Annotation: dorsal/arxiv

Authors	F. Krmpotić, S. Shelly Sharma
Categories	nucl-th
ArXiv ID	nucl-th/9312007
URL	https://arxiv.org/abs/nucl-th/9312007
DOI	10.1016/0375-9474(94)90178-3
Journal	Nucl.Phys. A572 (1994) 329-348

Authors

F. Krmpotić, S. Shelly Sharma

Abstract

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 $<m_{\nu}>\cong 1$ eV. The dependence of the nuclear matrix elements on the size of the configuration space has been also analyzed.

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