Relation of isospin-symmetry breaking correction for superallowed beta decay to energy of charge-exchange giant monopole resonance

Abstract

After application of an analytical transformation, a new exact representation for the nuclear isospin-symmetry breaking correction ${\delta }_C$ to superallowed beta decay is obtained. The correction is shown to be essentially the reciprocal of the square of an energy parameter ${\Omega }_M$ which characterizes the charge-exchange monopole strength distribution. The proportionality coefficient in this relation is determined by basic properties of the ground state of the even-even parent nucleus, and should be reliably calculable in any realistic nuclear model. Therefore, the single parameter ${\Omega }_M$ contains all the information about the properties of excited $0^{+}$ states needed to describe ${\delta }_C$. This parameter can possibly be determined experimentally by charge-exchange reactions. Basic quantities of interest are calculated within the isospin-consistent continuum random phase approximation, and the values of ${\delta }_C$ are compared with the corresponding results from other approaches.

10 pages, 2 tables, matches the published version

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• Coulomb corrections to Fermi beta decay in nuclei
• A Search for $0^{+}$ States in ${}^{50}$Cr: Implications for the Superallowed $\beta$-decay of ${}^{50}$Mn