Inelastic scattering of X-rays and gamma rays

Kane, P.P.

doi:10.1016/j.radphyschem.2006.08.001

Cited by 15 publications

(10 citation statements)

References 63 publications

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“…The results predicted by ISF are valid when variable x and momentum transfer K become large, which has been confirmed by experiments [36,39,55]. However, there are limitations on the ISF approach.…”

Section: Incoherent Scattering Factor / Incoherent Scattering Functionsupporting

confidence: 62%

“…The same as Compton profile discussed in section III, the ISF could also reflects the property of target materials in Compton scattering process. Therefore, the ISF also opens up a bride between Compton scattering and interdisciplinary studies, offering an opportunity to learn the electronic structure and properties of target materials from Compton scattering process [27,55].…”

Section: Incoherent Scattering Factor / Incoherent Scattering Functionmentioning

confidence: 99%

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An Overview of the Compton Scattering Calculation

Qiao,

Wei,

Chen

2021

Preprint

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The Compton scattering process plays a significant role in atomic, condensed matter, nuclear physics and material science. It could provide us useful information on the electromagnetic interaction between light and matter. Several aspects of many-body physics, such us electronic structures, electron momentum distributions, many-body interactions between bound electrons, and other properties, can be revealed by virtue of Compton scattering experiments. In this work, we give an review on ab initio calculation of Compton scattering process. We shall focus on several approachesfree electron approximation (FEA), impulse approximation (IA), incoherent scattering function / incoherent scattering factor (ISF) and scattering matrix (SM) -and discuss the main features as well as the available ranges for each approach. Furthermore, in this work, we also briefly introduce the databases and applications for Compton scattering.

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Section: Incoherent Scattering Factor / Incoherent Scattering Functionsupporting

confidence: 62%

Section: Incoherent Scattering Factor / Incoherent Scattering Functionmentioning

confidence: 99%

An Overview of the Compton Scattering Calculation

Qiao,

Wei,

Chen

2021

Preprint

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“…See Refs. [15][16][17][18] for some examples of the many measurements and calculations done on Compton DDCS at high ω 1 . A value of θ = 180 • was chosen to maximize relativistic effects on the Compton peak magnitude.…”

Section: A Identification Of the Relativistic Contributions To The Cmentioning

confidence: 99%

“…In this approach the RIA formula for DDCS is given by Eq. (15) in [9]. Ribberfors derived an explicit expression for DDCS from RIA theory, starting with the relativistic S-matrix formulation of Jauch and Rohrlich for the Compton matrix element [10], namely,…”

Section: Introductionmentioning

confidence: 99%

Low-momentum-transfer nonrelativistic limit of the relativistic impulse approximation expression for Compton-scattering doubly differential cross sections and characterization of their relativistic contributions

LaJohn¹

2010

Phys. Rev. A

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The nonrelativistic (nr) impulse approximation (NRIA) expression for Compton-scattering doubly differential cross sections (DDCS) for inelastic photon scattering is recovered from the corresponding relativistic expression (RIA) of Ribberfors [Phys. Rev. B 12, 2067(1975] in the limit of low momentum transfer (q → 0), valid even at relativistic incident photon energies ω 1 > m provided that the average initial momentum of the ejected electron p i is not too high, that is, p i < m. This corresponds to a binding energy E b < 10 keV. This q → 0 nr limit is simultaneous with the approach of the scattering angle θ to 0 • (θ → 0 • ) around the Compton peak maximum. This explains the observation that it is possible to obtain an accurate Compton peak (CP) even when ω 1 > m using nr expressions when θ is small. For example, a 1% accuracy can be obtained when ω 1 = 1 MeV if θ < 20 • . However as ω 1 increases into the MeV range, the maximum θ at which an accurate Compton peak can be obtained from nr expressions approaches closer to zero, because the θ at which the relativistic shift of CP to higher energy is greatest, which starts at 180 • when ω 1 < 300 keV, begins to decrease, approaching zero even though the θ at which the relativistic increase in the CP magnitude remains greatest around θ = 180 • . The relativistic contribution to the prediction of Compton doubly differential cross sections (DDCS) is characterized in simple terms using Ribberfors further approximation to his full RIA expression. This factorable form is given by DDCS = KJ , where K is the kinematic factor and J the Compton profile. This form makes it possible to account for the relativistic shift of CP to higher energy and the increase in the CP magnitude as being due to the dependence of J (p min , ρ rel ) (where p min is the relativistic version of the z component of the momentum of the initial electron and ρ rel is the relativistic charge density) and K(p min ) on p min . This characterization approach was used as a guide for making the nr QED S-matrix expression for the Compton peak kinematically relativistic. Such modified nr expressions can be more readily applied to large systems than the fully relativistic version. L. A. LAJOHNPHYSICAL REVIEW A 81, 043404 (2010) taking the nr limit of the second-order perturbation relativistic QED S-matrix element to obtain expressions for DDCS and triply differential cross sections (TDCS), free of spurious singularities but having a separable A 2 and p · A form (not separable in the fully relativistic S-matrix expression). He then introduced relativistic kinematics, resulting in expressions that can be used to obtain reasonably accurate K-shell DDCS at all θ if ω 1 < 300 keV. At higher energies this expression only works at smaller scattering angles. This was illustrated by their example calculation in which ω 1 = 661 keV and θ 60 • .In NRIA theory, DDCS are proportional to the Compton profile, given bywhere p is the initial electron momentum. ρ nr (p) is the Fourier transform of the nr charge density ρ nr (r)...

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“…Compton scattering has been studied in a broad energy range (Kane, 1997). Recent second-order S-matrix relativistic calculations raise the question regarding the limitations of validity (Suric´et al, 1991) the user-friendly and widely available data based on the approximations, like the impulse approximation (IA) or incoherent scattering function (Hubbell, 1997).…”

Section: Introductionmentioning

confidence: 99%