The collective excitation spectra of sigma , omega mesons in the Walecka model of nuclear matter

We calculate the collective excitation spectra of sigma , omega mesons in nuclear matter by calculating the relativistic particle-hole excitation polarization insertion of the propagator in the Walecka model. In the mean field approximation and without sigma - omega mixing the spectra splits into the meson branch and acoustic sound branch; for the most part the acoustic sound modes are damped. The transverse omega meson has meson branch excitation spectra only. When sigma - omega mixing sets in, the acoustic sound excitation spectra of the sigma meson disappears and that of the longitudinal omega meson is suppressed. In the relativistic Hartree approximation and with sigma - omega mixing, all acoustic sound excitation spectra disappear and the spectra in the meson branch do not change very much for all cases.