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, 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. 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.

Elastic scattering and breakup reactions of the proton drip-line nucleus B8 on Pb208 at 238 MeV

“…The nature of these channels can be very different depending on the structure of the colliding nuclei. Whereas in the case of stable, well bound nuclei cou-plings to collective excitations of the projectile and/or target nuclei (such as quadrupole and octupole couplings) play a major role [4][5][6], in the case of weakly bound nuclei other modes gain relevance, such as transfer and breakup modes, due to the very low binding energies and extended spatial distributions of the valence particles in these nuclei [7]. For 11 Li and 11 Be the breakup can be considered mainly responsible for the large total reaction cross sections [8][9][10][11], while for 6,8 He the transfer reaction is mainly responsible for the enhancement of total reaction cross sections [12][13][14][15][16].…”

“…For weakly bound nuclei in the proton-rich side, such as 8 B, the situation is less clear. With a separation energy of S p = 0.136 MeV, 8 B is a proton halo nucleus, which has a cluster configuration of an inert 7 Be core and a valence proton occupying the p-wave orbital. The spatial extension and cluster configuration of the 8 B nucleus are rather important for describing the elastic and breakup reaction channels.…”

“…The spatial extension and cluster configuration of the 8 B nucleus are rather important for describing the elastic and breakup reaction channels. The structure of this nucleus is also very important in astrophysics since the radioactive capture 7 Be(p, γ ) 8 B reaction plays a major role in the production of high-energy neutrinos in the standard solar model [20][21][22]. The first measurement of the 8 B matter radius, which yielded a root-mean-square (rms) value of R rms = 2.38(4) fm, was based on the interaction cross sections [23].…”

Elastic scattering angular distributions of neutron halo nucleus $$^{11}$$Be studied via dynamic polarization potentials

“…This is especially relevant for nuclei that are far away from the β-stability line, which are usually weakly bound and are modeled as composed of clusters of core nuclei and valence particles. Because of the weakly bound nature, these nuclei are easily broken up during their collisions with the other nuclei, and the breakup channels can have strong coupling effects to the other reaction chana e-mail: dypang@buaa.edu.cn (corresponding author) nels, such as nuclear fusion, transfer reactions and elastic scattering [1][2][3][4][5][6].…”

“…It is well-known that the Coulomb-nuclear interference peaks, which are typically seen in the differential cross sections of heavy ion elastic scattering from a medium-mass or heavy target, disappear with some neutron rich nuclei, such as 6 He [7,8], 11 Li [9], and 11 Be [10][11][12][13]. Such phenomena have been found to be due mainly to the coupling effects from the breakup channels and have been successfully described by the continuum discretized coupled channel (CDCC) method or the extended CDCC method (XCDCC) which takes into account the effect of core excitation.…”