engleski

Validity of impulse approximation for the description of Compton scattering

Impulse approximation (IA) is commonly used in the description of Compton scattering from atoms, the inelastic scattering of a photon in which an electron is ejected. In IA it is assumed that scattering from bound electrons can be described as scattering from a momentum distribution $\rho ({; ; \bf p}; ; )$ of free electrons, where $\rho ({; ; \bf p}; ; )=\vert \Psi({; ; \bf p}; ; )\vert^2$ and $\Psi({; ; \bf p}; ; )$ is the Fourier transform of the coordinate space electron wave function. The description of the Compton line [or Compton peak region of the doubly differential cross section (DDCS), which is just one of the three main features of the Compton spectrum (the others being infrared divergences and resonances)] has involved either IA, [or its relativistic version (RIA)] or independent particle approximations (IPA) (based on $A^2$ approximation or including a full S-matrix treatment). In IA the DDCS (scattered photon energy $\omega_{; ; f}; ; $ and angle $\Omega_{; ; f}; ; $ are observed while ejected electrons are not observed) for Compton scattering of a photon with ejection from a given subshell is a product of a simple kinematic factor $F_{; ; K}; ; $ and the Compton profile $J(p_{; ; z}; ; )$, and $p_{; ; z}; ; $ is the component of the initial state electron momentum in the direction of photon momentum transfer ${; ; \bf k}; ; $. The importance of IA is in this simple connection between the observable (DDCS) and the structure [$\rho (p)]$. We will discuss the validity of impulse approximation, with particular attention to the kinematic region in which the photon momentum transfer $k$ is not much larger than the average bound electron momentum $a$ of a given shell, $a/k < 1$. IA has been justified in the Compton peak region of the spectrum if $a/k<< 1$ in scattering. However, for the doubly differential cross section of photon-atom scattering (ejected electrons not observed) IA is commonly used, and viewed as adequate, while only requiring that $a/k < 1$. We will discuss how this comes about. Based on our recent findings we will discuss: 1) the validity of IA (and the relativistic version RIA) for doubly and triply differential cross sections ; 2) the asymmetry around the IA peak of the Compton profile, and 3) the contribution of the ${; ; \bf p}; ; \cdot{; ; \bf A}; ; $ interaction term (neglected in IA) in the peak region for $a/k\simeq 1$. We argue that the observed asymmetry of the Compton profile is to a large extent just a shift of the IA profile. We find that the ${; ; \bf p}; ; \cdot{; ; \bf A}; ; $ contribution to the peak region for $a/k\simeq 1$ is important only for scattering from high Z K--shells.

Compton scattering ; Impulse approximation

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