Neutron skin impurity from Coulomb core polarization in $^{208}\text{Pb}$: Insights from PREX-II and validation via the $(^{3}\text{He}, t)$ isobaric analog state reaction

TL;DR

This paper examines Coulomb core-polarization effects in $^{208}$Pb and their influence on neutron skin measurements, validating findings with the $(^{3} ext{He}, t)$ reaction and proposing experimental extensions for improved accuracy.

Contribution

It introduces a detailed analysis of Coulomb core-polarization impact on neutron skin measurements and suggests extending existing experiments to better determine neutron skin thickness.

Findings

Coulomb boundary radius is crucial for neutron skin probing.

Core-polarization effects can introduce impurity into the neutron skin region.

Extending the $(^{3} ext{He}, t)$ reaction measurements can improve neutron skin accuracy.

Abstract

I investigate the effect of Coulomb core-polarization in $^{208}\text{Pb}$, highlighting its impact on uncertainties in neutron distribution measurements due to the discrepancy between neutron excess and neutron skin regions at the surface. This effect is validated using the $(^{3}\text{He}, t)$ isobaric analog state (IAS) reaction at 420 MeV. My findings reveal that the Coulomb boundary radius, where core-polarization becomes negligible, is critical for accurately probing the neutron skin region in the target nucleus. Consequently, I propose extending the $^{208}\text{Pb}(^{3}\text{He}, t)$IAS reaction experiment conducted by Zegers et al. [Phys. Rev. Lett. 99, 202501 (2007)] to measure cross sections up to 3$^\circ$ angles to more precisely determine the neutron skin thickness in $^{208}\text{Pb}$ from theoretical reaction analysis. Additionally, I observe that, under the assumption of a large neutron skin in $^{208}\text{Pb}$, as suggested by the PREX-II result, the core-polarization effect introduces impurity into the neutron skin region.