Theory of a superfluid fermi liquid. II. Collective oscillations

The long-wavelength, low-frequency "collisionless" collective oscillations of a superfluid Fermi liquid are studied throughout the region 0<T<Tc with the help of a field-theoretic formalism developed in a previous paper. It is found that any collective mode (other than the density fluctuation) that is possible in the normal phase persists below Tc as an oscillation of the normal component, but disappears at some finite temperature which in general depends on the Landau interaction parameters F0,F1,Z0, etc. The behavior of the density-fluctuation mode depends critically on F0, if the latter is negative, there is a well-defined collective oscillation only for TTc, while if it is small and positive, the oscillation is well defined for TTc and T-TcTc but not in the intermediate region. If F0 is large and positive, the density-fluctuation collective mode exists throughout the whole region 0<T<Tc and its velocity is approximately temperature-independent.