, d^2sigma/d omega dE, for Compton scattering in germanium was measured by observing detector-to-detector scattering using the coincidence method. The experiment was performed at incident energies of 55.791 and 54.612 keV and scattering angle of J = 180°. The method applied is compared with the corresponding measurements in the singles mode, i.e. using the source-scatterer-detector assembly. We found that the coincidence method yields better results, especially in the region below the peak due to scattering on weakly bound electrons. However, it is restricted to the investigation of Compton scattering in detector materials. Experimental results are compared with theoretical calculations based on the "A^2-Born" and the impulse approximations

Detector-to-detector Compton backscattering in germanium at 59.5 keV

The differential cross section for Compton scattering d2σ/dΩdE in germanium (Z=32) was measured using the sensitive volume of a Ge detector as the scatterer and another Ge detector for detection of the scattered radiation, at an incident energy of 59.537 keV and a scattering angle of about 170°. The application of the coincidence technique and the requirement of a constant energy sum yield a clear spectrum in a broad energy range. Detailed analyses of the processes involved in the detector-to-detector scattering were made, including various double-scattering processes. Calculations show that bremsstrahlung of photoelectrons dominates at low energies, while all double-scattering processes weakly contribute to the coincidence rates. The influence of Compton-Rayleigh and Rayleigh-Compton scattering on Compton data is relatively stronger at high energy, while an approximate proportionality of Compton-Compton and single Compton spectra at scattering angles close to 180° was obtained, assuming the impulse approximation. Single and double Compton scattering on stationary electrons at 180° have been shown to produce photons of exactly the same energy. The measured differential cross sections for Compton scattering and results of calculations based on the impulse approximation are in fair agreement

Accurate determination of Compton backscattering in germanium at 86.5 keV on an absolute scale

The double-differential cross section d2σ/dΩdE for Compton backscattering in germanium was measured at the photon energy of 86.5 keV. The experimental setup with two high-purity germanium detectors operating in the coincidence mode was applied. A multiline radioactive source of ^155_63Eu was used as the source of photons. The Compton spectrum with a very small background was obtained. A fast cascade was found to little influence the data due to the 86.5 keV crossover transition. The contribution of a group of processes, which is described as double cross talk between the two detectors, was also studied and results of calculations show their weak intensity. The calculations of other processes were made as in our earlier papers. The values of d2σ/dΩdE were determined to an accuracy of better than 4% on an absolute scale in a broad energy region. The calculated values using the impulse approximation with hydrogenlike wave functions do not reproduce well the cross sections in some energy regions

Absolute-scale determination of bremsstrahlung following photoabsorption of incident x and γ rays

The spectrum of bremsstrahlung due to photoelectrons ejected by incident photons of energy 59.5 keV was measured on an absolute scale. A coincidence experimental setup with two high-purity germanium detectors was used. One detector served as the target as well as the detector of ejected electrons and another (second) detector served as the detector of bremsstrahlung radiation. The applied experimental method gives a very clean bremsstrahlung spectrum which can be reliably determined on an absolute scale in the low- and mid-energy range. Detailed processing of the data is presented, including calculations of all other processes that have also been recorded in the experiment. A simple theoretical model for the bremsstrahlung of photoelectrons in an infinitely thick target is applied and the results are compared with experimental values. Good agreement between the theoretical and experimental results has been obtained

Comptonovo raspršenje unatrag HF rendgenskog zračenja u germaniju

The differential cross section, d2σ/dΩdE, for Compton scattering in germanium was measured by observing detector-to-detector scattering using the coincidence method. The experiment was performed at incident energies of 55.791 and 54.612 keV and scattering angle of ϑ = 180◦ . The method applied is compared with the corresponding measurements in the singles mode, i.e. using the source-scattererdetector assembly. We found that the coincidence method yields better results, especially in the region below the peak due to scattering on weakly bound electrons. However, it is restricted to the investigation of Compton scattering in detector materials. Experimental results are compared with theoretical calculations based on the ”A2 -Born” and the impulse approximations.Diferencijalni udarni presjek, d2σ/dΩdE, za Comptonovo raspršenje unatrag mjerio se opažanjem raspršenja iz detektora u detektor i primjenom sudesne metode. Energije fotona bile su 55,791 keV i 54,612 keV i kut raspršenja ϑ = 180◦ . Nova metoda daje bolje rezultate od ranije u kojoj se rabio sustav izvor–raspršivač– detektor. Rezultati mjerenja se uspoređuju s teorijskima, proračunatim na osnovi ”A2 -Bornove” i na osnovi impulsne aproksimacije

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