Transformation between statistical ensembles in the modelling of nuclear fragmentation

TL;DR

This paper derives a formula to convert between grand canonical and canonical ensemble predictions in nuclear fragmentation, showing that mass conservation corrections are accurate except near phase transitions, aiding interpretation of experimental data.

Contribution

It introduces an analytical formula linking grand canonical and canonical results, enabling precise corrections for nuclear fragmentation observables.

Findings

Canonical results can be extracted from grand canonical calculations for certain observables.

Corrections are highly accurate away from phase transitions.

Mass conservation corrections are reliable for typical experimental observables.

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.