Compton scattering: Test of the double differential cross section in the relativistic impulse approximation

Reineking, A.; Wenskus, R.; Baumann, A.; Schaupp, D.; Rullhusen, P.; Smend, F.; Schumacher, M.

doi:10.1016/0375-9601(83)90773-9

Cited by 18 publications

(4 citation statements)

References 12 publications

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“…At the high-energy end of the spectrum, the experimental points for holmium at 115° are consistent with the A 2 approximation within 2 standard deviations while our results are higher by 3 or more standard deviations. At 45° for holmium these measurements, unlike those reported in whole atom Compton profile experiments [21], are much smaller than all of the theoretical predictions for the high-energy end of the spectrum. Because of large experimental errors attributed to bremsstrahlung the authors do not present results in the infrared regime.…”

Section: Compton Scattering Of Photons By Inner-shell Electronscontrasting

confidence: 61%

Compton scattering of photons by inner-shell electrons

et al. 1991

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We have developed an exact second-order S-matrix code for the relativistic numerical calculation of cross sections for Compton scattering of photons by bound electrons within the independent-particle approximation. We find good agreement with less exact treatments in regions where such theories are valid, recovering the impulse approximation and the soft-photon infrared divergence. We do not find agreement with an earlier calculation of Whittingham. We compare with recent scattering experiments in the regime Za(ha)i)~~EB, where we find that the impulse approximation is not adequate.PACS numbers: 32.80.CyWe have developed a code for calculating cross sections for Compton scattering of photons by bound electrons [1]. There has been considerable recent interest [2][3][4][5] in measuring the inelastic (Compton) scattering cross sections on bound atomic electrons, in circumstances in which the composite structure of the initial atomic state modifies the scattering from free particles. Accurate theoretical cross sections for Compton scattering by bound inner-shell electrons are needed as basic data with which experiments may be compared, to provide insight into the nature of the response of the composite system and to separate this process from others of experimental concern. Inelastic scattering from bound inner-shell electrons is important in astrophysical and laser plasmas where ions have only a few electrons remaining and in condensed-matter studies where an accurate knowledge of inner-shell electron Compton profiles permits their separation and so an accurate determination of the properties of valence electrons. The Compton scattering process is one of the few low-order photon-bound-electron interactions that has resisted a reasonably exact treatment. An accurate calculation of Compton scattering requires the evaluation of thousands of slowly converging integrals. Some of the spectra that we present here required several hours of time on a Cray Y-MP supercomputer; such calculations have only recently become feasible. Our approach is exact within the framework of the independent-particle approximation to second-order relativistic external-field quantum electrodynamics. Our calculations use spherically symmetric atomic potentials, both screened (self-consistent) and point Coulombic. We present comparisons with simpler, more approximate calculations, and with experiment. Differences from the widely used simpler approaches are often substantial.The difficulty of performing such calculations of Compton scattering in the past has led to various more approximate theoretical treatments of the process. In the nonrelativistic domain, the interaction Hamiltonian for the electron-photon system is [6] H mt = j e 2 A 2 -ep-A.In this regime, two common approximations are used. One approach that is most widely used is based on the first term (A 2 ) in the nonrelativistic Hamiltonian [7-9]. The other is based on the second or p* A term in the non-relativistic Hamiltonian [10]. The precise criterion of validity of these approaches ...

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Section: Compton Scattering Of Photons By Inner-shell Electronscontrasting

confidence: 61%

Compton scattering of photons by inner-shell electrons

et al. 1991

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“…Of the two, the impulse approximation has formerly been tested in a preceding paper [17] by comparison with an experiment and found to be in an overall agreement except for the high-energy part of the spectrum, where discrepancies of up to 50% have been observed. In the present paper it was our first intention to see whether or not this discrepancy could be overcome by using the relativistic form factor instead of the relativistic impulse approximation.…”

Section: Discussionmentioning

confidence: 99%

Relativistic double differential cross sections for Compton scattering by bound electrons: Test at low photon energies and predictions at intermediate photon energies

et al. 1985

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Cross section profiles d2a/df2dco ' for Compton scattering of photons by bound electrons are calculated for all subshells of the atom. Results obtained from the form factor approximation and from a relativistic version of the impulse approximation are compared with experimental data for Cu and Pb at a scattering angle of 0=145 ~ and a photon energy of 662keV. The impulse approximation proves to be superior to the form factor approximation and is used to predict cross section profiles for a primary energy of 50 MeV and different scattering angles and charge numbers. It is shown that only for the heaviest atoms and scattering angles below 0= 5 ~ there is a non-negligible contribution of Compton scattering to the elastic peak.

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“…Schumacher's group (Reineking et al 1983, Wenskus et al 1985) calculated double differential bound Compton scattering cross sections in the relativistic impulse aproximation using DFHS (Dirac-Hartree-Fock-Slater) wave functions. They found good agreement with their measurements (Schumacher 1971, Rullhusen and Schumacher 1976, Reineking et al 1983 of Compton scattering of 279 and 662 keV photons by Cu, Sn and Pb targets at the peak of the profiles. However, on the high-energy sides of their measured profiles they noted discrepancies which were only partly explained by second-order S-matrix calculations.…”

Section: S-matrix Incoherent Scattering Theorymentioning

confidence: 99%

An examination and assessment of available incoherent scattering s-matrix theory, also compton profile information, and their impact on photon attenuation coefficient compilations

Hubbell¹

1999

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The Klein-Nishina formulae for the differential and integral cross sections for Compton (or incoherent) scattering of x-ray photons from atomic electrons assume that the electrons are free (unbound) and at rest, which is a good approximation for photons of the order of 1 MeV or higher, particularly for low-Z target materials. The probability for dislodging bound electrons can be taken into account at least approximately by including an incoherent scattering function S(x,Z) in the differential Klein-Nishina formula. Currently available systematic theoretical tabulations of S(x,Z), where x is a momentum transfer variable dependent on the photon deflection angle and the photon incident energy do not use S-matrix theory with its claimed higher accuracy. The currently most widely-used S(x,Z) tables are non-relativistic. Recently (1998) Kahane has used the Ribberfors-Berggren relativistic treatment to compute systematic tables of S(x,Z). These new values of S(x,Z)have not yet been exploited for computing relativistic bound-electron incoherent scattering integrated cross sections a^, nor for triplet (pair production in the field of the atomic electrons) cross sections K e which also require S(x,Z) for their computation. The motion of the atomic electrons around the atomic nucleus gives rise to a Doppler broadening of the apparent energy of the incident photon, resulting in a corresponding broadening of the Compton "modified line" for a given deflection angle of the outgoing scattered photon. The shape of this broadened line is called the "Compton profile." One task of this report is to examine the usefulness and advantages, if any, of S-matrix theory in providing significantly more accurate values of photon interaction cross sections and attenuation coefficients. The other task of this report is to examine the available Compton profile literature and to explore what, if any, effect our knowledge of this line-broadening has on theoretical computations of photon incoherent scattering cross sections and total mass attenuation coefficients.

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Compton scattering: Test of the double differential cross section in the relativistic impulse approximation

Cited by 18 publications

References 12 publications

Compton scattering of photons by inner-shell electrons

Compton scattering of photons by inner-shell electrons

Relativistic double differential cross sections for Compton scattering by bound electrons: Test at low photon energies and predictions at intermediate photon energies

An examination and assessment of available incoherent scattering s-matrix theory, also compton profile information, and their impact on photon attenuation coefficient compilations

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