Search for $2\beta$ decay of $^{106}$Cd with an enriched $^{106}$CdWO$_4$ crystal scintillator in coincidence with four HPGe detectors

A radiopure cadmium tungstate crystal scintillator, enriched in Cd-106 to 66%, with mass of 216 g (Cd-106 WO4), was used to search for double-beta decay processes in Cd-106 in coincidence with four ultra-low-background high-purity germanium detectors in a single cryostat. Improved limits on the double-beta processes in Cd-106 have been set on the level of 10(20) - 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 nu epsilon beta+) >= 1.1 x 10(21) yr, has reached the region of theoretical predictions. With this half-life limit the effective nuclear matrix element for the 2 nu epsilon beta(+) decay is bounded as M-eff(2 nu epsilon beta+) <= 1.1. The resonant neutrinoless double-electron captures to the 2718-, 2741-, and 2748-keV excited states of Pd-106 are restricted at the level of T-1/2 >= (8.5 x 10(20) - 1.4 x 10(21)) yr.