Improved calculation of the isospin-symmetry-breaking corrections to superallowed Fermi β decay

We report new shell-model calculations of the isospin-symmetry-breaking correction δC to superallowed 0⁺→0⁺ nuclear {β} decay. The most important improvement is the inclusion of core orbitals, which are demonstrated to have a significant impact on the mismatch in the radial wave functions of the parent and daughter states. We determine which core orbitals are important to include from an examination of measured spectroscopic factors in single-nucleon pickup reactions. In addition, where new sets of effective interactions have become available since our last calculation, we now include them; this leads to small changes in δNS as well. We also examine the new radiative-correction calculation by Marciano and Sirlin and, by a simple reorganization, show that it is possible to preserve the conventional separation into a nucleus-independent ``inner'' radiative term, ΔRV, and a nucleus-dependent ``outer'' term, δR'. We tabulate the new values for δC,δNS, and δR' for 20 superallowed transitions, including the 13 currently well-studied cases. With these new correction terms, the corrected Ft values for the 13 cases are statistically consistent with one another, and the anomalousness of the ⁴⁶V result disappears. These new calculations lead to a lower average Ft̄ value and a higher value for Vud. The sum of squares of the top-row elements of the Cabibbo-Kobayashi-Maskawa matrix now agrees exactly with unitarity.