The total reaction cross section of heavy-ion reactions induced by stable and unstable exotic beams: the low-energy regi
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Review
The total reaction cross section of heavy-ion reactions induced by stable and unstable exotic beams: the low-energy regime L. F. Canto1,a , V. Guimarães2 , J. Lubián3 , M. S. Hussein2,4,5 1
Instituto de Física, Universidade Federal do Rio de Janeiro, CP 68528, Rio de Janeiro, Brazil Instituto de Física, Universidade de São Paulo, Rua do Matão Nr. 1371, CEP 05508-090 São Paulo, SP, Brazil 3 Instituto de Física, Universidade Federal Fluminense, Av. Litoranea s/n, Gragoatá, 24210-340 Niterói, RJ, Brazil 4 Instituto de Estudos Avançados, Universidade de São Paulo C. P. 72012, 05508-970 São Paulo, SP, Brazil 5 Departamento de Física, Instituto Tecnológico de Aeronáutica, CTA, São José dos Campos, São Paulo, SP, Brazil
2
Received: 4 August 2020 / Accepted: 28 September 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Communicated by Nicolas Alamanos
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, 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 M. S. Hussein: Deceased a e-mail:
[email protected] (corresponding author)
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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 m
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