Probability of internal ionization duringβ+decay: Importance of the direct-collision mechanism

Abstract

A theory of the ionization of inner-shell electrons during ${\ensuremath{\beta}}^{+}$ decay is obtained by modifying a theory of inner-shell ionization during ${\ensuremath{\beta}}^{\ensuremath{-}}$ decay presented previously. The theory includes the contributions of both the shakeoff and direct-collision mechanisms and yields results whose relative accuracy is of order $Z\ensuremath{\alpha}$. Numerical results for the $K$-shell ionization probability are presented for several nuclides, including $^{58}\mathrm{Co}$, $^{64}\mathrm{Cu}$, and $^{65}\mathrm{Zn}$; they demonstrate that, contrary to the ${\ensuremath{\beta}}^{\ensuremath{-}}$ case, the direct-collision mechanism plays an essential role in inner-shell ionization during ${\ensuremath{\beta}}^{+}$ decay, confirming a conjecture by Law. When compared with the results of recent experiments, they are found to give significantly better agreement than do the results of previous theoretical work.