We perform 2νββ and 0νββ calculations for ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}$, ${}_{}{}^{128}{}_{}{}^{}\mathrm{Te}$, and ${}_{}{}^{130}{}_{}{}^{}\mathrm{Te}$ using effective interactions derived from the Paris and Bonn-A potentials. Extended model spaces are employed in setting up the quasiparticle random phase approximation (QRPA) equations, on which our present calculations are based. For ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}$ the model space consists of nine orbits, the two major shells from 0${\mathit{f}}_{7/2}$ to 2${\mathit{s}}_{1/2}$, and for the tellurium case we include eleven orbits spanning three major shells from 1${\mathit{p}}_{3/2}$ to 1${\mathit{f}}_{7/2}$. The bare-G-matrix elements are first calculated, with the Pauli exclusion operator carefully treated with a matrix inversion method, so that double counting between the calculated effective interaction and the above model spaces is strictly avoided. We then calculate the renormalized effective interaction, including corrections from core polarizations and folded diagrams. The effect of core polarization is found to be highly significant, especially for ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}$. There appears to be a compensating effect from the folded diagrams; the net results with core polarizations and folded diagrams both included become rather close to the bare-G results. Unlike earlier QRPA calculations, our calculated ${\mathit{M}}_{\mathrm{GT}}$ matrix elements for 2νββ do not seem to exhibit strong dependence on ${\mathit{g}}_{\mathrm{pp}}$, the particle-particle interaction strength parameter, in the vicinity of ${\mathit{g}}_{\mathrm{pp}}$=1.0.

For 0νββ decays, our calculated values for ${\mathit{T}}_{1/2}^{0\nu }$〈${\mathit{m}}_{\nu }$${\mathrm{〉}}^2$ are typically 5×${10}^{23}$ yr ${\mathrm{eV}}^2$ for ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}$, 2×${10}^{24}$ yr ${\mathrm{eV}}^2$ for ${}_{}{}^{128}{}_{}{}^{}\mathrm{Te}$, and 9×${10}^{22}$ yr ${\mathrm{eV}}^2$ for ${}_{}{}^{130}{}_{}{}^{}\mathrm{Te}$. Although the Bonn-A potential gives generally more pairing force, the final results for ββ decays given by the Paris and Bonn-A potentials are rather close to each other.

• Received 5 December 1991

DOI:https://doi.org/10.1103/PhysRevC.46.871