Isospin Non-Conservation in $sd$-Shell Nuclei

TL;DR

This paper develops a new shell-model Hamiltonian to accurately describe isospin-symmetry breaking in sd-shell nuclei, explaining mass splittings, the IMME coefficients, and Fermi decay corrections with high precision.

Contribution

A novel global parameterization of the INC shell-model Hamiltonian that incorporates Coulomb and nuclear charge-dependent forces, including short-range correlations, for improved accuracy.

Findings

Accurately describes isobaric mass splittings in sd-shell nuclei.

Provides high-precision modeling of the IMME staggering effect.

Calculates nuclear structure corrections to superallowed Fermi beta decay.

Abstract

The question of isospin-symmetry breaking in nuclei of the $sd$ shell is addressed. We propose a new global parameterization of the isospin-nonconserving (INC) shell-model Hamiltonian which accurately describes experimentally known isobaric mass splittings. The isospin-symmetry violating part of the Hamiltonian consists of the Coulomb interaction and effective charge-dependent forces of nuclear origin. Particular attention has been paid to the effect of the short-range correlations. The behavior of $b$ and $c$ coefficients of the isobaric-mass-multiplet equation (IMME) is explored in detail. In particular, a high-precision numerical description of the staggering effect is proposed and contribution of the charge-dependent forces to the nuclear pairing is discussed. The Hamiltonian is applied to the study of the IMME beyond a quadratic form in the A=32 quintet, as well as to calculation of nuclear structure corrections to superallowed $0^+ \to 0^+$ Fermi $\beta$ decay, and to amplitudes of Fermi transitions to non-analogue states in sd-shell nuclei.