Influence of configuration-interaction on isospin impurities and isospin symmetry breaking corrections to superallowed $0^{+}\to 0^{+}$ beta decays

Abstract

The symmetry-conserving density functional theory (DFT)-based no-core configuration-interaction (DFT-NCCI) framework is applied for the first time to investigate the impact of configuration interaction (CI) on the Coulomb (isospin) impurity, ${\alpha }_{\mathrm{C}}$, in the ground and excited states of ${}^{10}$C, ${}^{10}$B, and ${}^{14}$N, as well as on the isospin-symmetry-breaking (ISB) correction to the superallowed $0^{+}\to 0^{+}$ $\beta$ decay of ${}^{10}$C. We demonstrate, among other findings, that within the DFT-NCCI framework CI has a negligible effect on the ground-state isospin impurities, which are dominated by a single doorway state. In contrast, CI significantly modifies the impurities in excited states, including the isobaric analogue $I=0^{+},T=1$ state in ${}^{10}$B. Hence, it also has a non-negligible impact on the ISB correction to the superallowed $\beta$ decay of ${}^{10}$C. Our calculations yield ${\bar{\delta }}_{\mathrm{C}}=0.45(4)\%$ when the Coulomb interaction is taken as the sole source of ISB, and ${\bar{\delta }}_{\mathrm{ISB}}=0.46(6)\%$ when short-range charge-symmetry-breaking (CSB) terms are included in addition. Hence, no statistically significant dependence of the ISB correction on the short-range CSB interaction is observed for this decay. Comparison with our previous results reveals a strong sensitivity to the nuclear symmetry energy, which governs the strength of the isospin-restoring force and whose value in finite nuclei remains difficult to constrain because of its intricate dependence on the momentum-dependent terms of the effective interaction.

Comments: 12 pages, 10 figures