Analyses of the x-ray thresholds of Li, Na, Mg, and Al—a reply to comments by G. D. Mahan

Abstract

Criticisms of our work by Mahan are rebutted. Calculations of $d$- and $s$-wave dipole matrix elements, using precise Hartree-Fock core wave functions, are found to produce values of $d$ to $s$ intensity ratios an order of magnitude smaller than the values obtained by Mahan, who used approximate wave functions with unrealistically large core radii. Atomic calculations cited as supporting those approximate wave-function calculations refer to $2p\ensuremath{-}\mathrm{t}\mathrm{o}\ensuremath{-}3d$ transitions, not to the $2p\ensuremath{-}\mathrm{t}\mathrm{o}\ensuremath{-}3s$ transitions in question. Evaluation of the corrections to our ${L}_{2,3}$ edge analyses using Mahan's phase shifts reveals that the corrections lie well within our previously estimated uncertainties. The 2-eV energy gap (Stokes's shift) which the criticism has attributed to our phonon model is shown to occur only if lattice relaxation times (\ensuremath{\sim} ${10}^{\ensuremath{-}12}$ sec) are shorter than or comparable with Auger decay times (estimated by Mahan to be \ensuremath{\sim} 3 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}15}$ sec).