Gamow-Teller nuclear matrix elements (NMEs) for pairs of β ± ↔ + + 1 0 ground-state-to-ground-state transitions, in particular their geometric mean NME M m , are studied. The observed means M exp m in the medium-heavy mass region are compared with the corresponding single-quasiparticle (qp) NMEs and the means M QRPA m calculated by the proton neutron qp random-phase approximation (pnQRPA). The M m NMEs turn out to be insensitive to the nucleon occupancy/vacancy amplitudes and to the particle-particle interaction parameter g pp of the pnQRPA. The observed mean NMEs are found to be reduced by a coefficient ≈ k 0.23 relative to the effective qp NMEs and by a coefficient ≈ k 0.6 NM with respect to the pnQRPA NMEs. The reductions associated with the spin isospin correlations and nuclear medium effects, and their impact on nuclear double beta decays and astro-neutrino-nuclear interactions are discussed.Keywords: Gamow-Teller beta decay, beta decay matrix element, double beta decay, astro neutrino response, quenching of g A , QRPA nuclear matrix element, astro neutrino nucleosynthesis