Relating Breakup and Incomplete Fusion of Weakly Bound Nuclei through a Classical Trajectory Model with Stochastic Breakup

Abstract

A classical dynamical model that treats breakup stochastically is presented for low energy reactions of weakly bound nuclei. The three-dimensional model allows a consistent calculation of breakup, incomplete, and complete fusion cross sections. The model is assessed by comparing the breakup observables with continuum discretized coupled-channel quantum mechanical predictions, which are found to be in reasonable agreement. Through the model, it is demonstrated that the breakup probability of the projectile as a function of its distance from the target is of primary importance for understanding complete and incomplete fusion at energies near the Coulomb barrier. DOI: 10.1103/PhysRevLett.98.152701 PACS numbers: 25.70.Jj, 25.70.Mn Recent developments of radioactive isotope accelerators provide an opportunity to investigate on Earth the fusion reactions that form heavy elements in the cosmos. These involve reactions of nuclei far from stability, the most exotic of which are often very weakly bound. Breakup of weakly bound nuclei is thus an important process in their collisions with other nuclei. A major consequence of breakup is that not all the resulting breakup fragments might be captured by the target, termed incomplete fusion (ICF); capture of the entire projectile by the target is called complete fusion (CF). Such ICF processes can dramatically change the nature of the reaction products, as has been investigated in detail for the stable weakly bound nuclei 9 Be and 6;7 Li [1]. There, at energies above the fusion barrier, CF yields were found to be only 2=3 of those expected, the remaining 1=3 being in ICF products. Events where the projectile breaks up and none of the fragments are captured provide an important diagnostic of the reaction dynamics. This we call no-capture breakup (NCBU), also referred to as elastic breakup.In a conventional picture of fusion, two colliding nuclei will fuse if they overcome the potential barrier due to their mutual Coulomb and nuclear interactions. The additional breakup degrees of freedom when one of the colliding nuclei is weakly bound makes the process very much more complicated. An outstanding theoretical challenge is to model the CF and ICF processes in such collisions, since this separation is crucial to understand the effects of breakup on fusion [1,2]. Quantum mechanical few-body approaches, such as the continuum discretized coupledchannel (CDCC) method [3,4] and the time-dependent wave packet method [5], cannot separate incomplete and complete fusion contributions to their absorptive cross sections [6], since both result in depletion of the total few-body wave function. The CDCC method can, however, make reliable predictions of the NCBU process [7], as will be exploited here. What, then, are the alternatives to the above models? A novel optical decoherence model has been suggested [6] but has yet to be implemented. Another approach is to use the concept of classical trajectories which allow CF and ICF events to be separated, as in the two-dimensional model of Ref. [8]...

Suppression of complete fusion due to breakup in the reactionsB10,11+Bi209

“…To address this problem, a threedimensional classical dynamical model was recently developed [8], allowing the calculation of CF and ICF cross sections at energies above the fusion barrier. The model relates above-barrier CF and ICF yields with belowbarrier no-capture breakup, where the Coulomb barrier inhibits capture of charged fragments by the target nucleus.…”

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

“…Based on those trajectories, probabilities and (integrated and differential) cross sections are constructed. The PLATY-PUS model connects the sub-Coulomb breakup process to the above-barrier CF and ICF processes [3,4]. Figure 2 shows the above-barrier CF excitation function for 7 Li + 198 Pt (solid curve).…”

“…This approach has been developed in close collaboration with experimenters [3,4]. The model is implemented in the PLATYPUS code [5].…”

“…Other probability densities are employed in the PLATYPUS model, which can be found in Refs. [3,4]. The final destination of the projectile fragments (captured or non-captured by the target) is determined solving classical equations of motion.…”

Coupled-Channel Effects in Collisions Between Heavy Ions Near the Coulomb Barrier

“…We con- clude that the flux diverted from complete fusion to incomplete fusion would arise essentially from DBU processes via high-lying continuum (non-resonant) states of 6 Li; this is due to the fact that both the SBU mechanism and the low-lying DBU processes from low-lying resonant 6 Li states occur at large internuclear distances [39,40,41]. Work is in progress to study incomplete fusion for 6 Li+ 59 Co within a newly developed 3-dimensional classical trajectory model [51].…”