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

TL;DR

This study calculates the neutron skin thickness of $^{27}$Al using various nuclear models, finding it is mainly influenced by pairing forces and consistent with experimental PV asymmetry measurements.

Contribution

It provides a detailed analysis of neutron skin thickness in $^{27}$Al with different nuclear models, highlighting the role of pairing forces and comparing PV asymmetry predictions with experiments.

Findings

Neutron skin thickness $R_{np}$ ranges from 0.001 to 0.014 fm.

Pairing force is essential for positive $R_{np}$ values.

PV asymmetry $A_{pv}$ is predicted as (2.07--2.09) $ imes 10^{-6}$, matching experimental data.

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 ($A_{\rm pv}$) 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_{\rm 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.