Deformation Dependence of Breathing Oscillations in Bose - Fermi Mixtures at Zero Temperature

We study the breathing oscillationsin bose-fermi mixtures in the axially-symmetric deformed trap of prolate, spherical and oblateshapes, and clarify the def ormation dependence of the frequencies and the characteristics of collective oscillations. The co llective oscillationsof the mixtures in deformed traps are calculated in the scaling method. In largely-deformed prolateand oblatelimits and spherical limit, we obtain the analytical expressions of th e collective frequencies. The full calculation shows that the collective oscillationsbecome consistent with the analytically-obtained frequencies when the system is deformed into both prolateand oblateregions. The complicated changes of oscillationcharacters are shown to occur in the transcendentalr egions around the spherically-deformed region. We find that these critical changes of oscillationch aracters are explained by the level crossingbehaviors of the intrinsic oscillationmodes. The approximate expressions are obtained for the level crossingpoints that determine the transcendentalregions. We also compare the results of the scaling methods with those of the dynamical approach.