A COMPARATIVE-STUDY OF DOUBLE BETA-DECAY BY SHELL-MODEL AND QUASI-PARTICLE RPA

Nuclear matrix elements of the two-neutrino and neutrinoless beta-beta decays of Ca-48(0g.s.+) --> Ti-48(0g.s.+) are calculated by shell model and QRPA. The two-neutrino matrix element M(GT)2-nu is rather reliably evaluated in the QRPA approach by a careful fit of the particle-particle interaction strength in the 1+ channel, which governs the spinisospin ground-state correlations. The shell-model value of M(GT)2-nu depends not only on the 1+ interaction but largely on the pairing and quadrupole interactions. Concerning the neutrinoless-mode nuclear matrix elements, the shell model gives generally smaller values than the QRPA. A detailed analysis indicates that the discrepancies originate mainly from the truncation of shell-model configurations (f p-space). The QRPA calculation in a larger model space well takes into account transitions from/to single-particle orbits far from the Fermi surface, and those transitions give rise to sizable contributions because of large momentum transfers due to the exchange of a virtual neutrino.