Finite-temperature excitations of an inhomogeneous trapped Bose gas with Feshbach resonances

We derive and discuss the temperature dependence of the condensate and nonc ondensate density profile of a Bose-Einstein condensate gas with Feshbach r esonance in a parabolic trap. These quantities are calculated self-consiste ntly using the generalized Hartree-Fock-Bogoliubov (HFB) equations within t he Bogoliubov approximation. At zero temperature, the HFB equation can be s olved by means of a variation method that gives the low-excitation spectrum . Moreover, within the two-body collision theory, we estimate the relations hip between the number of atoms in the condensate and the external magnetic field B. The result is in good agreement with data from recent experiments .