The photoelectric absorption of γ-rays in heavy elements

Abstract

The photoelectric effect in hydrogen-like atoms has been treated by various authors, and the object of this paper is to co-ordinate the various results and to obtain values of σ, the absorption coefficient, which should be valid for all ranges of hv 0 , the energy of a quantum of the incident light, and for all values of Z, the atomic number of the atom. To this end we shall develop a method which is applicable in the range not previously examined—where Z is large and hv 0 ~ mc 2 , m being the mass of the electron and c the velocity of light. The problem may be stated briefly as follows. The nucleus of the atom is a heavy particle and may therefore be regarded as fixed at the origin of co-ordinates. We shall neglect exchange interaction between the atomic electrons, assuming that each K-electron may be treated separately. We may then consider the absorption by a simplified model consisting of a fixed nucleus and one K-electron, so that the results obtained have to be doubled to give the total absorption by the K-shell. The system is then perturbed by a beam of γ-rays travelling along the Z-axis, the perturbing potentials being given by A y = b 0 [ e 2π iv 0 ( t - z/c ) + e -2π iv 0 ( t - z/c ) ], A x = A z = 0, A 0 = 0.