Collective excitations of a degenerate Fermi vapour in a magnetic trap

We evaluate the small-amplitude excitations of a spin-polarized vapour of Fermi atoms confined inside a harmonic trap. The dispersion law omega = omega f[l + 4n(n + l + 2)/3](1/2) is Obtained for the vapour in the collisional regime inside a spherical trap of frequency omega(f), with n the number of radial nodes and l the orbital angular momentum. The low-energy excitations are also treated in the case of an axially symmetric harmonic confinement. The collisionless regime is discussed with main reference to a Landau-Boltzmann equation for the Wigner distribution function: this equation is solved within a variational approach allowing an account of non-linearities. A comparative discussion of the eigenmodes of oscillation for confined Fermi and Bose vapours is presented in an Appendix.