Overlap of quasiparticle random-phase approximation states for nuclear matrix elements of the neutrino-less double-β decay

Quasiparticle random-phase approximation (QRPA) is applied to two nuclei, and the overlap of the QRPA excited states based on the different nuclei is calculated. The aim is to calculate the overlap of intermediate nuclear states of the double-β decay. We use the like-particle QRPA after the closure approximation is applied to the nuclear matrix elements. The overlap is calculated rigorously by making use of the explicit equation of the QRPA ground state. The formulation of the overlap is shown, and a test calculation is performed. The effectiveness of the truncations used is shown