We present a seminal calculation of the nuclear matrix element for the two-neutrino double beta ($2\nu\beta\beta$) decay of ${ }^{ 48}\text{ Ca} \rightarrow { }^{ 48}\text{ Ti}$ 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 $qg_\text{ A} \approx 1$. 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.
Categories: nucl-th