Normal and Anomalous Photoelectric Absorption of X Rays in Crystals

The photoelectric absorption of x rays in atoms ($K-$, $L-$, and $M$-shell) is discussed for the nonrelativistic region, taking retardation effects into account. This is done by expanding the retardation factors in the transition probabilities in a Taylor series and this corresponds to an expansion in terms of electric multipoles. This expansion converges very rapidly and even the octupole transitions may be neglected. In the case of the anomalous absorption of x rays in perfect single crystals (Borrmann effect), the absorption cross sections become angular-dependent. This angular dependence allows in principle a direct experimental determination of the quadrupole term of the atomic photoelectric absorption cross section. Measurements by several authors indicate the existence of the electric quadrupole transitions.