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, and how from fits to the data on elastic scattering supplies the elastic element of (partial wave) S-matrix and correspondingly the differential cross section and the total reaction cross section. 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 semiclassical method is then analyzed and the Hill–Wheeler expression of the tunneling probability and the Wong formula for the fusion and the total reaction cross sections are discussed in details. The generalized optical theorem for charged particle scattering and the resulting sum-of differences method is then discussed. Also, the strong absorption model in its sharp cutoff form and its generalization, the smooth cutoff, is 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. A review of the experimental methods and techniques used to measure elastic scattering and breakup reactions is also presented. Emphasis is given to recent experiments and new techniques developed to deal with reactions induced by unstable beams. We discuss also the experimental challenges in these measurements and highlight the new techniques being developed to optimize measurements with radioactive ion beams.

在这篇综述文章中，我们详细介绍了强结合和弱结合，稳定和不稳定，奇异核的提取和总反应截面的计算。我们讨论了直接反应的光学模型和更一般的耦合通道模型，以及如何通过拟合弹性散射数据来提供（部分波）S矩阵的弹性元素，以及相应的微分截面和总反应截面。还讨论了由于耦合到目标中的激发态和弹丸中的破坏连续体而引起的远距离吸收的影响。然后分析了半经典方法，详细讨论了隧道概率的Hill-Wheeler表达式以及融合和总反应截面的Wong公式。然后讨论了带电粒子散射的广义光学定理和由此产生的差之和方法。此外，还讨论了其锐利截止形式的强吸收模型及其推广，即光滑截止。接下来讨论所谓的“四分之一点配方”，并且将四分之一点角作为一种简单而快速的方法引入以获得总反应截面。讨论的最后一个主题是减少总反应截面，这将使大量数据位于单个通用函数上。在融合数据的情况下存在这样的通用函数，并且本综述的最后一个主题是通过添加直接反应贡献将融合情况扩展到总反应。还讨论了包容性分解截面以及如何将其用于提取与目标分子相互作用的片段的总反应截面。该方法也称为替代方法，代表杂交反应的情况。完整的融合横截面与完整的融合破裂横截面之和提供了总融合横截面。还介绍了用于测量弹性散射和破裂反应的实验方法和技术。重点放在最近的实验和开发的新技术上，以处理由不稳定光束引起的反应。我们还将讨论这些测量中的实验挑战，并重点介绍为优化放射性离子束测量而开发的新技术。