Role of isospin in the nuclear liquid–gas phase transition

We study the thermodynamics of asymmetric nuclear matter using a mean-field approximation with a Skyrme effective interaction, in order to establish its phase diagram and more particularly the influence of isospin on the order of the transition. A new statistical method is introduced to study the thermodynamics of a multifluid system, keeping only one density fixed, the others being replaced by their intensive conjugated variables. In this ensemble, phase coexistence reduces to a simple one-dimensional Maxwell construction. For a fixed temperature under a critical value, a coexistence line is obtained in the plane of neutron and proton chemical potentials. Along this line, the grand potential presents a discontinuous slope, showing that the transition is first order except at the two ending points where it becomes second order. This result is not in contradiction with the already reported occurrence of a continuous transformation when a constant proton fraction is imposed. Indeed, the proton fraction being an order parameter in asymmetric matter, the constraint can only be fulfilled by gradual phase mixing along the first-order phase-transition line, leading to a continuous pressure.