[en] Gamow–Teller nuclear matrix elements (NMEs) for pairs of ${\mathrm{\beta <!--\; ??\; -->}}^{\pm <!--\; ??\; -->}$ $1^{+}\leftrightarrow <!--\; ???\; -->0^{+}$ ground-state-to-ground-state transitions, in particular their geometric mean NME $M^{\mathrm{m}}$, are studied. The observed means $M_{\mathrm{e}\mathrm{x}\mathrm{p}}^{\mathrm{m}}$ in the medium-heavy mass region are compared with the corresponding single-quasiparticle (qp) NMEs and the means $M_{\mathrm{Q}\mathrm{R}\mathrm{P}\mathrm{A}}^{\mathrm{m}}$ calculated by the proton neutron qp random-phase approximation (pnQRPA). The $M^{\mathrm{m}}$ NMEs turn out to be insensitive to the nucleon occupancy/vacancy amplitudes and to the particle–particle interaction parameter $g_{\mathrm{p}\mathrm{p}}$ of the pnQRPA. The observed mean NMEs are found to be reduced by a coefficient $k\approx <!--\; ???\; -->0.23$ relative to the effective qp NMEs and by a coefficient $k_{\mathrm{N}\mathrm{M}}\approx <!--\; ???\; -->0.6$ 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. (paper)