We present a calculation of the nuclear matrix element for the two-neutrino double-beta ($2\nu \beta \beta$) decay of ${}^{48}\mathrm{Ca}\to {}^{48}\mathrm{Ti}$ using a post-Hartree-Fock (HF) density functional theory–based no-core configuration-interaction framework developed by our group [Phys. Rev. C 94, 024306 (2016)]. In the present calculation, we utilize a variant of the approach that restores rotational symmetry and mixes states projected from self-consistent mean-field configurations obtained by solving the HF equations with the density-independent local Skyrme interaction. Our calculations yield $|{\mathcal{M}}_{2\nu \beta \beta }|=0.056\left(6\right){\mathrm{MeV}}^{-1}$ for the nuclear matrix element describing this process. This result is in very good agreement with shell-model studies—for example, with the calculations by Horoi et al. [Phys. Rev. C 75, 034303 (2007)], which yielded $0.054\left(0.064\right){\mathrm{MeV}}^{-1}$ for the GXPF1A (GXPF1) interactions, respectively. It is also in a reasonable agreement with the most recent experimental estimate from the review by Barabash, which is $0.068\left(6\right){\mathrm{MeV}}^{-1}$, assuming quenching $q{g}_{\text{A}}\approx 1$. The consistency of our prediction with the shell-model results increases our confidence in the nuclear modeling of this second-order, very rare process which is of paramount importance for further modeling of the neutrinoless double-beta ($0\nu \beta \beta$) decay process.

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• Double beta decay
• 39 ≤ A ≤ 58
• Nuclear density functional theory