Scaled variance, skewness, and kurtosis near the critical point of nuclear matter

The van der Waals (VDW) equation of state predicts the existence of a first-order liquid-gas phase transition and contains a critical point. The VDW equation with Fermi statistics is applied to a description of the nuclear matter. The nucleon number fluctuations near the critical point of nuclear matter are studied. The scaled variance, skewness, and kurtosis diverge at the critical point. It is found that the crossover region of the phase diagram is characterized by the large values of the scaled variance, the almost zero skewness, and the significantly negative kurtosis. The rich structures of the skewness and kurtosis are observed in the phase diagram in the wide region around the critical point; namely, they both may attain large positive or negative values.

Figure 1

The (a) particle number density $n(T,\mu )$ (6) and (b) scaled variance $\omega \left[N\right]$ (10) calculated for the symmetric nuclear matter in $(T,\mu )$ coordinates within the VDW equation of state for fermions. The open circle at $T=0$ denotes the ground state of nuclear matter, the solid circle at $T=T_c$ corresponds to the CP, and the phase transition curve $\mu ={\mu }_{\mathrm{mix}}\left(T\right)$ is depicted by the solid line.

Figure 2

The (a) skewness $S\sigma$ [Eq. (12)] and (b) kurtosis $\kappa {\sigma }^2$ [Eq. (13)] calculated for the symmetric nuclear matter in $(T,\mu )$ coordinates within VDW equation of state for fermions.