12/25/2023 0 Comments Compton scatteringThe aforementioned atomic binding effects and electron pre-collision motion make the IA results significantly different from FEA results. Therefore, the DDCS of the Compton scattering process is achieved through a summation of the scattering probability for all possible momentum eigenstates Many-body interactions and interference terms between electrons with different momentum eigenstates ( | p 〉 and | p ′ 〉) in the dynamical process of Compton scattering are omitted for simplicity. In this way, electron momentum eigenstate | p 〉 scattered with incident photon γ independently as free electrons. This scattering process is too quick to be disturbed by other electrons. In the Compton scattering process, suppose electron in momentum eigenstate | p 〉 is scattered with incoming photon γ very rapidly, like an impulse acting on the electron. In principle, the momentum distribution for bound electrons is determined by ground state wavefunctions in atomic or molecular systems. Because of atomic binding and electrons many-body interactions, the bound electrons in atomic and molecular systems have a momentum distribution ρ ( p ) when moving around atomic or molecular nuclei. The basic starting point of IA approach can be shown in the following way. In the impulse approximation (IA) method, the atomic binding effects are effectively considered, and the electron pre-collision motions around atomic nuclei are also included. Recently, there are many studies in which electronic structures and properties (include electron interactions, electron correlations, electron momentum distributions, band structures and fermi surfaces) are investigated through Compton profile and scattering function. They can offer opportunities to learn the electronic structure and properties of target materials from Compton scattering process. ![]() The Compton profile J ( p z ) and scattering function S F ( ω i, θ ) provide a bridge between Compton scattering and interdisciplinary studies in many branches of science. On the other hand, they can also be predicted by theoretical ab initio calculations in atomic, molecular, and condensed matter physics. On the one hand, J ( p z ) and S F ( ω i, θ ) can be measured from Compton scattering experiments with high precision. Same as Compton profile J ( p z ), the scattering function S F ( ω i, θ ) can also reflect the electronic properties of target materials. This kind of approach, in which the angular distribution of Compton scattering is given by Equation ( 4), is called the incoherent scattering function or incoherent scattering factor (ISF) approach. In other words, scattering function S F ( ω i, θ ) can also be calculated by other methods, such as the nonrelativistic Waller-Hartree theory. It should be mentioned that apart from IA, there are other approaches which can give the same results in Equation ( 4). Here, d σ / d Ω f FEA is the angular distribution calculated in FEA approach as shown in Equation ( 1), and the correction factor S F ( ω i, θ ) is called the scattering function. ![]() It is worth noting that in the IA approach, all the many-body effects in atomic and molecular systems in Compton scattering processes are incorporated into Compton profiles J ( p z ). In actual ab initio calculations, the Compton profile J ( p z ) can be obtained using the nonrelativistic Hartree–Fock theory (HF), the relativistic Dirac–Hartree–Fock theory (DHF), and the density functional theory (DFT). It can be determined from theoretical calculations and experimental measurements. The Compton profile can reflect electronic structures, physical and chemical properties of target materials. The factor J ( p z ), which is known as the Compton profile, is related to the momentum distributions of bound electrons in the atomic or molecular systems. In Equation ( 3), Y IA is a factor dependent on kinematical and dynamical properties of atomic Compton scattering, and irrelevant to the electronic structure of target materials. Where Ω f is the solid angle for final state outgoing photon.
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