Two neutrino double beta decay within the ξ\xi-approximation

We examine the contributions of odd-parity nuclear operators to the two-neutrino double beta decay $0^+\rightarrow 0^+$ amplitude, which come from the $P$-wave Coulomb corrections to the electron wave functions and the recoil corrections to the nuclear currents. Although they are formally of higher order in $\alpha Z/2$ or $v/c$ of the nucleon than the usual Fermi and Gamow-Teller matrix elements, explicit calculations performed within the QRPA show that they are significant when confronted with the experimental data.Comment: 9 pages, latex, no figure

Nuclear moments for the neutrinoless double beta decay II

The recently developed formalism for the evaluation of nuclear form factors in neutrinoless double beta decay is applied to $^{48}Ca$, $^{76}Ge$, $^{82}Se$, $^{100}Mo$, $^{128}Te$ and $^{130}Te$ nuclei. Explicit analytical expressions that follows from this theoretical development, in the single mode model for the decay of $^{48}Ca$, have been worked out. They are useful both for testing the full numerical calculations, and for analytically checking the consistency with other formalisms. Large configuration space calculations are compared with previous studies, where alternative formulations were used. Yet, besides using the G-matrix as residual interaction, we here use a simple $\delta$-force. Attention is paid to the connected effects of the short range nuclear correlations and the finite nucleon size. Constraints on lepton number violating terms in the weak Hamiltonian (effective neutrino Majorana mass and effective right-handed current coupling strengths) are deduced.Comment: 18 pages, latex, minor changes, to appear in Nucl. Phys.

Double Beta Decay in pn-QRPA Model with Isospin and SU(4) Symmetry Constraints

The transition matrix elements for the $0^{+}\to 0^{+}$ double beta decays are calculated for $^{48}Ca$, $^{76}Ge$, $^{82}Se$, $^{100}Mo$, $^{128}Te$ and $^{130}Te$ nuclei, using a ${\delta}$-interaction. As a guide, to fix the particle-particle interaction strengths, we exploit the fact that the missing symmetries of the mean field approximation are restored in the random phase approximation by the residual interaction. Thus, the T=1, S=0 and T=0, S=1 coupling strengths have been estimated by invoking the partial restoration of the isospin and Wigner SU(4) symmetries, respectively. When this recipe is strictly applied, the calculation is consistent with the experimental limit for the $2\nu$ lifetime of $^{48}Ca$ and it also correctly reproduces the $2\nu$ lifetime of $^{82}Se$. In this way, however, the two-neutrino matrix elements for the remaining nuclei are either underestimated (for $^{76}Ge$ and $^{100}Mo$) or overestimated (for $^{128}Te$ and $^{130}Te$) approximately by a factor of 3. With a comparatively small variation ($<10$) of the spin-triplet parameter, near the value suggested by the SU(4) symmetry, it is possible to reproduce the measured $T_{1/2}^{2\nu}$ in all the cases. The upper limit for the effective neutrino mass, as obtained from the theoretical estimates of $0\nu$ matrix elements, is $\cong 1$ eV. The dependence of the nuclear matrix elements on the size of the configuration space has been also analyzed.Comment: 25 pages (LaTex) and 3 figures upon request, to be published in Nucl. Phys.