Spin-dipole nuclear matrix elements for double beta decays and astro-neutrinos

Spin-dipole (SD) nuclear matrix elements (NMEs) M±(SD2)M±(SD2) for unique first forbidden β±2−→0+ ground-state-to-ground-state transitions are studied by using effective microscopic two-nucleon interactions in realistic single-particle model spaces. The observed values of the NMEs Mexp±(SD2) are compared with the values of the single-quasiparticle NMEs Mqp±(SD2) without nucleon spin–isospin (στ  ) correlation and the QRPA NMEs MQRPA±(SD2) with the στ   correlation. The observed SD matrix elements are found to be reduced by the factor k≈0.2k≈0.2 with respect to Mqp±(SD2) and by the factor kNM≈0.5kNM≈0.5 with respect to MQRPA±(SD2). We then infer that the SD NME is reduced considerably partly by the nucleon στ correlations and partly by other non-nucleonic and nucleonic correlations which are not explicitly included in the QRPA. Impact of the found reduction factors on the magnitudes of the NMEs involved in neutrino-less double beta decays and astro-neutrino interactions are discussed.