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A systematic study of quasi-elastic and deep-inelastic collisions at Fermi energies is presented with the aim of obtaining insight into the underlying dynamics and the nuclear equation of state (EOS). Comparisons of experimental heavy-residue data to detailed calculations using the semiclassical microscopic model CoMD (Constrained Molecular Dynamics) are shown. The CoMD code implements an effective interaction with a nuclear-matter compressibility of K=200 (soft EOS) or K=380 (stiff EOS) with several forms of the density dependence of the nucleon-nucleon symmetry potential and imposes a constraint in the phase space occupation for each nucleon, restoring the Pauli principle during the collision. Preliminary results from these comparisons point to a soft equation of state (K=200) with a rather stiff density dependence of the isovector part (symmetry energy). The nuclear equation of state (EOS) and, especially, its isospin part (symmetry energy) have recently received an exceptionally strong attention by the nuclear physics community. The EOS, being intimately connected to the underlying nucleon-nucleon effective interaction, plays a pivotal role in a broad range of phenomena in both nuclear physics, e.g. the structure and dynamics of exotic/drip-line nuclei and in astrophysics, e.g. the structure and evolution of neutron stars and the dynamics of supernova explosions (e.g. [1,2] and references therein). During the last several years we have undertaken a systematic study of heavy residues formed in quasi-elastic and deep-inelastic collisions near and below the Fermi energy. One of the motivations of these studies was the understanding and the optimization of the production of very neutron-rich rare isotopes in these collisions [3–5]. In parallel, we became motivated to pursue these studies further in hopes of extracting information on the properties of the nuclear effective interaction as manifested in the mechanism of nucleon exchange and the course towards N/Z equilibration [6]. = 0 C sym ( ) 2 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 70:00 65:00 60:00 55:00 50:00 45:00 40:00 35:00 30:00 25:00 20:00 15:00 10:00 5:00 0:00 Fig. 1. (Color Online) Density dependence of the nuclear symmetry energy Csym(ρ) corresponding to the forms of the nucleon-nucleon symmetry potential in the CoMD code. Blue (dotted): asy-soft, red (solid): asy-stiff, green (dashed): super asy-stiff and grey (lower dotted) line: no symmetry potential. The black (solid) line represents the form 31.6(ρ/ρ0) 0.69 consistent with the isoscaling analysis of fragments from central heavy-ion collisions [2]. Recently, we focussed our interest on the possibility of extracting information on the isospin part of the nuclear equation of state by comparing our heavy residue data to detailed calculations using microscopic models of heavy-ion collisions at these energies [7]. After some initial efforts with one-body transporttype codes (BUU, BNV) [8], we turned our attention to the N-body quantum molecular dynamics approach (QMD) [9]. To date, we have performed detailed calculations using the recent version of the constrained molecular dynamics (CoMD) code of A. Bonasera and M. Papa [10,11]. The CoMD code is especially designed for reactions near and below the Fermi energy. Following the general philosophy of the QMD approach [9], in the CoMD model, nucleons are described as localized Gaussian wave packets. The wave function of the N-body nuclear system is assumed to be the product of these single-particle wave functions. With the Gaussian description, the N-body time-dependent Schöndinger equation leads to (classical) Hamilton’s equations of motion for the centroids of the nucleon wavepackets. The potential part of the Hamiltonian consists of a Skyrme-like effective interaction. The isoscalar part of this effective interaction corresponds to a nuclear-matter compressibility of K=200 (soft EOS) or K=380 (stiff EOS). For the isovector part,

Probing the Nuclear Equation of State with Peripheral Heavy Ion Collisions at Fermi Energies