The coherent scattering of γ -rays by K electrons in heavy atoms - I. Method

Abstract
A method for evaluating transition amplitudes for bound electrons in second order in the effects of the radiation field is outlined. An example of the type of problem concerned is the coherent scattering of $\gamma $-rays by the K electrons in heavy atoms. The static field in which the electron moves is taken into account exactly; no expansion is made in its effects. In the usual perturbation theory this is equivalent to summing matrix elements over intermediate states which are solutions of the wave equation including the static potential. In the method presented here, however, the sum over radial eigenstates for a particular angular momentum of intermediate state is replaced by quadratures of the products of known functions with the solution of a pair of coupled inhomogeneous differential equations.

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