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

Abstract

Spin-dipole (SD) nuclear matrix elements (NMEs) 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 M± exp(SD2) are compared with the values of the single-quasiparticle NMEs M± qp(SD2) without nucleon spin–isospin (σ τ ) correlation and the QRPA NMEs M± QRPA(SD2) with the σ τ correlation. The observed SD matrix elements are found to be reduced by the factor k ≈ 0.2 with respect to M± qp(SD2) and by the factor kNM ≈ 0.5 with respect to M± QRPA(SD2). We then infer that the SD NME is reduced considerably partly by the nucleon σ τ 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.