Exploring sensitivity of charge-exchange ($p,n$) reactions to the neutron density distribution

Abstract

$Background:$ The determination of the nuclear neutron properties suffers from uncontrolled uncertainties, which attracted considerable attention recently, such as in the context of the PREX experiment. $Purpose:$ Our aim is to analyze the sensitivity of charge-exchange ($p,n$) reactions to the neutron density distribution ${\rho }_n$ and constrain the neutron characteristics in the nuclear structure models. $Method:$ By combing the folding and the mean-field models, the nucleon-nucleus ($NA$) potential can be obtained from the nuclear density distribution. Further, the ($p,p$) and ($p,n$) cross sections for ${}^{48}$Ca and ${}^{208}$Pb are calculated following the distorted-wave Born approximation (DWBA) method. $Results:$ Compared with the ($p,p$) cross section, the effects of ${\rho }_n$ variation on the ($p,n$) cross section are significant, which is due to the impact of isovector properties. Based on the global folding model analyses of data, it is found that ${}^{48}$Ca and ${}^{208}$Pb have relatively large neutron skin thickness $\Delta R_{np}$. $Conclusions:$ Results illustrate that the charge-exchange ($p,n$) reaction is a sensitive probe of ${\rho }_n$. The results in this paper can offer useful guides for future experiments of neutron characteristics.

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