KCapture—Positron Ratios for First-Forbidden Transitions:Sb122,Rb84,I126,As74

Abstract

The theory for the relative probabilities of $K$-electron capture and of positron emission is reinvestigated in the cases of allowed and first-forbidden transitions. Effects of screening and of finite nuclear size are discussed and calculated. Careful comparison is made between theory and available experimental results for allowed and "unique" first-forbidden transitions; details and results of a new measurement for the transition ${\mathrm{Sb}}^{122}$→${\mathrm{Sn}}^{122}$ ($\Delta J=2\mathrm{}$, yes) are presented. Other types of first-forbidden transitions are analyzed in terms of the relative contributions of the various matrix elements which appear in the interaction combinations $S$, $T$, $P$ and $V$, $A$; and the experimental results for the $\Delta J=0\mathrm{}$, yes transitions in ${\mathrm{As}}^{74}$, ${\mathrm{Rb}}^{84}$, and ${\mathrm{I}}^{126}$ are discussed. Simple formulas are presented for the evaluation of the coefficients of the several matrix elements.