High-energy atomic photoelectric effect and bremsstrahlung.

Abstract

The relativistic photoionization cross sections from ${\mathrm{ns}}_{1/2}$,${\mathrm{np}}_{1/2}$,${\mathrm{np}}_{3/2}$ subshells, in the high-energy limit, have been analytically obtained. The main effects of screening enter through their effects on bound-state normalizations and energy levels. To estimate further effects, the screened potential at small distances is analytically described by a power-series expansion in the small distance r. For this high-energy-limit situation, both bound and continuum wave functions are expanded in power series for small r. The bound-free transition cross sections are then calculated analytically. Our results show that, beyond the known screening effect described by normalization factors, the screening effect enters the cross sections primarily through the change in bound-state energy and is otherwise not too sensitive to the expansion coefficients of the potential. The formulas contain no explicit n dependence. Comparisons with existing finite-energy numerical results indicate that ratios, though not absolute values, of cross sections attain their high-energy limits relatively early. Using Poincar\'e's theorem, all the photoionization results may be analytically continued to the high-frequency region of the spectrum of electron bremsstrahlung. Screening is dominated by the ``extra'' screening (namely, the screening which is not described by the known ``normalization screening'') except in the very tip region (a few eV above threshold), where normalization screening is much more important. The extension to positron bremsstrahlung is also discussed.