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 $0<T<\mathrm{}{T}_c$ 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 $T_c$ as an oscillation of the normal component, but disappears at some finite temperature which in general depends on the Landau interaction parameters $F_0$,$F_1$,$Z_0$, etc. The behavior of the density-fluctuation mode depends critically on $F_0$, if the latter is negative, there is a well-defined collective oscillation only for $T\ll T_c$, while if it is small and positive, the oscillation is well defined for $T\ll T_c$ and $T-T_c\ll T_c$ but not in the intermediate region. If $F_0$ is large and positive, the density-fluctuation collective mode exists throughout the whole region $0<T<\mathrm{}{T}_c$ and its velocity is approximately temperature-independent.