Investigation of Low-Density Symmetry Energy via Nucleon and Fragment Observables

Abstract

With stochastic transport simulations we study in detail central and peripheral collisions at Fermi energies and suggest new observables, sensitive to the symmetry energy below normal density. Keywords: symmetry energy, isospin transport coefficients, neck fragmentationThere has been much interest in recent years in the determination of the nuclear symmetry energy as a function of density, which is important for the structure of exotic nuclei as well as for astrophysical processes. Heavy ion collisions (HIC) present an attractive way to constrain the the existing models for this poorly-determined isovector equation-of-state (iso-EOS), 1 which can be investigated both at densities above and below normal density with relativistic energies and in the Fermi energy domain, respectively. However, observables, which are both sensitive to the iso-EOS and testable experimentally, still have to be identified clearly. 2,3In this report we discuss dissipative collisions at Fermi energies. Isospin dynamics at low and intermediate energies and its relation to the symmetry energy has, in fact, attracted much attention in recent years in experiment as well as in theory. 4-7Here we focus our attention on pre-equilibrium emission in central collisions and on the charge equilibration dynamics in peripheral collisions, where we expect to see

Probing the density dependence of the symmetry energy via multifragmentation at subsaturation densities

“…The difference at high kinetic energy between theoretical and experimental results for the neutron-rich system is due to the large uncertainty in the measurement of R N/Z . By using the single-ratio observable, one can reach a partial conclusion that the asymmetric nuclear matter favors the soft symmetry energy at subsaturation densities, which is also consistent with the other findings in the literature [4,[15][16][17]19,20,24].…”

“…Moving one step ahead to the IBUU04 results [16], where the symmetry energy is introduced with the help of momentum-dependent interactions, the results are very far from the experimental data. The same is true for the BNV calculations performed by the Catania group in 2007 [17]. The closest agreement between the data and the calculation was observed by the ImQMD model in 2009 [19].…”

“…Recently, at the Michigan State University (MSU) National Superconducting Cyclotron Labortory (NSCL), Famiano et al [13] measured the single and double ratios of free neutrons to protons for 112 Sn + 112 Sn and 124 Sn + 124 Sn at 50 MeV/nucleon. The results of the double ratio of the above data have also been reproduced by different theoretical models, such as Boltzmann-Uehling-Uhlenbeck in 1997 (BUU97) [15], Isospin-dependent Boltzmann-Uehling-Uhlenbeck in 2004 (IBUU04) [16], Boltzmann-Nordeim-Vlasov (BNV) [17], and Improved Quantum Molecular Dynamics (ImQMD) [19]. Even so, there are a lot of uncertainties in the determination of the symmetry energy in terms of different parameters such as the cross section, the symmetry energy coefficient, the impact parameter, and the method of clusterization.…”

“…The symmetry energy is found to be the prominent candidate to study the isospin dependence of the NEOS. In past years, many studies have been performed on the density dependence of symmetry energy at subsaturation densities by using isotopic scaling [7][8][9][10][11], isobaric ratio [12], single and double ratios [13][14][15][16][17]19,20], isospin diffusion [6,21], isospin distillation and fractionation [6,22], and isospin migration and drift [4,6,23]. Apart from these, transverse and elliptic flows of neutrons and protons are also considered good candidates to emphasize the importance of the density dependence of symmetry energy [24][25][26].…”