Possible Charged Pion Condensation in Neutron Matter with Small Proton Admixture

Abstract

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