Calculation of the $\beta^+\beta^+$, $\beta^+$/EC and EC/EC half-lives for 106Cd with the second quasi random phase approximation method
Abstract.The double-beta decay matrix elements and half-lives for 106Cd are computed with the second quasi random phase approximation (SQRPA) method and using two single-particle (s.p.) bases. For the neutrino-emitting decay modes the two-positron emission ($\beta^+\beta^+$), the positron emission/electron capture ($\beta^+$/EC) and the double electron capture (EC/EC) processes are treated. It was found that the nuclear matrix elements (NME) display a strong dependence on the strength of the particle-particle interaction and an important contribution to the decay amplitude is coming from the 1+ ground state of the intermediate nucleus 106Ag. Their values depend weakly on the s.p. basis used. For both bases the deviations from the Ikeda sum rule are only within 2-3%. We got half-lives for the $\beta^+$/EC of the order of $\sim 10^{21} $ y which is not far from the actual experimental limits. For the neutrinoless $\beta^+\beta^+$ and $\beta^+$/EC decay modes the NME relevant both for the mass mechanism and the right-handed (RH) currents were calculated. They are found to be slightly larger than those obtained in our previous calculations (M. Hirsch, K. Muto, T. Oda, H.V. Klapdor-Kleingrothaus, Z. Phys. A 334, 151 (1994)). Using the value of the neutrino mass parameter extracted from the recently reported first experimental evidence of the neutrinoless decay mode (i.e. 0.39 eV) (H.V. Klapdor-Kleingrothaus, A. Dietz, H.I. Harney, I.V. Krivosheina, hep-ph/0201231; Mod. Phys. Lett. A 16, 2409 (2001); H.V. Klapdor-Kleingrothaus, A. Dietz, I.V. Krivosheina, Part. Nucl. Lett. 110, 57 (2002); Found. Phys. 32, 1181 (2002)), we got half-lives of $\sim 10^{28}$ y and 1027 y, for the $0\nu\beta^+\beta^+$ and $0\nu\beta^+$/EC processes, respectively. An experimental investigation of these decays could be useful for testing the importance of the right-handed current mechanism to the occurrence of neutrinoless $\beta\beta$ decay.