Isobaric process

Spectral line

Symmetry breaking

Quantum mechanics

Pure mathematics

Mathematical physics

Effective mass (spring–mass system)

Atomic physics

Physical chemistry

Polarization (electrochemistry)

Thermodynamics

Physics

Effective nuclear charge

Coulomb

Mathematics

Mass formula

Quantum electrodynamics

Quadratic equation

Quartic function

Geometry

Charge (physics)

Chemistry

Electron

Isospin

Multiplet

Physical review. C

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.

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