Landau Ginzburg Theory and Nuclear Matter at Finite Temperature

Based on recent studies of the temperature dependence of the energy and specific heat of liquid nuclear matter, a phase transition is suggested at a temperature ∼ .8 MeV. We apply Landau Ginzburg theory to this transition and determine the behaviour of the energy and specific heat close to the critical temperature in the condensed phase. The existence of an energy gap in the spectrum of even-even nuclei due to paired states of either protons or neutrons [1] similar to that described by Bardeen, Cooper and Schrieffer (BCS) for electrons in a superconductor [2] has led to the suggestion that nuclear matter should also exist in a condensed phase for some range of temperatures [3]. The properties of this superfluid phase in both nuclear and neutron matter have been studied in the BCS approximation using a variety of phenomenological forces [4] as well as more realistic interactions [5]. Remarkably, all calculations yield qualitatively similar results for 1S0 pairing, namely that neutron matter exists in a condensed phase for kF less than about 1.3− 1.5 fm. Recent calculations, using the Paris potential [6], by the Catania group [7] have shown that only slight deviations occur in nuclear matter. Such modifications, which can be characterized by the use of a smaller nuclear effective mass in the case of nuclear matter, are known to give rise to a slight decrease in the gap, ∆. Although such calculations suggest that such a low temperature phase should exist in both nuclear as well as neutron matter this has not been taken into account in, for example, astrophysical calculations since it is thought that it may be masked by other instabilities [8]. In field theoretic language BCS theory is considered as the spontaneous symmetry breaking of phase symmetry. The condensed phase, e.g. the superconducting phase, is characWe dedicate this paper to Prof. R. H. Lemmer on the occassion of his 65 birthday.