Role of breakup processes in fusion enhancement of drip-line nuclei at energies below the Coulomb barrier

Abstract

We carry out realistic coupled-channels calculations for 11 Be + 208 Pb reaction in order to discuss the effects of break-up of the projectile nucleus on sub-barrier fusion. We discretize in energy the particle continuum states, which are associated with the break-up process, and construct the coupling form factors to these states on a microscopic basis. The incoming boundary condition is employed in solving coupled-channels equations, which enables us to define the flux for complete fusion inside the Coulomb barrier. It is shown that complete fusion cross sections are significantly enhanced due to the couplings to the continuum states compared with the no coupling case at energies below the Coulomb barrier, while they are hindered at above barrier energies.Quantum tunneling in systems with many degrees of freedom [1] has attracted much interest in recent years in many fields of physics and chemistry [2]. In nuclear physics, heavy-ion fusion reactions at energies near and below the Coulomb barrier are typical examples for this phenomenon. In order for fusion processes to take place, the Coulomb barrier created by the cancellation between the repulsive Coulomb force and the attractive nuclear interaction has to be overcome. It has by now been well established that the coupling of the relative motion of the colliding nuclei to nuclear intrinsic excitations as well as to transfer reaction channels cause large enhancements of the fusion cross section at subbarrier energies over the predictions of a simple barrier penetration model [3].The effect of break-up processes on fusion, on the other hand, has not yet been understood very well, and many questions have been raised during the last few years both from the experimental [4][5][6][7][8] and theoretical [9-12] points of view. The issue has become especially relevant in recent years due to the increasing availability of radioactive beams. These often involve weakly-bound systems close to the drip lines for which the possibility of projectile dissociation prior to or at the point of contact cannot be ignored. Different theoretical approaches to the problem have led to controversial results, not only quantitatively but also qualitatively. The probability for fusion at energies below the barrier has been in fact predicted to be either reduced [9,10] or enhanced [11,12] by the coupling to the continuum states.These investigations, however, were not satisfactory in view of the rather simplified assumptions used in the treatment of both the structure and reaction aspects of the problem.

Low-energy fusion dynamics of weakly bound nuclei: A time dependent perspective

“…A few wave-packet propagations allows one to calculate the converged ICF excitation function in a broad range of incident energies. In contrast to the usual CDCC fusion calculations [17][18][19], this ICF excitation function includes ICF from the projectile bound state(s) [20].…”

Nuclear reactions studied by quasi-elastic measurements with high precision at backward angles

“…Fig. 8 shows the excitation functions of elastic, quasielastic, breakup, and quasi-elastic plus breakup for the 6,7 Li+ 208 Pb systems. The theoretical calculations by the ECIS code [35] are also shown in the figure for reference.…”

“…Guiding by the above thought, the quasi-elastic scatterings for the weakly-bound systems 6,7 Li, 9 Be+ 208 Pb were measured at backward angles with high precision. Fig.…”

“…However, large numbers of open questions still remain to be solved, for instance, i) the surface diffuseness anomaly in interaction potential [1][2][3], ii) the coupled-channels effects of neutron transfers with positive Q value [4][5][6], iii) the breakup effects of weakly-bound nuclei on the fusion processes [7][8][9][10], and so on. Quasi-elastic scatterings and fusion reactions are complementary processes because they undergo the same interaction potential and share the mutual information on the reaction mechanism.…”

Fusion and breakup in the reactions of 6,7Li and 9Be

“…Process (ii) is referred to as an incomplete fusion reaction, while both of processes (i) and (iii) lead to complete fusion. Calculations based on the continuum-discretized coupled-channels method may account for the total fusion cross section (the sum of all the processes) and/or the separate contribution of process (i) [ 5,6], but it is not easy to compute cross sections for process (iii), that is, the breakup followed by complete fusion. In order to model this process, we need to follow the trajectories of the breakup fragments to determine whether one or both fragments are captured by the target nucleus.…”