Comparative study of the double $K$-shell-vacancy production in single- and double-electron capture decay

We carried out the comparative study of the signal from the decay of double $K$-shell vacancy production that follows after single $K$-shell electron capture of ${}^{81}$Kr and double $K$-shell electron capture of ${}^{78}$Kr. The radiative decay of a the double $1s$ vacancy state was identified by detecting the triple coincidence of two $K$ X-rays and several Auger electrons in the $ECEC$-decay, or by detecting two $K$ X-rays and (Auger electrons + ejected $K$-shell electron) in the $EC$ decay. The number of $K$-shell vacancies per the $K$-electron capture, produced as a result of the shake-off process, has been measured for the decay of ${}^{81}$Kr. The probability for this decay was found to be $P_{KK}=(5.7\pm 0.8)\times {10}^{-5}$ with a systematic error of $(\mathrm{\Delta }{P}_{KK}{)}_{syst}=\pm 0.4\times {10}^{-5}$. For the ${}^{78}\mathrm{K}\mathrm{r}(2\nu 2K)$ decay, the comparative study of single- and double-capture decays allowed us to obtain the signal-to-background ratio to be 15/1. The half-life $T_{1/2}^{2\nu2K}(g.s. \rightarrow g.s.) = [1.9^{+1.3}_{-0.7}(stat)\pm0.3(syst)]\times 10^{22}$ y is determined from the analysis of data that have been accumulated over 782 days of live measurements in the experiment that used samples consisted of 170.6 g of ${}^{78}$Kr.