RelativisticL-Shell Photoeffect

Abstract

The expressions of the relativistic $L$ shell photoeffect differential and total cross sections, for the case of light elements, are established. Coulomb wave functions are used for the description of the electron states in the calculation of the matrix elements, but it is shown how the results should be corrected so as to take screening effects into consideration. For the final continuum state wave function of the ejected electron, whose exact analytic form is not known, the Born approximation is used. In the case of $L_{\mathrm{I}}$ subshell the calculation runs similarly to the one performed previously by the author for the $K$ shell. For the other two subshells new tedious trace evaluations have to be carried out. Thus, for the $L_{\mathrm{I}}$ subshell, cross sections correct to first order in $\alpha Z$ (inclusive) are determined, whereas in the case of the $L_{\mathrm{II}}$ and $L_{\mathrm{III}}$ subshells, only their zero-order approximation is calculated. The cross sections are discussed and compared. It is shown that they reduce in the nonrelativistic and extreme relativistic limits to results established by other means.