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Recent measurement of the parity-violating (PV) asymmetry in the elasticelectron scattering on $^{27}$Al target evokes the interest in the distributionof the neutron in the nucleus. In this work, we calculate the neutron skinthickness ($R_{np}$) of $^{27}$Al with nonrelativistic nuclear structuremodels. We focus on the role of the effective mass, symmetry energy and pairingforce. Models are selected to have effective masses in the range $(0.58-1.05)M$where $M$ is the nucleon mass in free space, and stiffness of the symmetryenergy is varied by choosing the slope of the symmetry energy in the range 9.4-- 100.5 MeV. Effect of pairing force is investigated by calculating $R_{np}$with and without pairing, and using two different forms of the pairing force.With nine models, we obtain $R_{np} = 0.001 - 0.014$ fm. The result isindependent of the effective mass, symmetry energy, and the form of pairingforce. However, $R_{np}$ is negative when the pairing force is switched off, sothe pairing force plays an essential role to make $R_{np}$ positive andconstrained in a narrow range. We also calculate the PV asymmetry ($A_{\rmpv}$) in the elastic electron-$^{27}$Al scattering in the Born approximation atthe kinematics of the Qweak experiment. We obtain a very narrow-ranged result$A_{\rm pv} = $ (2.07 -- 2.09) $\times 10^{-6}$. The result is consistent withthe experiment and insensitive to the effective mass, symmetry energy andpairing force.

Neutron skin of $^{27}$Al with Skyrme and Korea-IBS-Daegu-SKKU density functionals