On the free volume in nuclear multifragmentation

Abstract

In many statistical multifragmentation models the volume available to the \(N\) nonoverlapping fragments forming a given partition is a basic ingredient serving to the simplification of the density of states formula. One therefore needs accurate techniques for calculating this quantity. While the direct Monte-Carlo procedure consisting of randomly generating the fragments into the freeze-out volume and counting the events with no overlapped fragments is numerically affordable only for partitions with small \(N\), the present paper proposes a Metropolis - type simulation which allows accurate evaluations of the free volume even for cases with large \(N\). This procedure is used for calculating the available volume for various situations. Though globally this quantity has an exponential dependence on \(N\), variations of orders of magnitude for partitions with the same \(N\) may be identified. A parametrization based on the virial approximation adjusted with a calibration function, describing very well the variations of the free volume for different partitions having the same \(N\) is proposed. This parametrization was successfully tested within the microcanonical multifragmentation model from [Al. H. Raduta and Ad. R. Raduta, Phys. Rev. C {\bf 55}, 1344 (1997); {\it ibid.}, {\bf 56}, 2059 (1997)]. Finally, it is proven that parametrizations of the free volume solely dependent on \(N\) are rather inadequate for multifragmentation studies producing important deviations from the exact results.