Abstract
We explore the conditions under which the particle number conservation constraint deforms the predictions of fragmentation observables as calculated in the grand canonical ensemble. We derive an analytical formula allowing to extract canonical results from a grand canonical calculation and vice versa. This formula shows that exact canonical results can be recovered for observables varying linearly or quadratically with the number of particles, independent of the grand canonical particle number fluctuations. We explore the validity of such grand canonical extrapolation for different fragmentation observables in the framework of the analytical Grand Canonical or Canonical Thermodynamical Model [(G)CTM] of nuclear multifragmentation. It is found that corrections to the grand canonical expectations can be evaluated with high precision, provided the system does not experience a first order phase transition. In particular, because of the Coulomb quenching of the liquid–gas phase transition of nuclear matter, we find that mass conservation corrections to the grand canonical ensemble can be safely computed for typical observables of interest in experimental measurements of nuclear fragmentation, even if deviations exist for highly exclusive observables.
Highlights
Statistical ensembles are known to give different predictions in finite systems, and to converge at the thermodynamical limit if interactions are short-range
Neutral nuclear systems do not exist in nature, but this simplification is often introduced in the context of nuclear matter
We show that the modification of grand canonical results due to particle number conservation can be exactly computed for observables varying linearly or quadratically with the number of particles, even in the regime of very small systems where particle number fluctuations in the grand canonical ensemble cannot be neglected
Summary
Statistical ensembles are known to give different predictions in finite systems, and to converge at the thermodynamical limit if interactions are short-range. In the framework of nuclear models with cluster degrees of freedom, a finite counterpart to nuclear matter can be realized in practice by switching off the Coulomb interactions both in the cluster energy functional and in the inter-cluster interactions, and allowing any arbitrary cluster size in the statistical equilibrium Such a system exhibits a first order liquid-gas phase transition at the thermodynamic limit, which makes ensembles strongly inequivalent for any finite size N[3, 4]. This is confirmed in ref.[6], where it is shown that typical inclusive fragmentation variables converge if temperature is not too low and multiplicity is sufficiently high to avoid important finite number effects Motivated by these works, in this paper we concentrate on finite charged nuclear systems without any electron screening, described in the framework of a statistical model with cluster degrees of freedom, and work out analytical relations connecting the different statistical ensembles.
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