Isospin dependent multifragmentation in 112 Sn 1 112 Sn and 124 Sn 1 124 Sn collisions

Percolation models have proven highly successful in the simulation of multifragmentation reactions in the past @1,2#. Within these models, fragmentation is described by first distributing a set of points or sites, each representing a nucleon, on a three-dimensional lattice, which represents the bonds between the sites. In the case of a simple rectangular lattice, each site is connected to six nearest neighbors, however, it has been shown that the model is to a large degree independent of the lattice structure @1,3#. In the second step, some lattice bonds are randomly broken with a probability that in nonisospin dependent percolation models is the only free parameter. The remaining connected clusters are identified with the fragments of the reaction, the bond-breaking probability with the excitation energy per nucleon @4#. In this work, the percolation model of Bauer et al. @1# is modified by the explicit inclusion of isospin degrees of freedom, i.e., the lattice is comprised of protons and neutrons instead of just nucleons. The question in this paper is whether the isospin dependence found in the comparison between experimental multifragmentation data of Sn1 Sn and Sn1 Sn collisions @5# can be reproduced within the framework of percolation simulations. Again, we especially focus on the average number of intermediate mass fragments ~IMF’s, 3<Z<20) versus the number of charged particles ~Fig. 1, left panels! ^N IMF&(Nc) and the number of neutrons ~Fig. 1, right panels! ^N IMF&(Nn). The full circles denote the experimental results for the Sn1 Sn reaction, the open circles the results for the Sn1 Sn reaction. The striking feature about these distributions is the ‘‘splitting’’ of ^N IMF&(Nc), and the position of the maxima in ^N IMF&(Nn). Both do not agree with common multifragmentation models, in which the distributions ^N IMF&(Nc) should lie on top of each other, and the positions of the maxima in ^N IMF&(Nn) should simply correspond to the ratio of neutron abundances in the respective isotopes. For each simulated collision event, first the impact parameter is randomly selected. Then with a simple Monte Carlo integration, the number of protons and neutrons in the overlap zone of the two nuclei is determined. We employ an approximation in which the nucleons outside the overlap zone are neglected — we found this approximation to be appropriate by studying Boltzmann-Uehling-Uhlenbeck ~BUU! simulations @6# of the collisions at different impact parameters, which clearly showed distinct spectator regions