Consistent large-scale shell-model analysis of the two-neutrino $\beta \beta$ and single $\beta$ branchings in ${}^{48}\mathrm{Ca}$ and ${}^{96}\mathrm{Zr}$

Abstract

Two-neutrino double-beta-decay matrix elements $M_{2\nu }$ and single beta-decay branching ratios were calculated for ${}^{48}$Ca and ${}^{96}$Zr in the interacting nuclear shell model using large single-particle valence spaces with well-tested two-body Hamiltonians. For ${}^{48}$Ca the matrix element $M_{2\nu }=0.0511$ is obtained, which is 5.5\% smaller than the previously reported value of 0.0539. For ${}^{96}$Zr this work reports the first large-scale shell-model calculation of the nuclear matrix element, yielding a value $M_{2\nu }=0.0747$ with extreme single-state dominance. If the scenario where the first $1^{+}$ state in ${}^{96}$Nb is at 694.6 keV turns out to be correct, the matrix element is increased to 0.0854. These matrix elements, combined with the available $\beta \beta$-decay half-life data, yield effective values of the weak axial coupling which in turn are used to produce in a consistent way the $\beta$-decay branching ratios of $(7.5\pm 2.8)$ % for ${}^{48}$Ca and $(18.4\pm 0.09)$ % for ${}^{96}$Zr. These are larger than obtained in previous studies, implying that the detection of the $\beta$-decay branches could be possible in dedicated experiments sometime in the (near) future.

13 pages, 8 figures

References in corpus (5)

• Nuclear matrix elements for double-β decay
• Value of the axial-vector coupling strength in $\beta$ and $\beta \beta$ decays: A review
• Shell model studies of the ${}^{130}Te$ neutrinoless double-beta decay
• Shell-model calculations of two-neutrino double-beta decay rates of ${}^{48}$Ca with GXPF1A interaction
• Quenching of $g_{\mathrm{A}}$ deduced from the $\beta$-spectrum shape of ${}^{113}$Cd measured with the COBRA experiment

Cited by in corpus (11)

• Toward the discovery of matter creation with neutrinoless double-beta decay
• Second-forbidden nonunique ${\beta }^{-}$ decays of ${}^{59,60}$Fe: Possible candidates for $g_A$ sensitive electron spectral-shape measurements
• Present Status of Nuclear Shell-Model Calculations of Neutrinoless Double-Beta Decay Matrix Elements
• Two-neutrino double-beta decay matrix elements based on relativistic nuclear energy density functional
• Large-scale shell-model study of two-neutrino double-beta decay of ${}^{82}$Se, ${}^{94}$Zr, ${}^{108}$Cd, ${}^{124}$Sn, ${}^{128}$Te, ${}^{130}$Te, ${}^{136}$Xe, and ${}^{150}$Nd
• Estimation of nuclear matrix elements of double-$\beta$ decay from shell model and quasiparticle random-phase approximation
• Radiative and exchange corrections for two-neutrino double-beta decay
• Systematic shell-model analysis of $2\nu \beta \beta$ decay of ${}^{76}$Ge and ${}^{96}$Zr to the ground and excited states of ${}^{76}$Se and ${}^{96}$Mo
• Large-scale shell-model study of 2$\nu$ECEC process in ${}^{78}$Kr
• A Semi-Empirical Formula for Two-Neutrino Double-Beta Decay
• Large-scale shell-model investigation of $2\nu$ECEC in ${}^{132}$Ba and ${}^{78}$Kr