Vacancy Cascade in the Reorganization of Krypton Ionized in an Inner Shell

Charge distributions of krypton ions following ionization in the $1s,2s$, or $2p$ shell are calculated under the assumption that reorganization occurs by successive steps in a vacancy cascade in which Auger and radiative transitions partake. These distributions compare favorably with experimental charge spectra arising from photo-ionization in the $K$ or $L$ shell (this paper), from electron capture in ${}_{}{}^{79}{}_{}{}^{}\mathrm{Kr}$, and from $\beta$ decay in ${}_{}{}^{85}{}_{}{}^{}\mathrm{Kr}$ (Snell and Pleasonton's earlier work). If the electron-shakeoff process is also incorporated in the calculation, good agreement with experiment is achieved. Possible applications of the vacancy-cascade model are briefly discussed for other modes of inner-shell ionization and for molecular and solid-state systems. Probabilities of electron shakeoff from any shell of krypton are calculated for photo-ionization in the $1s,2s$, or $2p$ shell, for ${\beta }^{+}$ and ${\beta }^{-}$ decay, and for Auger processes $1s-2p2p,2p-3p3p$, and $2p-3d3d$.