Tracking the phase-transition energy in the disassembly of hot nuclei

In efforts to determine phase transitions in the disintegration of highly excited heavy nuclei, a popular practice is to parametrize the yields of isotopes as a function of temperature in the form ${Y\left(z\right)=z}^{-\tau }f\left(z^{\sigma }\right(T-T_0\left)\right),$ where $Y\left(z\right)\mathrm{}$’s are the measured yields and $\tau ,$ $\sigma ,$ and $T_0$ are fitted to the yields. Here $T_0$ would be interpreted as the phase transition temperature. For finite systems such as those obtained in nuclear collisions, this parametrization is only approximate and hence allows for extraction of $T_0$ in more than one way. In this work we look in detail at how values of $T_0$ differ, depending on methods of extraction. It should be mentioned that for finite systems, this approximate parametrization works not only at the critical point, but also for first-order phase transitions (at least in some models). Thus the approximate fit is no guarantee that one is seeing a critical phenomenon. A different but more conventional search for the nuclear phase transition would look for a maximum in the specific heat as a function of temperature $T_2.$ In this case $T_2$ is interpreted as the phase transition temperature. Ideally $T_0$ and $T_2$ would coincide. We invesigate this possibility, both in theory and from the ISiS data, performing both canonical (T) and microcanonical ${(e=E}^{*}/A)$ calculations. Although more than one value of $T_0$ can be extracted from the approximate parametrization, the work here points to the best value from among the choices. Several interesting results, seen in theoretical calculations, are borne out in experiment.