Reaction Cross Section in Heavy-Ion Collisions

TL;DR

This paper derives and refines a compact formula for calculating total reaction cross sections in heavy-ion collisions, assessing its accuracy and providing practical rules for experimental data analysis.

Contribution

It introduces a corrected, more accurate formula for reaction cross sections and practical methods to determine barrier heights and penetration probabilities from experimental data.

Findings

The continuum approximation's accuracy is evaluated and improved.

A simple modification enhances the formula's precision.

Rules for extracting barrier heights from experimental data are provided.

Abstract

Previously a compact formula for total reaction cross section for heavy-ion collisions as a function of energy was obtained by treating the angular momentum $l$ as a continuous variable. The accuracy of the continuum approximation is assessed and corrections are evaluated. The accuracy of the compact equation can be improved by a simple modification, if a higher accuracy is required. Simple rules to determine the barrier heights and the penetration probability for the $l$ partial wave from experimental data are presented, for the collision of identical or non-identical light nuclei.