Quantum Nature of a Nuclear Phase Transition

At finite temperatures and low densities, nuclei may undergo a phase change similar to a classical liquid-gas phase transition. Temperature is the control parameter while density and pressure are the conjugate variables. In the nucleus the difference between the proton and neutron concentrations acts as an additional order parameter, for which the symmetry potential is the conjugate variable. We present experimental results which reveal the $N/Z$ dependence of the phase transition and discuss possible implications of these observations in terms of the Landau free energy description of critical phenomena.

Figure 1

Mass distribution for the ${}^{64}\mathrm{Ni}+{}^{232}\mathrm{Th}$ system at $40\mathrm{MeV}/\mathrm{\text{nucleon}}$ for $I=1$ (circles) and $I=3$ (squares). The lines are power law fits with exponents $\tau =2.40\pm 0.08$, $1.99\pm 0.17$, $0.57\pm 0.11$, $-0.39\pm 0.26$, respectively. The fits are shown separately for odd (open symbols) and even (full symbols) $Z$.

Figure 2

Ratio versus symmetry energy for the ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ case at $40\mathrm{MeV}/\mathrm{\text{nucleon}}$. The dashed lines are fits using a ground state symmetry energy, Eq. (1), and a “temperature” of 6 MeV. The $I<0$ and $I>0$ isotopes are indicated by the open circles and the full circles, respectively. The $I=0$ isotopes are given by the full squares.

Figure 3

Free energy versus symmetry term for the case ${}^{64}\mathrm{Ni}+{}^{58}\mathrm{Ni}$ (upper panel) and ${}^{64}\mathrm{Ni}+{}^{232}\mathrm{Th}$ at $40\mathrm{MeV}/\mathrm{\text{nucleon}}$ (lower panel). The dashed lines are fits based on Landau $O(m^6)$ free energy either for vaporization (long-dashed curve) or first-order (short-dashed curve) phase transition (see text).

Figure 4

“Critical” $I/A$ (upper panel, solid circles) and “apparent temperature” (lower panel, solid circles) versus ratio of the compound nucleus symmetry to Coulomb energies for all the experimentally investigated systems. The same quantities are plotted for AMD calculations (open symbols). The lines are drawn to guide the eye.