Determination of the Al 27 Neutron Distribution Radius from a Parity-Violating Electron Scattering Measurement
In this paper, we report the first measurement of the parity-violating elastic electron scattering asymmetry on 27 Al. The 27 Al elastic asymmetry is $A_{\text{PV}}$ = 2.16 ± 0.11(stat) ± 0.16(syst) ppm, and was measured at $\langle Q^2\rangle$ = 0.02357 ± 0.00010 GeV$^2$, $\angleθ_{\text{lab}}$ = 7.61° ± 0.02°, and $\langle E_{\text{lab}}$ = 1.157 GeV with the Q weak apparatus at Jefferson Lab. Predictions using a simple Born approximation as well as more sophisticated distorted-wave calculations are in good agreement with this result. From this asymmetry the 27 Al neutron radius $R_n$ = 2.89 ± 0.12 fm was determined using a many-models correlation technique. The corresponding neutron skin thickness $R_n – R_p$ = –0.04 ± 0.12 fm is small, as expected for a light nucleus with a neutron excess of only 1. This result thus serves as a successful benchmark for electroweak determinations of neutron radii on heavier nuclei. A tree-level approach was used to extract the 27 Al weak radius $R_w$ = 3.00 ± 0.15 fm, and the weak skin thickness $R_{\text{wk}} – R_{\text{ch}}$ = –0.04 ± 0.15 fm. The weak form factor at this $Q^2$ is $F_{\text{wk}}$ = 0.39 ± 0.04.