On the relation between the long-wave instability and the pion condensation in nuclear matter

The solutions to the zero-sound frequency equation and pion dispersion equation are considered for the different values of the parameters of the effective particle-hole interaction. The branches of solutions, responsible for the long-wave instability [Pomeranchuk] of the nuclear matter \omega_P(k) are presented for the both equations. It is shown that in the pion dispersion equation the solutions \omega_P(k) result in the instability not only for values of the spin-isospin constant g'\leq -1/2, violating stability criteria, but for all g' < g'_p (|g'_p|\ll 1 and g'_p < 0). At g' > g'_p the branches \omega_P(k) turn into the solutions responsible for pion condensation.