Two-vacua RPA and the two-neutrino double-beta decay

Abstract

Abstract A new method “two-vacua random-phase approximation” (TVRPA) for the description of the two-neutrino nuclear double-beta decay is developed. The nuclear wave functions of the intermediate odd-odd nucleus are constructed as linear combinations of proton-particle neutron-hole excitations from the ground state of the initial even-even ( N , Z ) nucleus and, at the same time, as neutron-particle proton-hole excitations from the ground state of the final ( N − 2, Z + 2) nucleus. The Ritz variational principle is used to obtain RPA-like equations. The ground state in the initial and final nucleus is approximated with HFB wave functions including proton-neutron pairing. A projection on numbers of protons and neutrons is performed additionally on the wave functions in both nuclei to restore the exact number of particles, broken by the quasi-particle transformation. The method is applied, as a preliminary test, to the 2ν double-beta decay in 20 48 Ca 28 . More realistic B (GT − ) and B (GT + ) Gamow-Teller strength distributions than QRPA and PQRPA are obtained. No dependence is found on the particle-particle strength parameter g pp , renormalizing Brueckner reaction matrix elements of the Bonn potential.