Neutral pion condensation in hot and dense nuclear matter

From a viewpoint of the effective interaction and the equivalence between the potential and the field descriptions, a framework to treat the π0 condensation at finite temperature is presented. This framework is based on the finite-temperature Hartree-Fock method with use of effective two-nucleon potentials. It is successfully applied to the ALS model of π0 condensate and can be extended to the case including explicitly the isobar Δ(1232) degrees of freedom. In the studies on neutron matter, symmetric nuclear matter and supernova matter, the following points are found; (i) the transition density of π0 condensation increases remarkably with the temperature, (ii) the cause is a reduction of entropy in the ordered π0-condensed phase, (iii) the transition is of first-order and the phase diagram contains a wide mixed phase region, (iv) the equation of state is significantly softened even at finite temperature by the phase transition. A comment is given on the stability of the π0-condensed phase in macro-scopic scale relevant to supernova cores or very hot neutron stars. Also a possibility to realize the π0 condensate in laboratories by energetic nucleus-nucleus collisions is briefly discussed. (author)