Search for2βdecay ofCd106with an enrichedCd106WO4crystal scintillator in coincidence with four HPGe detectors

A radiopure cadmium tungstate crystal scintillator, enriched in $^{106}\mathrm{Cd}$ to 66%, with mass of 216 g $(^{106}\mathrm{Cd}{\text{WO}}_{4})$, was used to search for double-$\ensuremath{\beta}$ decay processes in $^{106}\mathrm{Cd}$ in coincidence with four ultra-low-background high-purity germanium detectors in a single cryostat. Improved limits on the double-$\ensuremath{\beta}$ processes in $^{106}\mathrm{Cd}$ have been set on the level of ${10}^{20}\ensuremath{-}{10}^{21}$ yr after 13 085 h of data taking. In particular, the half-life limit on the two-neutrino electron capture with positron emission, ${T}_{1/2}^{2\ensuremath{\nu}\ensuremath{\varepsilon}{\ensuremath{\beta}}^{+}}\ensuremath{\ge}1.1\ifmmode\times\else\texttimes\fi{}{10}^{21}$ yr, has reached the region of theoretical predictions. With this half-life limit the effective nuclear matrix element for the $2\ensuremath{\nu}\ensuremath{\varepsilon}{\ensuremath{\beta}}^{+}$ decay is bounded as ${M}_{\mathrm{eff}}^{2\ensuremath{\nu}\ensuremath{\varepsilon}{\ensuremath{\beta}}^{+}}\ensuremath{\le}1.1$. The resonant neutrinoless double-electron captures to the 2718-, 2741-, and 2748-keV excited states of $^{106}\mathrm{Pd}$ are restricted at the level of ${T}_{1/2}\ensuremath{\ge}(8.5\ifmmode\times\else\texttimes\fi{}{10}^{20}\ensuremath{-}1.4\ifmmode\times\else\texttimes\fi{}{10}^{21})$ yr.