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

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 $2\nu 2K$ 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 $P_{KK}=(5.7\pm 0.8)\times {10}^{-5}$ with a systematic error of ${\left(\mathrm{\Delta }{P}_{KK}\right)}_{\text{syst}}=\pm 0.4\times {10}^{-5}$. For the ${}^{78}\mathrm{Kr}\left(2\nu 2K\right)$ 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 $T_{1/2}^{2\nu 2K}(g.s.\to g.s.)=[1.9_{-0.7}^{+1.3}\left(\text{stat}\right)\pm 0.3\left(\text{syst}\right)]\times {10}^{22}y$ 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 ${}^{78}\mathrm{Kr}$.

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 $Z^{-2}$ 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 $2\nu 2K$ transition with a greater statistical accuracy than in our previous works.

Figure 1

Schematic of the TEOP (left) and OEOP (right) transitions and the atomic-level-decay diagram for the initial $K$-shell two-hole state ${}^1\mathrm{S}_0$ (middle).

Figure 2

Examples of current pulses of two types of events: (a) a two-point event for photoabsorption of an 88-keV photon with simultaneous emission of a 12.6-keV characteristic photon Kr $K_{\alpha }$ and a photoelectron $E_{\mathrm{p}.\mathrm{e}.}=\gamma 88-K_{\alpha }\left(\mathrm{Kr}\right)=75.4$ keV; (b) three-point event with simultaneous emission of two characteristic x ray and electrons. ${\tau }_{\mathrm{aft}}$ is the duration of the electron drift from the cathode to the anode.

Figure 3

The distributions of the events in the LPC filled with depleted krypton with energies 10–16 keV $({}^{81}\mathrm{Kr}$, red curve) and the background events of detector in the energy region 20–80 keV (blue histogram).

Figure 4

Variations of relative coefficient gas gain $\left(K_{\text{gain}}\right)$ and the centroid ${\lambda }^{\mathrm{c}}\left(t\right)$ and ${\tau }_{\mathrm{aft}}^{\mathrm{c}}\left(t\right)$ distribution versus time in each of the three stages ($I$, II, and III) of measurement sample depleted krypton.

Figure 5

Variations of energy resolution FWHM of LPC versus time in ($I$, II, and III) stage, respectively.

Figure 6

(a) The pulse height spectra of (1) single-, (2) two-, and (3) three-point events that form the total analyzed pulse amplitude spectrum of the counter detecting both background and ${}^{81}\mathrm{Kr}$ decays. (b) The pulse height spectrum of the two-point events with one subpulses in the energy range $E=K_{\alpha }\left(\mathrm{Kr}\right)\pm \mathrm{\Delta }E=12.6\pm 1.9$ keV for the two filling samples of LPC: with krypton enriched in ${}^{78}\mathrm{Kr}$ (dark line) and with depleted krypton containing ${}^{81}\mathrm{Kr}$ (shaded region).

Figure 7

The decay scheme of ${}^{81}\mathrm{Kr}$.

Figure 8

Two-dimensional distributions of amplitudes of energy depositions of individual components for two-point (left panel) and three-point (right) events extracted from the background measured by the LPC at filling the depleted (panels a, b, and c) and enriched sample of krypton (panel d). Panel (b) represents distribution of the amplitudes for two-point events from the internal $\left({}^{81}\mathrm{Kr}\right)$ source with a total energy of $13.5\pm 2.5$ keV (the total measurement time was 7 days). The dash-dot arrows (panel a) indicate to the response from interaction of a 46 keV photons from ${}^{210}\mathrm{Bi}$ with electrons of the inner and outer shell of the krypton atom.

Figure 9

(a) the spectrum Auger electrons (peak 1.6 keV) and $K_{\alpha }$ after the single-$K$-capture decay of ${}^{81}\mathrm{Kr}$ and (b) a fragment of the coincidence spectrum with Br $[K^h\otimes K^s]$.