Analytic calculation of screened photoeffect cross sections

Using the results of an analytic perturbation theory for screened Coulomb wave functions, closed-form expressions are given for screened $K$- and $L$-shell photoeffect total cross sections in the nonrelativistic dipole approximation. The analytic results agree very well with numerical dipole calculations for the same potential. These nonrelativistic dipole results are then compared with the full relativistic (including retardation) screened calculations of Scofield. Because of strong cancellations between relativistic and multipole effects, the nonrelativistic dipole results can be shown to yield accurate predictions for the photoeffect for photon energies ranging from threshold to nearly 100 keV.