The nuclear liquid-gas phase transition at large $N_c$ in the Van der Waals approximation

Understand

We examine the nuclear liquid-gas phase transition at large number of colors ($N_c$) within the framework of the Van Der Waals (VdW) model.

• We argue that the VdW equation is appropriate at describing inter-nucleon forces, and discuss how each parameter scales with $N_c$.
• We demonstrate that $N_c=3$ (our world) is not large with respect to the other dimensionless scale relevant to baryonic matter, the number of neighbors in a dense system $N_N$.
• Consequently, we show that the liquid-gas phase transition looks dramatically different at $N_c \to \infty$ with respect of our world: The critical point temperature becomes of the order of $\lqcd$ rather than below it.