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The inclusive breakup of three-fragment projectiles is discussed within a four-body spectator model. Both the elastic breakup and the non-elastic breakup are obtained in a unified framework. Originally developed in the 80s for two-fragment projectiles such as the deuteron, in this paper the theory is successfully generalized to three-fragment projectiles. The expression obtained for the inclusive cross section allows the extraction of the incomplete fusion cross section, and accordingly generalizes the surrogate method to cases such as (t,p) and (t,n) reactions. It is found that two-fragment correlations inside the projectile affect in a conspicuous way the elastic breakup cross section. The inclusive non-elastic breakup cross section is calculated and is found to contain the contribution of a three-body absorption term that is also strongly influenced by the two-fragment correlations. This latter cross section contains the so-called incomplete fusion where more than one compound nuclei are formed. Our theory describes both stable weakly bound three-fragment projectiles and unstable ones such as the Borromean nuclei.
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The optical potential of halo and weakly bound nuclei has a long range part due to the coupling to breakup that damps the elastic scattering angular distributions. In order to describe correctly the breakup channel in the case of scattering on a heavy target, core recoil effects have to be taken into account. We show here that core recoil and nuclear breakup of the valence nucleon can be consistently taken into account. A microscopic absorptive potential is obtained within a semiclassical approach and its characteristics can be understood in terms of the properties of the halo wave function and of the reaction mechanism. Results for the case of medium to high energy reactions are presented.
We present a recently developed theory for the inclusive breakup of three-fragment projectiles within a four-body spectator model cite{CarPLB2017}, for the treatment of the elastic and inclusive non-elastic break up reactions involving weakly bound three-cluster nuclei in $A,(a,b),X$ / $a = x_1 + x_2 + b$ collisions. The four-body theory is an extension of the three-body approaches developed in the 80s by Ichimura, Autern and Vincent (IAV) cite{IAV1985}, Udagawa and Tamura (UT) cite{UT1981} and Hussein and McVoy (HM) cite{HM1985}. We expect that experimentalists shall be encouraged to search for more information about the $x_{1} + x_{2}$ system in the elastic breakup cross section and that also further developments and extensions of the surrogate method will be pursued, based on the inclusive non-elastic breakup part of the $b$ spectrum.
We have performed CDCC calculations for collisions of $^{7}$Li projectiles on $^{59}$Co, $^{144}$Sm and $^{208}$Pb targets at near-barrier energies, to assess the importance of the Coulomb and the nuclear couplings in the breakup of $^{7}$Li, as well as the Coulomb-nuclear interference. We have also investigated scaling laws, expressing the dependence of the cross sections on the charge and the mass of the target. This work is complementary to the one previously reported by us on the breakup of $^{6}$Li. Here we explore the similarities and differences between the results for the two Lithium isotopes. The relevance of the Coulomb dipole strength at low energy for the two-cluster projectile is investigated in details.
A self-contained Fortran-90 program based on a classical trajectory model with stochastic breakup is presented, which should be a powerful tool for quantifying complete and incomplete fusion, and breakup in reactions induced by weakly-bound two-body projectiles near the Coulomb barrier. The code calculates complete and incomplete fusion cross sections and their angular momentum distribution, as well as breakup observables (angle, kinetic energy and relative energy distributions).
The incomplete fusion dynamics of $^6$Li + $^{209}$Bi collisions at energies above the Coulomb barrier is investigated. The classical dynamical model implemented in the {sc platypus} code is used to understand and quantify the impact of both $^6$Li resonance states and transfer-triggered breakup modes (involving short-lived projectile-like nuclei such as $^8$Be and $^5$Li) on the formation of incomplete fusion products. Model calculations explain the experimental incomplete-fusion excitation function fairly well, indicating that (i) delayed direct breakup of $^6$Li reduces the incomplete fusion cross-sections, and (ii) the neutron-stripping channel practically determines those cross-sections.
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