Indications of $2\nu 2K$ capture in ${}^{78}$Kr

Results from searches of double $K$ capture in ${}^{78}$Kr in an experiment with the large-volume copper proportional counter, using data samples corresponding of two independent series of measurements with different intrinsic radioactivity background are presented. The total exposure of the low-background measurements is 0.343 $\mathrm{kg}\times \mathrm{y}$. A combination of methods of selection of useful events with a unique set of characteristics and wavelet analysis of events allowed a reduction of the background by $\sim$2000 times in the energy region of interest. The statistical significance of combined data from two stages of operation equals $2.5\sigma$. Corresponding to such effect, the half-life of ${}^{78}$Kr relative to $2\nu 2K$ capture equals $T_{1/2}=[9.2_{-2.6}^{+5.5}\left(\mathrm{stat}\right)\pm 1.3\left(\mathrm{syst}\right)]\times {10}^{21}$ y. Half-life limits for other $2K$ transitions to the excited states in ${}^{78}$Se are obtained at the level of ${10}^{21}$ y in the first time. In particular, limits on $2\nu 2K$ capture to the excited level $0_1^{+}$ (1499 keV) and resonant neutrinoless double $K$ capture to the level $2^{+}$ (2838 keV) have been defined on the level of $T_{1/2}\ge 5.4\times {10}^{21}$ y at 90$\%$ C.L.

Figure 1

A depiction of idealized pulse shape single-point event from the LPC. The monotonically dashed curve $a$ is a charge pulse from the CSA output, and the front-back asymmetry solid curv $b$ is an electric current pulse (constructed by differentiating the charge pulse). $A$ and $B$ denote the area in the front and back halves of the midpoint of the current pulse, respectively.

Figure 2

A depiction of idealized pulse shape analysis parameters from three-point event expected from $2K$ capture in case of registering two characteristic photons and a cascade of low-energy Auger electrons from the LPC: (a) the electric current pulse, (b) the charge pulse. $t_{01}$ and $t_{09}$ are the baseline plus 10$\%$ and 90$\%$, respectively, of the pulse height; $t_f=t_{09}-t_{01}$ is the pulse rise time; ${\tau }_{\mathrm{p}}$ is the time of the after-pulse appearance since the beginning of the primary pulse.

Figure 3

(a) and (b) curves demonstrate the converted pulses of voltage (charge) normalized for $M1$ of an original CSA pulse and obtained by integrating electric current pulses owing to primary ionization electrons (c) and (d) from two real events which are candidates for $2K$ capture of ${}^{78}$Kr.

Figure 4

Signal modeling graphs with the added real noise (a) and denoise of signals for various levels of decomposition: (b) $L=3$, (c) $L=4$, and (d) $L=5$. (e) and (f), (g), (h) dependency's of entropy $H$ and coefficients $A$, $B$, $C$ from wavelet decomposition level, respectively.

Figure 5

Pulse-height $M1$ spectra (data of the first stage of measurements normalized for 1000 h) of the background of the LPC filled with krypton enriched in ${}^{78}$Kr (1, dark line) and with depleted krypton (2, light line): (a) all events, (b) single-point events, (c) two-point events, and (d) three-point events.

Figure 6

The three-point spectra selected under the conditions “C1” and “C2”.

Figure 7

(a) The solid angle under which the interior surface of the counter from different points of an anode wire is visible. (b) The density of distribution of the solid angle for the points uniformly distributed along the anode wire.

Figure 8

The distributions of the events in the LPC filled with depleted krypton with energies $11.5-15.5$ keV (${}^{81}$Kr, black histogram) and with energies $20-80$ keV (shaded region). The dash-dotted and dotted curves are the result of a fitting operation of the shaded region. (a) Single-point events, (b) two-point events, and (c) three-point events.

Figure 9

The three-point spectra selected under the conditions (C1 and C2) and $\lambda \ge 0.225$.

Figure 10

Pulse height $M1$ spectra (data of the second stage of measurements normalized for 1000 h) of the background of the LPC filled with krypton enriched in ${}^{78}$Kr (black line) and with depleted krypton (gray bar graph). (a) All events, (b) single-point events, (c), two-point events, and (d) three-point events.

Figure 11

$\lambda$ distributions of three-point events in the LPC filled with krypton enriched in ${}^{78}$Kr (black line) and with depleted krypton (gray bar graph).

Figure 12

The three-point spectra selected under the conditions (C1 and C2) and $\lambda \ge 0.155$: krypton enriched in ${}^{78}$Kr (black line), depleted krypton (gray bar graph), and model calculation spectrum for $2K$ capture.