Parametrizing yields of nuclear multifragmentation

We consider a model where, for a finite disintegrating system, yields of composites can be calculated to arbitrary accuracy. An analytic answer for yields is also known in the thermodynamic limit. In the range of temperature and density considered in this work, the model has a phase transition. This phase transition is first order. The analytic expression for yields of composites, in the thermodynamic limit, does not conform to the expression $〈{n}_{a}〉{=a}^{\ensuremath{-}\ensuremath{\tau}}f({a}^{\ensuremath{\sigma}}(T\ensuremath{-}{T}_{c}))$ where the usual identification would be that ${T}_{c}$ is the critical temperature and $\ensuremath{\tau},\ensuremath{\sigma}$ are critical exponents. Nonetheless, for finite systems, we try to fit the yields with the above expression. A minimization procedure is adopted to get the parameters ${T}_{c},\ensuremath{\tau},$ and $\ensuremath{\sigma}.$ While deviations from the formula are not negligible, one might believe that the deviations are consistent with the corrections attributable to finite particle number effects and might then conclude that one has deduced at least approximately the values of critical parameters. This exercise thus points to difficulties of trying to extract critical parameters from data on nuclear disintegration. An interesting result is that the value of ${T}_{c}$ deduced from the ``best'' fit is very close to the temperature at which the first order phase transition occurs in the model. The yields calculated in this model can also be fitted quite well by a parametrization derived from a droplet model.

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