Influence of configuration-interaction on isospin impurities and isospin symmetry breaking corrections to superallowed $0^+\rightarrow 0^+$ 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, $α<em>{\rm C}$, in the ground and excited states of $<sup>{10}$C, $<sup>{10}$B, and $<sup>{14}$N, as well as on the isospin-symmetry-breaking (ISB) correction to the superallowed $0⁺ \rightarrow 0<sup>+$ $β$ decay of $<sup>{10}$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 $I=0<sup>+,\,T=1$ state in $<sup>{10}$B. Hence, it also has a non-negligible impact on the ISB correction to the superallowed $β$ decay of $<sup>{10}$C. Our calculations yield $\barδ</em>{\rm C}=0.45(4)\%$ when the Coulomb interaction is taken as the sole source of ISB, and $\barδ_{\rm ISB}=0.46(6)\%$ 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.