Maxwell Construction and Phase Transitions in Fermi Fluids*'**

The use of the Maxwell construction, in conjunction with the van der Waals equation of state, to represent the liquefaction of gases is familiar to all students of thermodynamics. The present paper is concerned with the application of the Maxwell construction to Fermi fluids, and in particular with the question as to whether or not they can undergo a liquid-gas phase transition at T= 0. We shall be particularly interested in the case of nuclear matter in the low-energy domain, where there can be no question of any internal degrees of freedom of the nucleon being excited. Some of our considerations will also be relevant to fluid He. Liquid-gas phase transitions of nuclear matter certainly take place in collapsing stars, where nuclei become more and more neutron-rich as they capture high-energy degenerate electrons. Eventually, the neutron-drip line is reached and neutrons leak out, forming a vapour that is in equilibrium with the residual nuclei, which may be regarded as forming liquid droplets. However, this phase transition, which can occur even at absolute zero, T= 0, is rather difficult to compare with that of a van der Waals gas, since it takes place in what is essentially a two-component system: the neutron/proton ratio is quite different in the gas and liquid phases. Our considerations of nuclear matter will thus be limited to the single-component situation. Two different cases of this can be envisaged, although neither corresponds exactly to anything that can occur in reality.