Scaling properties of proton-nucleus total reaction cross sections

TL;DR

This paper investigates the scaling behavior of proton-nucleus total reaction cross sections and proposes an approximate formula that allows accurate predictions for stable nuclei based on known cross sections.

Contribution

It introduces a new approximate expression for proton-nucleus reaction cross sections based on nuclear Z and N, enabling predictions with about 10% accuracy.

Findings

The proposed formula correlates well with experimental data.

Predictions for stable nuclei are accurate within 10%.

The scaling law simplifies cross section estimations across nuclei.

Abstract

We study the scaling properties of proton-nucleus total reaction cross sections for stable nuclei and propose an approximate expression in proportion to Z^{2/3}\sigma_{pp}^{total} + N^{2/3} \sigma_{pn}^{total}. Based on this expression, we can derive a relation that enables us to predict a total reaction cross section for any stable nucleus within 10% uncertainty at most, using the empirical value of the total reaction cross section of a given nucleus.