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

TL;DR

This paper derives a new exact formula linking the isospin-symmetry breaking correction in superallowed beta decay to the charge-exchange giant monopole resonance energy, enabling more reliable calculations and potential experimental determination.

Contribution

It introduces an exact representation of the correction elta_Cased on a single energy parameter mega_Mrom charge-exchange reactions, simplifying and unifying previous models.

Findings

The correction elta_Cquals the reciprocal of mega_M, connecting nuclear structure to decay corrections.

Calculated elta_Cgrees with other approaches, validating the new formula.

mega_Man be experimentally determined, aiding future precision tests.

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.