Random-phase approximation study of collective excitations in the Bose-Fermi mixed condensate of alkali-metal gases

We perform a random-phase approximation study of collective excitations in a Bose-Fermi mixed degenerate gas of alkali-metal atoms at T=0. The calculation is done by diagonalization in a model space composed of particle-hole type excitations from the ground state, the latter being obtained from the coupled Gross-Pitaevskii and Thomas-Fermi equations. We investigate strength distributions for different combinations of Bose and Fermi multipole (L) operators with L=0,1,2,3. Transition densities and dynamical structure factors are calculated for collective excitations. A comparison with the sum rule prediction for the collective frequency is given. The time dependent behavior of the system after an external impulse is studied.