Abstract
The nuclear matrix element for 2\ensuremath{\nu} double-beta decay is calculated within the quasiparticle random-phase approximation. It is shown that the decay matrix element passes through zero as a function of the strength ${g}^{\mathrm{pp}}$ of the particle-particle component of the spin-isospin polarization force, neglected previously. The analysis of electron capture/${\ensuremath{\beta}}^{+}$ decay rates for semimagic neutron-deficient nuclei suggests values for ${g}^{\mathrm{pp}}$ in the very vicinity of this zero, which gives rise to long lifetimes. The qualitative features of nuclear \ensuremath{\beta}\ensuremath{\beta} decay are illustrated with the example of an exactly soluble model.
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