Proton-nucleus total reaction cross sections in the optical limit Glauber theory: Subtle dependence on the equation of state of nuclear matter

TL;DR

This study calculates proton-nucleus reaction cross sections using Glauber theory, revealing a subtle dependence on the nuclear matter equation of state, especially at lower energies and for neutron-rich isotopes.

Contribution

It introduces a detailed analysis of how the symmetry energy parameter L influences reaction cross sections within the optical limit Glauber framework.

Findings

Reaction cross section increases with L at ~40 MeV for neutron-rich isotopes.

At higher energies (~300 and 800 MeV), the cross section is nearly independent of L.

The exponential dependence on neutron skin thickness persists when proton-neutron cross sections are small.

Abstract

We calculate the proton-nucleus total reaction cross sections at different energies of incident protons within the optical limit approximation of the Glauber theory. The isospin effect has been taken into account. The nucleon distribution is obtained in the framework of macroscopic nuclear models in a way depending on the equation of state of uniform nuclear matter near the saturation density. We find that at an energy of order 40 MeV, the reaction cross section calculated for neutron- rich isotopes significantly increases as the parameter L characterizing the density dependence of the symmetry energy increases, while at energies of order 300 and 800 MeV, it is almost independent of L. This is a feature of the optical limit Glauber theory in which an exponential dependence of the reaction cross section on the neutron skin thickness remains when the total proton-neutron cross section is small enough.