We study the formalism to include isospin-symmetry-breaking corrections when extracting the up-down Cabibbo-Kobayashi-Maskawa matrix element from superallowed $0^{+}\to 0^{+}$ nuclear $\beta$ decay. We show that there are no first-order isospin-symmetry-breaking corrections to the relevant nuclear matrix elements. We find corrections to the treatment of Towner and Hardy, and assess these using schematic models of increasing complexity.

• Received 8 May 2008

DOI:https://doi.org/10.1103/PhysRevC.78.035501