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

Abstract

Background: A double-$K$-electron capture is a rare nuclear-atomic process in which two $K$ electrons are captured simultaneously from the atomic shell. A ``hollow atom'' is created as a result of this process. In single-$K$-shell electron-capture decays, there is a small probability that the second electron in the $K$ shell is excited to an unoccupied level or can (mostly) be ejected to the continuum. In either case, a double vacancy is created in the $K$ shell. The relaxation of the double-$K$-shell vacancy, accompanied by the emission of two $K$-fluorescence photons, makes it possible to perform experimental studies of such rare processes with the large-volume proportional gas chamber.Purpose: The purpose of the present analysis is to estimate a double-$K$-shell vacancy creation probability per $K$-shell electron capture ${P}_{KK}$ of $^{81}\mathrm{Kr}$, as well as to measure the half-life of $^{78}\mathrm{Kr}$ relative to $2\ensuremath{\nu}2K$ capture.Method: Time-resolving current pulse from the large low-background proportional counter (LPC), filled with the krypton sample, was applied to detect triple coincidences of ``shaked'' electrons and two fluorescence photons.Results: 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 $^{81}\mathrm{Kr}$. The probability for this decay was found to be ${P}_{KK}=(5.7\ifmmode\pm\else\textpm\fi{}0.8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ with a systematic error of ${(\mathrm{\ensuremath{\Delta}}{P}_{KK})}_{\text{syst}}=\ifmmode\pm\else\textpm\fi{}0.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$. For the $^{78}\mathrm{Kr}(2\ensuremath{\nu}2K)$ decay, the comparative study of single- and double-capture decays allowed us to obtain the signal-to-background ratio up to 15/1. The half-life ${T}_{1/2}^{2\ensuremath{\nu}2K}(g.s.\ensuremath{\rightarrow}g.s.)=[1.{9}_{\ensuremath{-}0.7}^{+1.3}(\text{stat})\ifmmode\pm\else\textpm\fi{}0.3(\text{syst})]\ifmmode\times\else\texttimes\fi{}{10}^{22}\phantom{\rule{4pt}{0ex}}y$ 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 $^{78}\mathrm{Kr}$.Conclusions: The data collected during low background measurements using the LPC were analyzed to search the rare atomic and nuclear processes. We have determined ${P}_{KK}^{\text{exp}}$ for the $EC$ decay of $^{81}\mathrm{Kr}$, which are in satisfactory agreement with ${Z}^{\ensuremath{-}2}$ dependence of ${P}_{KK}$ predicted by Primakoff and Porter. This made possible to more accurately determine the background contribution in the energy region of our interest for the search for the $2K$ capture in $^{78}\mathrm{Kr}$. The general procedure of data analysis allowed us to determine the half-life of $^{78}\mathrm{Kr}$ relative to $2\ensuremath{\nu}2K$ transition with a greater statistical accuracy than in our previous works.