First Determination of the $^{27}$Al Neutron Distribution Radius from a Parity-Violating Electron Asymmetry Measurement

The $Q_{weak}$ collaboration has made the first measurement of the parity-violating elastic electron-$^{27}$Al scattering asymmetry, an electroweak observable, using a spectrometer with an approximate energy acceptance of 150 MeV. This is a unique measurement as $^{27}$Al is a s-d shell nucleus with a $J^{p} = 5/2^{+}$ ground state, which is difficult to model compared to the doubly magic (closed shell) $J^{p} = 0^{+}$ ground state nuclei from similar experiments. The previous PREx and the upcoming PRExII and CREx experiments have used or plan to use these easier-to-model nuclei, $^{208}$Pb and $^{48}$Ca. The original intent of this measurement was as a background correction for the weak charge measurement of the proton. However, a 2014 paper outlined the possibility of extracting the $^{27}$Al neutron distribution radius from the elastic parity-violating asymmetry as a test of theoretical models. This elastic asymmetry can be extracted from this background measurement by correcting for known asymmetries that arise from non-elastic scattering processes. Presented here is a discussion of the analysis required to extract this asymmetry and the neutron distribution radius, along with its impact on theoretical models for lighter non-closed shell nuclei.