Influence of Screening on the Atomic Photoeffect

Abstract

The atomic photoeffect in a screened Coulomb field is considered. Numerical calculations of the differential and total cross sections for the $K$ and $L$ shells are given. Screening is introduced by including an exponential damping term in the potential. The bound-state wave function and the screening parameter $\lambda$ are determined by using a variational technique to fit the experimental ionization energy of the shell under consideration. The continuum electron is described by a partial-wave decomposition, and the interaction with the radiation field is treated in lowest order perturbation theory. A numerical program is developed to obtain the radial part of the continuum wave function. The cross sections are computed numerically and corrections to pure-Coulomb-field results are found to be small for the $K$ shell but significant for the $L$ shell. Results for $\lambda =0\mathrm{}$ are obtained and found to be in good agreement with previous theoretical work. This serves as a check on the accuracy of the numerical computations. A separate calculation using relativistic Hartree wave functions and potentials is carried out for mercury. Comparison of the results of this test calculation with the simplified exponential model indicates that the effects of screening are accounted for reasonably well by the model.