Low-energyK-shell Compton scattering

Abstract

We calculate the photon energy distribution and the total cross section for the Compton scattering on the K electrons for the case when the photon wave length is much smaller than the size of the K shell. We show that at the energies of the order of the binding energy I of the K electron most part of the spectrum is governed by the low-energy behavior. The total cross section has a local maximum at the energies (1.5-2)I , reaching the values of the order 1 barn. At higher photon energies the spectrum curves have two maxima, corresponding to low-energy ejected photons or electrons. The cross sections in the whole region are calculated. The actual calculations are carried out employing the nonrelativistic Coulomb functions, thus being valid for the single-electron atoms. However, the main features of the analysis are expected to be true for many-electron ions and neutral atoms. The results of the present analysis may be useful in calculations of the laser-induced and laser-assisted processes.

Relativistic impulse approximation in Compton scattering

“…Some studies have indicated that the RIA approach can be realized by making leading order approximations for more advanced methods [15,51,52]. In the past few years, several approaches beyond the IA formulation have been investigated [7,[51][52][53][54][55][56][57][58][59][60]. These works, which mainly employed low-energy theorems and S-matrix formulation, revealed many remarkable and nontrivial aspects of Compton scatterings and have gained a significant interests in interdisciplinary studies.…”

Compton scattering energy spectrum for Si and Ge systems

“…In the present work, we have studied the energy spectrum of Compton scattering through FEA and RIA formulations. However, in the past few years, several approaches beyond FEA and RIA have already been investigated recently [53][54][55][56][57][58][59]. These researches, which mainly employing low-energy theorems and S-matrix formulation, have revealed many nontrivial properties of Compton scatterings and have attracted lots of interests in interdisciplinary studies.…”

The photon scattering cross-sections of atomic hydrogen

“…This problem was more recently tackled by Drukarev et al [12], who also used the work of Gavrila, and also an approximation to numerically avoid the infra-red divergence. Their total Compton cross-section does fall at low energies, however, their highest-energy cross-sections at 100 eV are mismatched by an order-of-magnitude against those in Ref.…”

“…The sum of the individual cross-sections σR(ω) is also shown as the solid line, and is seen to monotonically decrease. Raman (σ R ) Raman 1s-3d (σ r;3d ) Raman 1s-2s (σ r;2s ) 1s-2s (Sadeghpour) photon frequencies ω ′ [12],…”

“…where the largest emitted photon frequency ω ′ max = ω − |E i |, whilst the smallest ω ′ min = 0. The infra-red problem is that dσC dω diverges as ω ′ → 0, resulting in an infinite cross-section, and thus previous analytic calculations of Bergstrom et al [8] assumed ω ′ min = 10 eV, whilst Drukarev et al [12] assumed ω ′ min = 1 eV. We, instead, adopt the approximation in Eqn.…”