We calculate the effects of two-body interactions on the low frequency oscillations of a normal Fermi gas confined in a harmonic trap. The mean field contribution to the collective frequencies is evaluated in the collisionless regime using a sum rule approach. We also discuss the transition between the collisionless and hydrodynamic regime with special emphasis to the spin dipole mode in which two atomic clouds occupying different spin states oscillate in opposite phase. The spin dipole mode is predicted to be overdamped in the hydrodynamic regime. The relaxation time is calculated as a function of temperature and the effects of Fermi statistics are explicitly pointed out.Comment: 4 pages, 1 figure include

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Various features of spin-polarized Fermi gases confined in harmonic traps are discussed, taking into account possible perspectives of experimental measurements. The mechanism of the expansion of the gas is explicitly investigated and compared with that of an interacting Bose gas. The role of interactions in the equilibrium and non-equilibrium behaviour of the fermionic component in Fermi-Bose mixtures is discussed. Special emphasis is given to the case of potassium isotope mixtures.

We study a confined mixture of bosons and fermions in the regime of quantal degeneracy, with particular attention to the effects of the interactions on the kinetic energy of the fermionic component. We are able to explore a wide region of system parameters by identifying two scaling variables which completely determine its state at low temperature. These are the ratio of the boson-fermion and bosonboson interaction strengths and the ratio of the radii of the two clouds. We find that the effect of the interactions can be sizeable for reasonable choices of the parameters and that its experimental study can be used to infer the sign of the boson-fermion scattering length. The interplay between interactions and thermal effects in the fermionic kinetic energy is also discussed.

Correlated-basis-function perturbation theory is used to evaluate the zero-temperature response S(q,) of 3 He mixtures for inelastic neutron scattering, at momentum transfers q ranging from 1.1 to 1.8 Å Ϫ1 . We adopt a Jastrow correlated ground state and a basis of correlated particle-hole and phonon states. We insert correlated one-particle-one-hole and one-and two-phonon states to compute the second-order response. The decay of the one-phonon states into two-phonon states is accounted for in the boson-boson approximation. The full response is split into three partial components S ␣␤ (q,), each of them showing a particle-hole bump and a one phonon, ␦-shaped peak, which stays separated from the multiphonon background. The cross term S 34 (q,) results to be of comparable importance to S 33 (q,) in the particle-hole sector and to S 44 (q,) in the phonon one. Once the response has been convoluted with the experimental broadening, the computed scattering function is in semiquantitative agreement with recent experimental measurements.