Isospin-symmetry breaking in superallowed Fermi β-decay due to isospin-nonconserving forces

Abstract We investigate isospin-symmetry breaking effects in the sd -shell region with large-scale shell-model calculations, aiming to understand the recent anomalies observed in superallowed Fermi β -decay. We begin with calculations of Coulomb displacement energies (CDE's) and triplet displacement energies (TDE's) by adding the T = 1 , J = 0 isospin nonconserving (INC) interaction into the usual isospin-invariant Hamiltonian. It is found that CDE's and TDE's can be systematically described with high accuracy. A total number of 122 one- and two-proton separation energies are predicted accordingly, and locations of the proton drip-line and candidates for proton-emitters are thereby suggested. However, attempt to explain the anomalies in the superallowed Fermi β -decay fails because these well-fitted T = 1 , J = 0 INC interactions are found no effects on the nuclear matrix elements. It is demonstrated that the observed large isospin-breaking correction in the 32 Cl β -decay, the large isospin-mixing in the 31 Cl β -decay, and the small isospin-mixing in the 23 Al β -decay can be consistently understood by introducing additional T = 1 , J = 2 INC interactions related to the s 1 / 2 orbit.