Excitation spectra of a confined 87Rb-40K mixture approaching collapse

We calculate the spectra of low-lying monopolar and dipolar excitations in a degenerate mixture of 87Rb-40K atoms, paying special attention to the dynamical signatures of the approach to collapse driven by the mutual attractive interactions of the two species. The mixture is under spherical harmonic confinement and dynamical correlations between bosonic and fermionic density fluctuations in the collisionless regime are taken into account by means of a random phase approximation. We find that bosons and fermions execute coherent oscillations in the monopolar modes with a progressive redshift of the bosonic eigenfrequencies as the number of bosons is increased. At the same time the frequency of the dipolar fermionic mode is appreciably blueshifted as a consequence of the increasing density of the atomic cloud