Energy and mass-number dependence of hadron-nucleus total reaction cross sections

TL;DR

This paper introduces a black-sphere model to analyze proton-nucleus reactions, revealing a crucial A^{1/6} dependence in total reaction cross sections and providing a unified length scale for elastic and reaction data.

Contribution

It develops a phenomenological black-sphere approximation that links nuclear size to reaction cross sections and elastic diffraction, highlighting the importance of A^{1/6} dependence.

Findings

Black-sphere radius correlates with reaction and diffraction data.

A^{1/6} dependence is key to energy variation of cross sections.

Model applicable to various strongly attenuated projectiles.

Abstract

We systematically analyze nuclear reaction data that are sensitive to nuclear size, namely, proton-nucleus total reaction cross sections and differential elastic cross sections, using a phenomenological black-sphere approximation of nuclei that we are developing. In this framework, the radius of the black sphere is found to be a useful length scale that simultaneously accounts for the observed proton-nucleus total reaction cross section and first diffraction peak in the proton elastic differential cross section. This framework is expected to be applicable to any kind of projectile that is strongly attenuated in the nucleus. On the basis of a cross-section formula constructed within this framework, we find that a less familiar $A^{1/6}$ dependence plays a crucial role in describing the energy dependence of proton-nucleus total reaction cross sections.