Transformation between statistical ensembles in the modelling of nuclear fragmentation
arXiv:1305.5660 · doi:10.1016/j.physletb.2013.05.035
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.
In press in Physics Letters B
References in corpus (11)
- Statistical mechanics and dynamics of solvable models with long-range interactions
- Generalized canonical ensembles and ensemble equivalence
- Bimodal behavior of the heaviest fragment distribution in projectile fragmentation
- Looking for bimodal distributions in multi-fragmentation reactions
- Calculations of canonical averages from the grand canonical ensemble
- Ensemble in-equivalence in supernova matter within a simple model
- Signals of bimodality in the fragmentation of Au quasi-projectiles
- Bimodality and Coulomb effects with a canonical thermodynamic model
- Specific heat and bimodality in canonical and grand canonical versions of the thermodynamic model
- Thermodynamics of clusterized matter
- Conditions for equivalence of Statistical Ensembles in Nuclear Multifragmentation