Shifts and widths of collective excitations in trapped Bose gases determined by the dielectric formalism

We present predictions for temperature-dependent shifts and damping rates. They are obtained by applying the dielectric formalism to set up a self-consistent model of a trapped Bose gas which can be shown to satisfy generalized Ward identities. Within the framework of the model we use lowest-order perturbation theory to determine the first-order correction to the results of Hartree-Fock-Bogoliubov-Popov theory for the complex collective excitation frequencies, and present numerical results for the temperature dependence of the damping rates and the frequency shifts. Good agreement with the experimental values measured by Jin et al. [Phys. Rev. Lett. 77, 420 (1996)] are found for the $m=2\mathrm{}$ mode, while we find disagreements in the shifts for $m=0.\mathrm{}$ The latter point to the necessity of a nonperturbative treatment for an explanation of the temperature dependence of the $m=0\mathrm{}$ shifts.