The first large-scale shell-model calculation of the two-neutrino double beta decay of $^{76}$Ge to the ground and excited states in $^{76}$Se

Abstract

Large-scale shell-model calculations were carried out for the half-lives and branching ratios of the 2νββ decay of 76 Ge to the ground state and the lowest three excited states 2 + 1 , 0 + 2 and 2 + 2 in 76 Se. In total, the wave functions of more than 10,000 intermediate 1 + states in 76 As were calculated in a three-step procedure allowing an efficient use of the available computer resources. In the first step, 250 lowest states, below some 5 MeV of excitation energy, were calculated without truncations within a full major shell 0f 5/2 − 1p − 0g 9/2 for both protons and neutrons. The wave functions of the rest of the states, up to some 30 MeV, were computed in two more steps by introducing two consecutive stages of truncation. The computed magnitudes of the 2νββ nuclear matrix elements, |M 2ν |, converged to the values 0.097, 7.0 × 10 −4 , 0.070 and 1.8 × 10 −3 for the 0 + g.s. , 2 + 1 , 0 + 2 and 2 + 2 states, respectively. Using up-to-date phase-space integrals, the corresponding branching ratios were derived to be 99.79%, 9.1×10 −5 %, 0.21% and 5.0×10 −7 %. The experimental half-life (1.926 ± 0.094) × 10 21 yr of the ground-state transition was used to derive the value g A = 1.248 ± 0.015 for the axial-vector coupling, which is consistent with its free-nucleon value 1.27. The branching ratios for the decays to the excited states were done using the derived value for g A .