A microcanonical approach of the multifragmentation phenomena in highly excited nuclear systems

Experimental data on multifragmentation indicate a rather independent fragment emission. This independence shows that the complexity of the phenomenon, as a result of the huge number of phase space options, justifies a statistical description of these processes. A binomial distribution for the n fragment emission was recently found. The elementary probability p depends on the energy of the radial expansion (transverse energy Et) (p∼e-B/T, where T∼ √E* and E* is the excitation energy and B a parameter related to the barrier height). A simple proof of the previous relation based on the statistical nature of multifragmentation is given. We consider a partition of A elements into groups of nj elements: {nj} (1n1, 2n2, ...., jnj,... ). In order to find the cluster size distribution, it is necessary to introduce constraints specific to each cluster. One considers a ladder of A rungs. A cluster of size i corresponds to each step. Each of the A particles of the system is placed on the corresponding rung according to the size of the cluster it belongs to. The total energy available to the system is distributed among the clusters. Each of the clusters can have a share of this energy given by the sum of the ground state energy and the excitation energy. The maximum excitation energy that a cluster can take and still exists as such is the binding energy, ib0, where b0 is the average binding energy per nucleon which, for a large part of the nuclides, is approximately constant. The picture described above resembles a micro canonical assemble in which various cluster sizes play the role of the single particle states in the usual level density problem. Our particles, the clusters, can occupy the same 'state' with no constrain other than the general conservation rules, therefore they will obey a Bose-Einstein statistics. Cluster size distribution in multifragmentation is expressed in terms of mean occupation numbers of the 'states' defined as the cluster size set of values. The distribution has the exponential shape. It has a large degree of generality and it can be applied to many phenomena whenever partition into groups is produced in a non preferential manner. (author)