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

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.

43 pages, 27 figures, submitted to EPJA (under review)

References in corpus (51)

• Towards a More Complete and Accurate Experimental Nuclear Reaction Data Library (EXFOR): International Collaboration Between Nuclear Reaction Data Centres (NRDC)
• Toward a global description of the nucleus-nucleus interaction
• Subbarrier fusion reactions and many-particle quantum tunneling
• Fusion and Direct Reactions of Halo Nuclei at Energies around the Coulomb Barrier
• Fusion versus Breakup: Observation of Large Fusion Suppression for ^9Be + ^{208}Pb
• Effect of continuum couplings in fusion of halo ${}^{11}$Be on ${}^{208}$Pb around the Coulomb barrier
• Role of break-up processes in fusion enhancement of drip-line nuclei at energies below the Coulomb barrier
• Transfer/Breakup Modes in the 6He+209Bi Reaction Near and Below the Coulomb Barrier
• How does breakup influence the total fusion of ${}^{6,7}$Li at the Coulomb barrier?
• Continuum-discretized coupled-channels method for four-body nuclear breakup in ${}^6$He+${}^{12}$C scattering
• Effect of the break-up on the fusion and elastic scattering of weakly bound projectiles on ${}^{64}$Zn
• Large-angle scattering and quasi-elastic barrier distributions
• Four-body continuum-discretized coupled-channels calculations using a transformed harmonic oscillator basis
• Elastic Scattering and Total Reaction Cross Section for the 6He + 27Al System
• Recent experimental results in sub- and near-barrier heavy ion fusion reactions
• Nuclear and Coulomb Interaction in the 8B to 7Be + p Breakup Reaction at sub-Coulomb Energies
• Reexamining closed-form formulae for inclusive breakup: Application to deuteron and ${}^6$Li induced reactions
• Influence of projectile <alpha>- breakup threshold on complete fusion
• New treatment of breakup continuum in the method of continuum discretized coupled channels
• Improved di-neutron cluster model for 6He scattering
• Four-body continuum-discretized coupled-channels calculations
• Toward a complete theory for predicting inclusive deuteron breakup away from stability
• Fusion of ${}^6$Li with ${}^{159}$Tb} at near barrier energies
• Systematic study of breakup effects on complete fusion at energies above the Coulomb barrier
• Continuum-Discretized Coupled-Channels calculations with core excitation
• Unbound excited states in 19,17C
• The study of threshold behaviour of effective potential for ${}^6$Li+${}^{58,64}$Ni systems
• Numerical assessment of post-prior equivalence for inclusive breakup reactions
• Texas Active Target (TexAT) detector for experiments with rare isotope beams
• Breakup of ${}^{17}$F on ${}^{208}$Pb near the Coulomb barrier
• Unraveling the reaction mechanisms leading to partial fusion of weakly bound nuclei
• Reaction and proton-removal cross sections of ${}^6$Li, ${}^7$Be, ${}^{10}$B, ${}^{9,10,11}$C, $^{12$N, ${}^{13,15}$O and ${}^{17}$Ne on Si at 15 to 53 MeV/nucleon
• Core excitation in the elastic scattering and breakup of ${}^{11}$Be on protons
• Understanding fusion and its suppression for the ${}^9$Be projectile with different targets
• Fusion reactions with the one-neutron halo nucleus 15C
• Elastic scattering and breakup of 17^F at 10 MeV/nucleon
• Exploring continuum structures with a pseudo-state basis
• Breakup mechanisms in the 6He+64Zn reaction at near-barrier energies
• Interplay of projectile breakup and target excitation in reactions induced by weakly-bound nuclei
• Approximate transmission coefficients in heavy ion fusion
• Fusion of Borromean nucleus ${}^9$Be with ${}^{197}$Au target at near barrier energies
• Four-body continuum effects in 11Be+d scattering
• Semiclassical calculations of complete and incomplete fusion in collisions of weakly bound nuclei
• Improved WKB approximation for quantum tunneling: Application to heavy ion fusion
• Evidence of strong dynamic core excitation in ${}^{19}$C resonant break-up
• Fusion reaction of halo nuclei: A real-time wave-packet method for three-body tunneling dynamics
• Extracting three-body breakup observables from CDCC calculations with core excitations
• 9Be scattering with microscopic wave functions and the CDCC method
• Derivation of reaction cross sections from experimental elastic backscattering probabilities
• Assessing the adequacy of the bare optical potential in near-barrier fusion calculation
• Two-step nuclear reactions: The Surrogate Method, the Trojan Horse Method and their common foundations

Cited by in corpus (8)

• Coupled-channels calculations for nuclear reactions: from exotic nuclei to superheavy elements
• Elastic scattering measurements for the ${}^{10}$C + ${}^{208}$Pb system at E${}_{\mathrm{lab}}$ = 66 MeV
• Systematic study of fusion barrier characteristics within the relativistic mean-field formalism
• Medium dependent relativistic NN potential: Application to the fusion dynamics
• Nuclear incompressibility and its enduring impact on fusion cross-section
• Role of nuclear deformation and orientation about symmetry axis of target nucleus on heavy-ion fusion dynamics
• Breakup dynamics of a neutron-halo projectile on heavy target at deep sub-barrier energies
• Elastic scattering and total reaction cross sections of ${}^6$Li studied with a microscopic continuum discretized coupled channels model