Orateur
Description
We investigate the correlation between the isospin-symmetry breaking correction to superallowed $0^+\rightarrow0^+$ nuclear $\beta$ decay of isotriplets and the $E0$-transition strength between the isobaric analog and the first excited $0^+$ states in the $T_z=1$ nuclei. Specifically, the correction, as obtained within the shell-model approach, is suppressed where the experimental $E0$ strength is pronounced and enhanced elsewhere. To clarify the physical origin of this behavior, we perform shell-model calculations of $E0$ strengths in $T_z=1$ and nearby nuclei with available data, using identical valence spaces and effective interactions. With appropriately chosen effective charges, the results obtained in the ZBM2 and lower-edge ZBM spaces agree fairly well with experiment for most cases. Nevertheless, ZBM-space calculations do not reasonably reproduce the $E0$ strengths in $^{20}$Ne and $^{24}$Mg, where experimental values are sizable, and an $sd$-shell description yields vanishing results. Accordingly, both the ZBM and $sd$ calculations are likely insufficient for describing the superallowed $0^+\rightarrow0^+$ nuclear $\beta$ decay of $^{22}$Mg and $^{22m}$Na, although the $E0$ strength in $^{22}$Ne is not experimentally known. Similarly, a $p$-shell description for the $A=10$ mass multiplet cannot reproduce the observed $E0$ strength in $^{10}$Be. We also derive a consistent analytical relation between the isospin-symmetry breaking correction and the $E0$ strength, under the assumption that isospin mixing occurs only between the lowest and first excited $0^+$ states in the initial and final nuclei. This result further reveals the influence of the charge radii and neutron-skin thicknesses, although this effect is generally less obvious than that associated with the $E0$ strength.