Zero-sound in nuclear matter with the asymmetry parameter $-1\leq β\leq 1$

Results for the frequencies of zero-sound excitations in the isospin asymmetric nuclear matter are presented for the different parameters of asymmetry -1\leqβ\leq 1. The dispersion equations are constructed within the random phase approximation. We use the effective Landau-Migdal quasiparticle interaction with the special isospin dependence of the phase volume in the normalization factor C_0. In the paper we present zero-sound branches of the dispersion equation solutions in the symmetric, asymmetric and neutron matter. The branches correspond to the different channels of decay of the zero-sound excitation in the nuclear matter or nuclei. In the asymmetric nuclear matter we obtain three branches of solutions on the physical and unphysical sheets of the complex frequency plane, ω_{s\,τ}(k,β), τ=p,n,np. We demonstrate the change of branches with βand conversion of the three branches into two branches in symmetric nuclear matter (β=0) and into one branch in the neutron matter (β=1).

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