Toward realistic treatment of neutral pion-condensed state

We describe several realistic treatments of the neutral pion (π0)-condensed state or ALS structure. Treatments we call 'realistic' here aim to incorporate the effects from (1) the isobar Δ(1232), (2) the reduction of the OPE-tensor force in the short range due to ρ meson, (3) the central force due to 'σ' and ω meson, and (4) the short-range correlations between baryons. We present the following approaches to take account of these effects, i.e., an OBEP one with a schematic short-range correlation, a reaction-matrix one and two kinds of effective interaction approach. The transition density ρt(π0) is found to be (2-3)ρ0 in neutron matter and about 2.5ρ0 in symmetric nuclear matter(ρ0 being the nuclear density): The new phase is realized by the attractive effect of the OPE-tensor force enhanced by the Δ mixing which overwhelms the increase of the kinetic energy including the rest mass energy. The mechanism of the phase transition is clarified also in terms of the partial-wave contributions of the potential energy. It is found that the odd-state central potential plays an important role in assuring the stability of the ρ0-condensed phase. It is shown that the effective nucleon mass ia large in this phase in comparison with that in the Fermi gas phase. (author)