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We investigate the reaction path followed by Heavy Ion Collisions with exotic nuclear beams at low energies. We will focus on the interplay between reaction mechanisms, fusion vs. break-up (fast-fission, deep-inelastic), that in exotic systems is expected to be influenced by the symmetry energy term at densities around the normal value. The evolution of the system is described by a Stochastic Mean Field transport equation (SMF), where two parametrizations for the density dependence of symmetry energy (Asysoft and Asystiff) are implemented, allowing one to explore the sensitivity of the results to this ingredient of the nuclear interaction. The method described here, based on the event by event evolution of phase space quadrupole collective modes will nicely allow to extract the fusion probability at relatively early times, when the transport results are reliable. Fusion probabilities for reactions induced by 132Sn on 64,58Ni targets at 10 AMeV are evaluated. We obtain larger fusion cross sections for the more n-rich composite system, and, for a given reaction, in the Asysoft choice. Finally a collective charge equilibration mechanism (the Dynamical Dipole) is revealed in both fusion and break-up events, depending on the stiffness of the symmetry term just below saturation.
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There is now a large and increasing body of experimental data and theoretical analyses for reactions that remove a single nucleon from an intermediate-energy beam of neutron- or proton-rich nuclei. In each such measurement, one obtains the inclusive cross section for the population of all bound final states of the mass A-1 reaction residue. These data, from different regions of the nuclear chart, and that involve weakly- and strongly-bound nucleons, are compared with theoretical expectations. These calculations include an approximate treatment of the reaction dynamics and shell-model descriptions of the projectile initial state, the bound final states of the residues, and the single-particle strengths computed from their overlap functions. The results are discussed in the light of recent data, more exclusive tests of the eikonal dynamical description, and calculations that take input from more microscopic nuclear structure models.
We use a three-body Continuum Discretized Coupled Channel (CDCC) model to investigate Coulomb and nuclear effects in breakup and reaction cross sections. The breakup of the projectile is simulated by a finite number of square integrable wave functions. First we show that the scattering matrices can be split in a nuclear term, and in a Coulomb term. This decomposition is based on the Lippmann-Schwinger equation, and requires the scattering wave functions. We present two different methods to separate both effects. Then, we apply this separation to breakup and reaction cross sections of 7Li + 208Pb. For breakup, we investigate various aspects, such as the role of the alpha + t continuum, the angular-momentum distribution, and the balance between Coulomb and nuclear effects. We show that there is a large ambiguity in defining the Coulomb and nuclear breakup cross sections, since both techniques, although providing the same total breakup cross sections, strongly differ for the individual components. We suggest a third method which could be efficiently used to address convergence problems at large angular momentum. For reaction cross sections, interference effects are smaller, and the nuclear contribution is dominant above the Coulomb barrier. We also draw attention on different definitions of the reaction cross section which exist in the literature, and which may induce small, but significant, differences in the numerical values.
The body of experimental measurements of intermediate-energy reactions that remove a single nucleon from a secondary beam of neutron- or proton-rich nuclei continues to grow. These data have been analysed consistently using an approximate, eikonal-model treatment of the reaction dynamics combined with appropriate shell-model descriptions of the projectile initial state, the bound final states spectrum of the reaction residue and single-particle removal strengths computed from their wave-function overlaps. The systematics of the ratio $R_s$ of the measured inclusive cross-section to all bound final states and the calculated cross-section to bound shell-model states -- in different regions of the nuclear chart and involving both very weakly-bound and strongly-bound valence nucleons -- is important in relating the empirically deduced orbital occupancies to those from the best available shell-model predictions. Importantly, several new higher-energy measurements, for which the sudden-approximation aspect of the dynamical description is placed on an even stronger footing, now supplement the previously-analysed measurements. These additional data sets are discussed. Their $R_s$ values are shown to conform to and reinforce the earlier-observed systematics, with no indication that the approximately linear reduction in $R_s$ with increasing nucleon separation energy is a consequence of a breakdown of the sudden approximation.
Three typical algorithms of Pauli blocking in the quantum molecular dynamics type models are investigated in the nuclear matter, the nucleus and the heavy ion collisions. The calculations in nuclear matter show that the blocking ratios obtained with the three algorithms are underestimated 13-25% compared to the analytical values of blocking ratios. For the finite nucleus, the spurious collisions occur around the surface of the nucleus owing to the defects of Pauli blocking algorithms. In the simulations of heavy ion collisions, the uncertainty of stopping power from different Pauli blocking algorithms is less than 5%. Furthermore, the in-medium effects of nucleon-nucleon ($NN$) cross sections on the nuclear stopping power are discussed. Our results show that the transport models calculations with free $NN$ cross sections result in the stopping power decreasing with the beam energy at the beam energy less than 300 MeV/u. To increase or decrease the values of stopping power, an enhanced or suppressed model dependent in-medium $NN$ cross section is required.
We explore the influence of in-medium nucleon-nucleon cross section, symmetry potential and impact parameter on isospin sensitive observables in intermediate-energy heavy-ion collisions with the ImQMD05 code, a modified version of Quantum Molecular Dynamics model. At incident velocities above the Fermi velocity, we find that the density dependence of symmetry potential plays a more important role on the double neutron to proton ratio $DR(n/p)$ and the isospin transport ratio $R_i$ than the in-medium nucleon-nucleon cross sections, provided that the latter are constrained to a fixed total NN collision rate. We also explore both $DR(n/p)$ and $R_i$ as a function of the impact parameter. Since the copious production of intermediate mass fragments is a distinguishing feature of intermediate-energy heavy-ion collisions, we examine the isospin transport ratios constructed from different groups of fragments. We find that the values of the isospin transport ratios for projectile rapidity fragments with $Zge20$ are greater than those constructed from the entire projectile rapidity source. We believe experimental investigations of this phenomenon can be performed. These may provide significant tests of fragmentation time scales predicted by ImQMD calculations.
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