Collective excitations in a confined, interacting dilute Bose-condensed fluid

In the Thomas - Fermi (TF) regime, S. Stringari [Phys. Rev. Lett., 77, 2360 ( 1996)] established the hydrodynamic normal modes of an interacting dilute Bose-condensed fluid confined in an isotropic harmonic trap. Here, we extend this treatment beyond the TF condensate using the work of B. Hu, G. Huang and Y. Ma [ Phys. Rev. A, 69, 063608 ( 2004)] as a starting point. Both numerical results for low-lying eigenfrequencies, for various angular momentum quantum numbers l and n = 0, and also samples of corresponding eigenfunctions, are presented. Finally, eigenfrequencies are also given for some collective excitations in an axially symmetrical trap.