Large-basis shell-model calculation of the ${}^{10}{\mathrm{C}\to }^{10}\mathrm{B}$ Fermi matrix element

We use a 4ħΩ shell-model calculation with a two-body effective interaction derived microscopically from the Reid93 potential to calculate the isospin-mixing correction for the ${}^{10}{\mathrm{C}\to }^{10}\mathrm{B}$ superallowed Fermi transition. The effective interaction takes into account the Coulomb potential as well as the charge dependence of $T=1\mathrm{}$ partial waves. Our results suggest the isospin-mixing correction ${\delta }_C\approx 0.1\%,$ which is compatible with previous calculations. The correction obtained in those calculations, performed in a 0ħΩ space, was dominated by deviation from unity of the radial overlap between the converted proton and the corresponding neutron. In the present calculation this effect is accommodated by the large model space. The obtained ${\delta }_C$ correction is about a factor of 4 too small to obtain unitarity of the Cabibbo-Kobayashi-Maskawa matrix with the present experimental data.