Two-neutrino $0^{+}\to 0^{+}$ double beta decay of ${}^{48}\mathrm{Ca}$ within the DFT-NCCI framework

Abstract

We present a seminal calculation of the nuclear matrix element for the two-neutrino double beta ($2\nu \beta \beta$) decay of ${}^{48}\text{Ca}\to {}^{48}\text{Ti}$ using a post-Hartree-Fock (HF) Density Functional Theory-based No-Core Configuration-Interaction (DFT-NCCI) 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 $|{\mathcal{M}}_{2\nu \beta \beta }|=0.056(6)$ 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 {\it et al.\/} [Phys. Rev. C 75, 034303 (2007)], which yielded 0.054 (0.064) 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(6) 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.