Fermi surface quasi particle model nuclear matrix elements for two neutrino double beta decays

Nuclear matrix elements (NMEs $M^{2\nu }$) for two neutrino double beta decays (DBDs) are discussed in terms of the Fermi surface quasi particle model (FSQP). The NMEs for $0^{+}\leftrightarrow 0^{+}$ ground-state-to-ground-state DBDs depend on the Fermi surface shell configuration and the nuclear core polarization. The evaluated NMEs $M^{2\nu }\left(FSQP\right)$ reproduce well the observed NMEs $M^{2\nu }\left(EXP\right)$ for $2\nu {\beta }^{-}{\beta }^{-}$ decays. The NMEs $M^{2\nu }\left(FSQP\right)$ for the 2ν DBDs of ⁷⁸Kr, ¹⁰⁶Cd, ¹³⁰Ba and ¹¹⁰Pd are evaluated on the basis of FSQP. The dependence of $M^{2\nu }\left(FSQP\right)$ and $M^{2\nu }\left(EXP\right)$ on the shell configuration is found to be seen in theoretical NMEs for neutrinoless DBDs. Impacts of $M^{2\nu }\left(FSQP\right)$ on $0\nu \beta \beta$ NMEs and $0\nu \beta \beta$ experiments are discussed. (paper)