New results for the two neutrino double beta decay in deformed nuclei with angular momentum projected basis

Abstract

Four nuclei which are proved to be $2\nu \beta \beta$ emitters (${}^{76}$Ge, ${}^{82}$Se, ${}^{150}$Nd, ${}^{238}$U), and four suspected, due to the corresponding Q-values, to have this property (${}^{148}$Nd, ${}^{154}$Sm, ${}^{160}$Gd, ${}^{232}$Th), were treated within a proton-neutron quasiparticle random phase approximation (pnQRPA) with a projected spherical single particle basis. The advantage of the present procedure over the ones using a deformed Woods Saxon or Nilsson single particle basis is that the actual pnQRPA states have a definite angular momentum while all the others provide states having only K as a good quantum number. The model Hamiltonian involves a mean field term yielding the projected single particle states, a pairing interaction for alike nucleons and a dipole-dipole proton-neutron interaction in both the particle-hole (ph) and particle-particle (pp) channels. The effect of nuclear deformation on the single beta strength distribution as well as on the double beta Gamow-Teller transition amplitude (M${}_{\mathrm{GT}}$) is analyzed. The results are compared with the existent data and with the results from a different approach, in terms of the process half life T${}_{1/2}$. The case of different deformations for mother and daughter nuclei is also presented.

Comments: 45 pages, 13 figures