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Since Migdal!) and Sawyer-Scalapino ) pointed out the possibility of pion condensation in nuclear matter, it has intensively studied not only on the pionic instability but also on the structure of pion condensed state. ) Possible spin, isospin and space structures of pion condensate were also considered in detail in both pure neutron matter and isosymmetric nuclear matter. 3 ).4) In a realistic neutron star. there exists an admixture of protons, equilibrating with electrons. These protons give rise to the characteristic pion condensate, so-called Jr, +-condensate, above some critical density. Its possibility has originally been suggested by Migdal, Markin and Mishustin in pure neutron matter though much qualitative as follows: even in pure neutron matter (Z = 0) there exists the energy branch of sound (w~+)<o) with the same quantum number as the positive pion. Iw~+)1 increases as the nucleon density P (=Pn, the neutron density in the case) to lead to overcome the neutron Fermi energy, that is w~+) +EW)=O. Then there occurs the instability of Jr, + in a sense of the Landau 2nd order phase transition. More rigorous statements will be done later. The critical density is estimated as Pc(Jr,+)/Po~O.4, where po is the normal density (Po'" 0.5*»). The purpose of this paper is to study the Jr, +-condensate in a realistic iso-asymmetric nuclear matter (N;p.Z*O). In the case, the *) We take the natural unit as h= c= m~=l. critical density of this mode is considered to be the lowest as compared with the other kind of pion condensates. *) The energy gain of the system, the structure of the nucleon system and the relation with the so-called Jr±pair condensation leading from the instability of spontaneous production of Jr, +-sound excitation and Jr--pion one are the main subjects. On the transition mechanism from Jr, +-condensate to Jr±-pair one, it has been pointed oue) that the instability corresponding to Jr±-pair condensation does not arise, if the existence of Jr. +-condensate is taken into account. And the transition from Jr, +-condens ate to Jr±-pair one was suggested ) in the system with Z*O. On this subject we consider in detail. In order to get the qualitative understandings, we take only p-wave Jr-N interaction. First, we consider the behavior of the total energy of the system near the critical point in terms of the Landau formalism. The effective Hamiltonian is given as

Possible Charged Pion Condensation in Neutron Matter with Small Proton Admixture