Quantum Oscillations in Thomas-Fermi Atoms.

The Fermi fluid with external potential V(r) is treated by using a model which assumes the free propagation of bulk-medium longitudinal density waves, in which static inhomogeneities are created from forced static amplitudes of these waves in response to a time independent external potential. The model predicts correctly density profiles at fluid interfaces and satisfies the cusp condition exactly at the origin. The modified linear responses of the first period atoms, magnesium and the hydrogen molecular ion, as obtained from the collective model, are compared to the exact linear responses obtained from a uniform Fermi fluid and the linear responses expressed in terms of the two-particle density: with the appropriate reference densities. The responses agree exactly in the k (--->) 0 and k (--->)(INFIN) wavevector domains. An approximate relationship is developed for the effective linear response of the non-uniform Fermi fluid. The various density profiles for interacting atoms are determined and the results are compared to the experimental data.