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 quadrupolequadrupole 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.