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

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.

arXiv comment13 pages, 4 figures

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Cited by in corpus (6)

• $B\rho$-defined Isochronous Mass Spectrometry and Mass Measurements of ${}^{58}$Ni Fragments
• Effects of Coulomb and isospin symmetry breaking interactions on neutron-skin thickness
• Mass measurements for $T_z=-2$ $fp$-shell nuclei ${}^{40}$Ti, ${}^{44}$Cr, ${}^{46}$Mn, ${}^{48}$Fe, ${}^{50}$Co and ${}^{52}$Ni
• First Penning trap mass measurement of ${}^{36}$Ca
• Isobaric-multiplet mass equation in a macroscopic-microscopic approach
• Relativistic correction of the Coulomb interaction in the local density approximation for energies and radii in doubly-magic nuclei