Effect of fluctuations of quadrupole deformation and neutron-proton correlations on double-beta decay nuclear matrix element

We describe the initial and final states of the nuclei involved in the ββ decay of ⁷⁶Ge with the generator coordinate method, and evaluate the associated nuclear matrix elements for neutrinoless ββ decay. Proton-neutron pairing amplitudes and the axial quadrupole deformation are used as generator coordinates. The results with a simplified Hamiltonian that does not include a quadrupole–quadrupole interaction are compared with those of the proton-neutron quasiparticle random-phase approximation, and the behavior around the transition region from the isovector pairing phase to the isoscalar proton-neutron pairing phase is discussed. Then a more realistic calculation that includes both proton-neutron pairing and quadrupole deformation are presented. (author)