Consistent large-scale shell-model analysis of the two-neutrino ββ and single β branchings in 48Ca and 96Zr

Abstract

Two-neutrino double-beta-decay matrix elements M2ν and single beta-decay branching ratios were calculated for 48Ca and 96Zr in the interacting nuclear shell model using large single-particle valence spaces with well-tested two-body Hamiltonians. For 48Ca the matrix element M2ν=0.0511 is obtained, which is 5.5% smaller than the previously reported value of 0.0539. For 96Zr this work reports the first large-scale shell-model calculation of the nuclear matrix element, yielding a value M2ν=0.0747 with extreme single-state dominance. These matrix elements, combined with the available ββ-decay half-life data, yield effective values of the weak axial coupling which in turn are used to produce in a consistent way the β-decay branching ratios of (7.5±2.8)% for 48Ca and (18.4±0.09)% for 96Zr. These are larger than obtained in previous studies, implying that the detection of the β-decay branches could be possible in dedicated experiments sometime in the (near) future.