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Resolving the PREX-CREX puzzle in covariant density functional theory

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

Abstract

The PREX-CREX puzzle, an apparent tension between parity-violating electron-scattering results for $^{208}$Pb and $^{48}$Ca revealed by modern density functional analyses, has posed a major challenge for nuclear theory. We show that this puzzle can be resolved within covariant density-dependent point-coupling density functional theory by introducing an enhanced isovector tensor coupling. A nonrelativistic reduction identifies the resulting strong isovector spin-orbit interaction as the key mechanism that reconciles the PREX and CREX measurements.

Resolving the PREX-CREX puzzle in covariant density functional theory

Abstract

The PREX-CREX puzzle, an apparent tension between parity-violating electron-scattering results for Pb and Ca revealed by modern density functional analyses, has posed a major challenge for nuclear theory. We show that this puzzle can be resolved within covariant density-dependent point-coupling density functional theory by introducing an enhanced isovector tensor coupling. A nonrelativistic reduction identifies the resulting strong isovector spin-orbit interaction as the key mechanism that reconciles the PREX and CREX measurements.

Paper Structure

This paper contains 4 equations, 3 figures, 1 table.

Figures (3)

  • Figure 1: Predicted charge-weak form-factor differences $\Delta F_{\mathrm{CW}}^{48}$ and $\Delta F_{\mathrm{CW}}^{208}$ for $^{48}\mathrm{Ca}$ and $^{208}\mathrm{Pb}$ from the three newly constructed covariant EDFs: ZH-1, ZH-2, and ZH-3 (open stars). For comparison, results from PCF-PK1 Zhao:2022xhq (diamonds), other covariant EDFs CREX:2022kgg (squares), and nonrelativistic Skyrme-like EDFs CREX:2022kggYue:2021yfx (circles) are also shown. The solid (dashed) ellipse indicates the joint $67\%$ ($90\%$) confidence contour from the PREX-II and CREX measurements. Experimental values are shown with error bars, corresponding to $\Delta F_{\mathrm{CW}}^{208}(q=0.3977~\mathrm{fm}^{-1}) = 0.041 \pm 0.013$ from PREX-II PREX:2021umo and $\Delta F_{\mathrm{CW}}^{48}(q=0.8733~\mathrm{fm}^{-1}) = 0.0277 \pm 0.0055$ from CREX CREX:2022kgg.
  • Figure 2: The charge (solid lines) and weak (dashed lines) radial density distributions in $^{48}\mathrm{Ca}$ (a) and $^{208}\mathrm{Pb}$ (b) predicted by ZH-1 (red), ZH-2 (purple), ZH-3 (blue), and PCF-PK1 (green). Experimental charge densities DEVRIES1987495 are shown as open circles.
  • Figure 3: Radial dependence of the isoscalar and isovector spin-orbit strength parameters, $b_{\mathrm{IS}}$ (top panels) and $b_{\mathrm{IV}}$ (middle panels), together with their ratio (bottom panels) in $^{48}$Ca, obtained from the nonrelativistic reduction of the ZH-1 (red), ZH-2 (purple), ZH-3 (blue), and PCF-PK1 (green) covariant EDFs. Dashed lines labeled “w/o IST (w/o IVT)” denote the results obtained without the corresponding tensor terms. The shaded region in the bottom panels indicate the nucleon density distributions in $^{48}$Ca.