“Reading” the photoelectronβ-parameter spectrum in a resonance region

Abstract

The behavior of the dipole photoelectron angular distribution parameter ${\ensuremath{\beta}}_{nl}(\ensuremath{\omega})$ in the vicinity of autoionizing resonances is discussed. It is shown that from this behavior, surprisingly, many photoionization parameters that cannot be measured experimentally can be extracted. These are the energy positions and ordering of autoionizing resonance minima in the partial photoionization cross sections ${\ensuremath{\sigma}}_{l+1}$ and ${\ensuremath{\sigma}}_{l\ensuremath{-}1}$, the energies at which these two cross sections intersect, and signs and magnitudes of the $\mathrm{cos}({\ensuremath{\delta}}_{l+1}\ensuremath{-}{\ensuremath{\delta}}_{l\ensuremath{-}1})$ (${\ensuremath{\delta}}_{l\ifmmode\pm\else\textpm\fi{}1}$ being the phase shifts of the dipole photoionization amplitudes ${D}_{l\ifmmode\pm\else\textpm\fi{}1}$, respectively) through the autoionizing resonance energy region. Based on this, a deeper interpretation of such effects as the width-narrowing, width-fluctuating, and $q$-reversal in the ${\ensuremath{\beta}}_{nl}$ parameter spectrum in the autoionizing resonance energy region is given. As an example, calculated data for partial photoionization cross sections ${\ensuremath{\sigma}}_{3d\ensuremath{\rightarrow}f}$ and ${\ensuremath{\sigma}}_{3d\ensuremath{\rightarrow}p}$, and ${\ensuremath{\beta}}_{3d}$ parameters for $3d$ photoelectrons from ${\mathrm{Cr}}^{+}$ are presented.