Effects of isovector spin-orbit interaction on the charge-weak form factor difference in $^{48}$Ca, $^{208}$Pb, $^{90}$Zr and $^{62}$Ni

TL;DR

This study investigates how the isovector spin-orbit interaction influences the charge-weak form factor differences in various nuclei, proposing experimental measurements to better constrain nuclear interaction models.

Contribution

It reveals that certain nuclei's form factor differences are sensitive to the IVSO interaction, suggesting targeted experiments to constrain this aspect of nuclear energy density functionals.

Findings

$^{90}$Zr shows similar sensitivity to $^{48}$Ca in $ riangle F_{CW}$ due to IVSO.

$^{62}$Ni and $^{208}$Pb are largely insensitive to IVSO effects.

Future experiments on $^{48}$Ca and $^{90}$Zr can constrain IVSO strength.

Abstract

The nucleon spin-orbit interaction is a cornerstone of nuclear structure theory, yet its isospin dependence remains insufficiently constrained within modern nuclear energy density functional (EDF) theory. It was recently shown that, within the framework of extended Skyrme EDFs, the charge-weak form factor difference $\Delta F_{\rm CW}$ in $^{48}$Ca exhibits remarkable sensitivity to the effective isovector spin-orbit (IVSO) interaction, whereas $\Delta F_{\rm CW}$ in $^{208}$Pb is much less sensitive to this channel. Extending this analysis to other nuclei, we find that $^{90}$Zr, with its ten spin-orbit unpaired $1\mathrm{g}_{9/2}$ neutrons, displays a $\Delta F_{\rm CW}$ sensitivity to the IVSO strength similar to that of $^{48}$Ca, arising from modifications to the central mean-field potential rather than the one-body spin-orbit potential. In contrast, $^{62}$Ni, like $^{208}$Pb, remains largely insensitive to the IVSO interaction. This structure-driven distinction suggests an experimental strategy: future parity-violating electron scattering measurements, e.g., the MREX experiment at the MESA facility, on $^{48}$Ca and $^{90}$Zr would help constrain the effective IVSO strength, while measurements on $^{208}$Pb and $^{62}$Ni can provide a cleaner probe of the density dependence of the symmetry energy with reduced IVSO sensitivity.