The limiting temperature of hot nuclei from microscopic equation of state

The limiting temperature $T_{\mathit{lim}}$ of a series of nuclei is calculated employing a set of microscopic nuclear equations of state (EOS’s). It is shown that the value of $T_{\mathit{lim}}$ is sensitive to the nuclear matter equation of state used. Comparison with the values extracted in recent phenomenological analysis appears to favor a definite selection of EOS’s. On the basis of this phenomenological analysis, it therefore seems possible to check the microscopic calculations of the nuclear EOS at finite temperature, which is hardly accessible through other experimental information.

Figure 1

(a) Free energy per particle as a function of Fermi momentum at different temperatures for the Bonn potential. From top to bottom the different curves correspond to temperatures $T=2,8,12,16,20,24,28\text{MeV}$. The points represent the results of the Brueckner-Hartree-Fock calculations at finite temperature and, the curves are the corresponding polynomial fits. (b) Isotherms of pressure vs Fermi momentum corresponding to the free energy plots of (a). The sequence of temperatures is the same as in 1a (from bottom to top).

Figure 2

Chemical potential vs pressure for the Bonn potential from the Brueckner-Hartree-Fock calculations of Figs. 1a, 1b (full line) at a given temperature. The dotted line indicates the corresponding plot for the nucleus ${}^{208}\mathrm{Pb}$. At this temperature the nucleus starts to be unstable, see the text for details.

Figure 3

Limiting temperatures as a function of mass numbers for different equations of state in comparison with the phenomenological values (open squares with error bars).