Superconductivity of pion condensate in neutron stars

The influence of the magnetic field on the properties of an inhomogeneous pion condensate within a neutron star is studied in the framework of the meson σ model with allowance for the pion-nucleon interaction. A London equation describing the distribution of the magnetic field in the system is obtained. It is shown that the condensate is a superconductor of the second kind in which a laminar structure of the mixed state is realized. The lower critical field Hcl for the occurrence of the laminar structure is found. It is shown that because the condensate momentum →k is perpendicular to the direction of the magnetic field →H a distinguished direction z perpendicular to the (→k, →H) plane occurs in the star. This leads to an explanation of pulsed radiation of the neutron star even when the magnetic field and rotation axis are parallel. It is shown that allowance for the N* resonance in the model of a developed pion condensate (Θ = π/2) does not change these results