Precision Determination of the Neutral Weak Form Factor of ${}^{48}\mathrm{Ca}$

We report a precise measurement of the parity-violating (PV) asymmetry $A_{\mathrm{PV}}$ in the elastic scattering of longitudinally polarized electrons from ${}^{48}\mathrm{Ca}$. We measure $A_{\mathrm{PV}}=2668\pm 106(\mathrm{stat})\pm 40(\mathrm{syst})$ parts per billion, leading to an extraction of the neutral weak form factor $F_W(q=0.8733{\mathrm{fm}}^{-1})=0.1304\pm 0.0052(\mathrm{stat})\pm 0.0020(\mathrm{syst})$ and the charge minus the weak form factor $F_{\mathrm{ch}}-F_W=0.0277\pm 0.0055$. The resulting neutron skin thickness $R_n-R_p=0.121\pm 0.026(\exp )\pm 0.024(\mathrm{model})\mathrm{fm}$ is relatively thin yet consistent with many model calculations. The combined CREX and PREX results will have implications for future energy density functional calculations and on the density dependence of the symmetry energy of nuclear matter.

Figure 1

Measurements of $A_{\mathrm{PV}}$ with statistical uncertainty; each $\approx 40$ hour period includes two states with complementary HWP settings. The three run periods demarcate injector spin orientation reversals.

Figure 2

Difference between the charge and weak form factors of ${}^{48}\mathrm{Ca}$ (CREX) versus that of ${}^{208}\mathrm{Pb}$ (PREX-2) at their respective momentum transfers. The blue (red) data point shows the PREX-2 (CREX) measurements. The ellipses are joint PREX-2 and CREX 67% and 90% probability contours. The gray circles (magenta diamonds) are a range of relativistic (nonrelativistic) density functionals. For clarity, only some of these functionals are labeled (SI [39], SIII [51], SV-sym34 [54], TOV-min [55], and UNEDF1 [57]) The complete list is in Ref. [31].

Figure 3

The difference between the charge and weak form factors for ${}^{48}\mathrm{Ca}$ as a function of momentum transfer $q=\sqrt{Q^2}$. The curves show results for nonrelativistic (SI, SLY4, UNEDF0, UNEDF1) and relativistic (NL3) density functional models. The CREX measurement is indicated by a circle with the inner black error bar showing the contribution from statistics and the total experimental error bar in red.

Figure 4

(a) ${}^{48}\mathrm{Ca}$ weak minus charge rms radius versus charge minus weak form factor at the CREX momentum transfer. The CREX experimental value and uncertainty is shown (red square). The gray circles (magenta diamonds) show a range of relativistic (nonrelativistic) density functionals. (b) ${}^{48}\mathrm{Ca}$ neutron minus proton rms radius versus charge minus weak form factor.

Figure 5

${}^{48}\mathrm{Ca}$ neutron minus proton radius versus that for ${}^{208}\mathrm{Pb}$. The $\mathrm{PREX}\text{−}2+\mathrm{PREX}\text{−}1$ experimental result is shown as a blue square, while that for CREX is shown as a red square with the inner error bars indicating the experimental error and the outer error bars including the model error. The gray circles (magenta diamonds) show a variety of relativistic (nonrelativistic) density functionals. Coupled cluster [8] and dispersive optical model (DOM) predictions [72] are also shown.