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

Abstract

Recent measurement of the parity-violating (PV) asymmetry in the elastic electron scattering on ${}^{27}$Al target evokes the interest in the distribution of the neutron in the nucleus. In this work, we calculate the neutron skin thickness ($R_{np}$) of ${}^{27}$Al with nonrelativistic nuclear structure models. We focus on the role of the effective mass, symmetry energy and pairing force. 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 symmetry energy 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 is independent of the effective mass, symmetry energy, and the form of pairing force. However, $R_{np}$ is negative when the pairing force is switched off, so the pairing force plays an essential role to make $R_{np}$ positive and constrained in a narrow range. We also calculate the PV asymmetry ($A_{\mathrm{pv}}$) in the elastic electron-${}^{27}$Al scattering in the Born approximation at the kinematics of the Qweak experiment. We obtain a very narrow-ranged result $A_{\mathrm{pv}}=$ (2.07 -- 2.09) $\times 10^{-6}$. The result is consistent with the experiment and insensitive to the effective mass, symmetry energy and pairing force.

Comments: 5 pages, 2 figures