Abstract
The singularities of x-ray absorption or emission in metals are studied by a new "one-body" method, which describes the scattering of conduction electrons by the transient potential due to the deep hole. Using the linked-cluster theorem, the net transition rate in the time representation is expressed as the product of two factors: a one-electron transient Green's function , and the deep-level Green's function . These factors obey simple Dyson equations, which can be solved asymptotically by using Muskhelishvili's method. The x-ray transition rate is found to behave as , where is the frequency measured from the threshold, and an exponent involving the various phase shifts which describe scattering by the deep hole. may be >0 (infinite threshold) or <0 (zero threshold). The experimental implications of these results and their relation to the Friedel sum rule are briefly discussed.
DOI:https://doi.org/10.1103/PhysRev.178.1097
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