Qualitative Modification of the High Energy Atomic Photoionization Cross Section

Abstract

It is demonstrated that the nonrelativistic high energy $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\infty}$ behavior of the photoionization cross section of an $\mathrm{nl}$ atomic subshell, ${\ensuremath{\sigma}}_{\mathrm{nl}}(\ensuremath{\omega})$, for $l>0$ is independent of $l$ and is given by ${\ensuremath{\sigma}}_{\mathrm{nl}}(\ensuremath{\omega})\ensuremath{\sim}1/{\ensuremath{\omega}}^{9/2}$, rather than the previously generally accepted ${\ensuremath{\sigma}}_{\mathrm{nl}}(\ensuremath{\omega})\ensuremath{\sim}1/{\ensuremath{\omega}}^{l+7/2}$. Furthermore, for $l\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$, although the exponent does not change, the coefficient is significantly altered. This modification of ${\ensuremath{\sigma}}_{\mathrm{nl}}(\ensuremath{\omega})$ is due to the interchannel interaction between $\mathrm{ns}$ photoionization channels and $l\ensuremath{\ne}0$ channels in the atom. As a result, for the photoionization of $l\ensuremath{\ne}0$ electrons, the single-particle approximation is never correct in the $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. This has important consequences for sum rule calculations.