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

Tong-Gang Yue, Zhen Zhang, Lie-Wen Chen

Abstract

The nucleon spin-orbit interaction is a cornerstone of modern nuclear theory, yet its isospin dependence remains elusive due to the lack of clean experimental probes. It has been recently demonstrated that within Skyrme-like energy density functionals, the charge-weak form factor difference $ΔF_{\rm CW}$ in $^{48}$Ca exhibits remarkable sensitivity to the isovector spin-orbit (IVSO) interaction, and that a significantly enhanced IVSO strength can resolve the PREX-CREX puzzle. Extending this analysis to other nuclei, we identify that $^{90}$Zr, with its ten spin-orbit unpaired $1\mathrm{g}_{9/2}$ neutrons, displays a $ΔF_{\text{CW}}$ 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, $^{208}$Pb and $^{62}$Ni remain largely insensitive to the IVSO interaction. Furthermore, this structure-driven distinction suggests a distinct experimental strategy: future parity-violating electron scattering measurements on $^{48}$Ca and $^{90}$Zr would enable a more precise determination of the IVSO strength, while measurements on $^{208}$Pb and $^{62}$Ni can serve as purer constraints on the symmetry energy slope.

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

Abstract

The nucleon spin-orbit interaction is a cornerstone of modern nuclear theory, yet its isospin dependence remains elusive due to the lack of clean experimental probes. It has been recently demonstrated that within Skyrme-like energy density functionals, the charge-weak form factor difference in Ca exhibits remarkable sensitivity to the isovector spin-orbit (IVSO) interaction, and that a significantly enhanced IVSO strength can resolve the PREX-CREX puzzle. Extending this analysis to other nuclei, we identify that Zr, with its ten spin-orbit unpaired neutrons, displays a sensitivity to the IVSO strength similar to that of Ca, arising from modifications to the central mean-field potential rather than the one-body spin-orbit potential. In contrast, Pb and Ni remain largely insensitive to the IVSO interaction. Furthermore, this structure-driven distinction suggests a distinct experimental strategy: future parity-violating electron scattering measurements on Ca and Zr would enable a more precise determination of the IVSO strength, while measurements on Pb and Ni can serve as purer constraints on the symmetry energy slope.
Paper Structure (11 sections, 21 equations, 3 figures, 1 table)

This paper contains 11 sections, 21 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methods
  3. Extended Skyrme EDF within Hartree-Fock-Boguliubov (HFB) theory
  4. Charge and weak form factors
  5. Results
  6. Single-particle energy spectrum of $\rm ^{48}Ca$ and $\rm ^{208}Pb$
  7. Sensitivity of $\Delta F_{\rm CW}$ to the IVSO interaction for $^{48}$Ca, $^{208}$Pb, $^{90}$Zr, and $^{62}$Ni
  8. $^{48}$Ca and $^{208}$Pb
  9. $^{90}$Zr and $^{62}$Ni
  10. Neutron skin $R_{\rm np}$ of $^{48}$Ca, $^{208}$Pb, $^{90}$Zr, $^{62}$Ni, $^{22}$O and $^{24}$O
  11. Conclusions

Figures (3)

  • Figure 1: Single-particle energy levels for $^{48}$Ca and $^{208}$Pb. Panel (a) shows neutron levels in $^{48}$Ca; panels (b)-(d) display proton levels in $^{48}$Ca, neutron levels in $^{208}$Pb, and proton levels in $^{208}$Pb, respectively.
  • Figure 2: Orbital contributions to $F_{\rm C}$ and $F_{\rm W}$ obtained with the eS53 and eS250 EDFs. Panels (a) and (c) show the contributions to $F_{\rm C}$ and $F_{\rm W}$ for $^{90}$Zr, respectively. Panels (b) and (d) show the corresponding results for $^{62}$Ni. The analyzed orbitals (from left to right) include $1{\rm s}_{1/2}$, $1{\rm p}_{3/2}$, $1{\rm p}_{1/2}$, $1{\rm d}_{5/2}$, $1{\rm d}_{3/2}$, $2{\rm s}_{1/2}$, $1{\rm f}_{7/2}$, $1{\rm f}_{5/2}$, $2{\rm p}_{3/2}$, $2{\rm p}_{1/2}$, and $1{\rm g}_{9/2}$, both for $^{90}$Zr and $^{62}$Ni.
  • Figure 3: Momentum-transfer dependence of $\Delta F_{\rm CW}$ for various nuclei. Panels (a)-(d) show the results for $^{48}$Ca, $^{208}$Pb, $^{90}$Zr, and $^{62}$Ni, respectively, as functions of the momentum transfer $q$ (in fm$^{-1}$). For comparison, the CREX and PREX-II data CREX:2022kgg (with one sigma uncertainty) are also included in panels (a) and (b), respectively.