Nuclear isospin mixing and elastic parity-violating electron scattering

TL;DR

This paper investigates how nuclear isospin mixing affects parity-violating elastic electron scattering in certain N=Z nuclei, using advanced mean-field models and comparing different approximations to inform future experiments.

Contribution

It provides a detailed analysis of isospin mixing effects on parity-violating asymmetries using self-consistent mean-field calculations and compares results with shell-model approaches.

Findings

Differences from shell-model calculations in isovector Coulomb form factors.

Expanded results in a spherical harmonic oscillator basis.

Comparison of plane-wave and distorted-wave Born approximations.

Abstract

The influence of nuclear isospin mixing on parity-violating elastic electron scattering is studied for the even-even, N=Z nuclei 12C, 24Mg, 28Si, and 32S. Their ground-state wave functions have been obtained using a self-consistent axially-symmetric mean-field approximation with density-dependent effective two-body Skyrme interactions. Some differences from previous shell-model calculations appear for the isovector Coulomb form factors which play a role in determining the parity-violating asymmetry. To gain an understanding of how these differences arise, the results have been expanded in a spherical harmonic oscillator basis. Results are obtained not only within the plane-wave Born approximation, but also using the distorted-wave Born approximation for comparison with potential future experimental studies of parity-violating electron scattering. To this end, for each nucleus the focus is placed on kinematic ranges where the signal (isospin-mixing effects on the parity-violating asymmetry) and the experimental figure-of-merit are maximized. Strangeness contributions to the asymmetry are also briefly discussed, since they and the isospin mixing contributions may play comparable roles for the nuclei being studied at the low momentum transfers of interest in the present work.