The total reaction cross section of heavy-ion reactions induced by stable and unstable exotic beams: The low-energy regime

TL;DR

This review comprehensively discusses methods for extracting and calculating the total reaction cross section in heavy-ion reactions involving stable and unstable exotic nuclei at low energies, including models, experimental techniques, and universal scaling approaches.

Contribution

It introduces a unified framework for analyzing total reaction cross sections, extending fusion data concepts to include direct reactions and unstable beams, with new methodologies like the quarter-point recipe and the Surrogate method.

Findings

The quarter-point angle provides a rapid estimate of the total reaction cross section.

Universal functions can describe total reaction cross sections across different systems.

The Surrogate method enables extraction of reaction cross sections from inclusive breakup data.

Abstract

In this review paper we present a detailed account of the extraction and the calculation of the total reaction cross section of strongly bound and weakly bound, stable and unstable, exotic, nuclei. We discuss the optical model and the more general coupled channels model of direct reactions. The effect of long-range absorption due to the coupling to excited states in the target and to the breakup continuum in the projectile is also discussed. The generalized optical theorem for charged particle scattering and the resulting sum-of differences method is then discussed. The so-called "quarter-point recipe" is discussed next, and the quarter-point angle is introduced as a simple and rapid mean to obtain the total reaction cross section. The last topic discussed is the reduction of the total reaction cross section that would allow a large body of data to sit on a single universal function. Such a universal function exists in the case of the fusion data, and the aim of this last topic of the review is to extend the fusion case to the total reaction, by adding the direct reaction contribution. Also discussed is the inclusive breakup cross section and how it can be used to extract the total reaction cross section of the interacting fragment with the target. This method is also known as the Surrogate method and represents a case of hybrid reactions. The sum of the integrated inclusive breakup cross section with the complete fusion cross section supplies the total fusion cross section. The main experimental methods to determine the total reaction cross section are also discussed, with emphasis in recent techniques developed to deal with reactions induced by unstable beams.