We report the first measurement of the parity-violating elastic electron scattering asymmetry on ${}^{27}\mathrm{Al}$. The ${}^{27}\mathrm{Al}$ elastic asymmetry is $A_{\mathrm{PV}}=2.16\pm 0.11(\mathrm{stat})\pm 0.16(\text{syst})\mathrm{ppm}$, and was measured at $⟨Q^2⟩=0.02357\pm 0.00010{\mathrm{GeV}}^2$, $⟨{\theta }_{\mathrm{lab}}⟩=7.61°\pm 0.02°$, and $⟨E_{\mathrm{lab}}⟩=1.157\mathrm{GeV}$ with the ${\mathrm{Q}}_{\mathrm{weak}}$ 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 ${}^{27}\mathrm{Al}$ neutron radius $R_n=2.89\pm 0.12\mathrm{fm}$ was determined using a many-models correlation technique. The corresponding neutron skin thickness $R_n-R_p=-0.04\pm 0.12\mathrm{fm}$ 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 ${}^{27}\mathrm{Al}$ weak radius $R_w=3.00\pm 0.15\mathrm{fm}$, and the weak skin thickness $R_{\mathrm{wk}}-R_{\mathrm{ch}}=-0.04\pm 0.15\mathrm{fm}$. The weak form factor at this $Q^2$ is $F_{\mathrm{wk}}=0.39\pm 0.04$.

• Received 30 December 2021
• Accepted 2 March 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.132501