Beyond Wigner's isobaric multiplet mass equation: Effect of charge-symmetry-breaking interaction and Coulomb polarization

TL;DR

This paper derives explicit forms of cubic and quartic terms in the isobaric multiplet mass equation, attributing deviations from Wigner's original quadratic form to charge-symmetry-breaking interactions and Coulomb polarization effects, with systematic shell-dependent behavior.

Contribution

It introduces a theoretical derivation of higher-order terms in the IMME beyond first-order perturbation, linking them to specific nuclear interactions and polarization effects.

Findings

Cubic and quartic Tz-terms originate from charge-symmetry-breaking and Coulomb polarization.

Deviations from IMME show oscillation-like behavior with mass number.

Systematic emergence of cubic Tz-term across sd- and lower fp-shells.

Abstract

The quadratic form of the isobaric multiplet mass equation (IMME), which was originally suggested by Wigner and has been generally regarded as valid, is seriously questioned by recent high-precision nuclear mass measurements. The usual resolution to this problem is to add empirically the cubic and quartic $T_z$-terms to characterize the deviations from the IMME, but finding the origin of these terms remains an unsolved difficulty. Based on a strategy beyond the Wigner's first-order perturbation, we derive explicitly the cubic and quartic $T_z$-terms. These terms are shown to be generated by the effective charge-symmetry breaking and charge-independent breaking interactions in nuclear medium combined with the Coulomb polarization effect. Calculations for the $sd$- and lower $fp$-shells explore a systematical emergence of the cubic $T_z$-term, suggesting a general deviation from the original IMME. Intriguingly, the magnitude of the deviation exhibits an oscillation-like behavior with mass number, modulated by the shell effect.