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Within the nuclear shell model, we investigate the correction $delta_{RO}$ to the Fermi matrix element due to a mismatch between proton and neutron single-particle radial wave functions. Eight superallowed $0^+ to 0^+$ $beta$ decays in the $sd$-shell, comprised of $^{22}$Mg, $^{26m}$Al, $^{26}$Si, $^{30}$S, $^{34}$Cl, $^{34}$Ar, $^{38m}$K and $^{38}$Ca are re-examined. The radial wave functions are obtained from a spherical Woods-Saxon potential whose parametrizations are optimized in a consistent adjustment of the depth and the length parameter to relevant experimental observables, such as nucleon separation energies and charge radii, respectively. The chosen fit strategy eliminates the strong dependence of the radial mismatch correction to a specific parametrization, except for calculations with an additional surface-peaked term. As an improvement, our model proposes a new way to calculate the charge radii, based on a parentage expansion which accounts for correlations beyond the extreme independent-particle model. Apart from the calculations with a surface-peak term and the cases where we used a different model space, the new sets of $delta_{RO}$ are in general agreement with the earlier result of Towner and Hardy [1]. Small differences of the corrected average $overline{mathcal{F}t}$ value are observed.
We investigate the radial-overlap part of the isospin-symmetry breaking correction to superallowed $0^+to 0^+$-decay using the shell-model approach similar to that of Refs. [1, 2]. The 8 sd-shell emitters with masses between $A=22$ and $A=38$ have be
textbf{Background}: Superallowed $0^+ rightarrow 0^+$ $beta$ decays of isospin $T=2$ nuclides can be used to test theoretical isospin symmetry breaking corrections applied to extract the CKM matrix element $V_{ud}$ from $T = 0,1$ decays by measuring
We report new shell-model calculations of the isospin-symmetry-breaking correction to superallowed nuclear beta decay. The most important improvement is the inclusion of core orbitals, which are demonstrated to have a significant impact on the mismat
A $^{52}$Cr$(p,t)$$^{50}$Cr two-neutron pickup reaction was performed using the Q3D magnetic spectrograph at the Maier-Leibnitz-Laboratorium in Garching, Germany. Excited states in $^{50}$Cr were observed up to an excitation energy of 5.3 MeV. Despit
The measured $ft$-values for superallowed $0^{+} to 0^{+}$ nuclear $beta$-decay can be used to obtain the value of the vector coupling constant and thus to test the unitarity of the Cabibbo-Kobayashi-Maskawa matrix. An essential requirement for this