Effects of fermion-boson interaction in neutral atomic systems

We investigate the collective excitations of ³He-⁴He mixture films at zero temperature within the random phase approximation and linear response theory. In a low concentration regime of ³He, a level repulsion between zero sound and third sound modes is derived, which opens the possibility to observe quantum mechanical coherence between a ³He particle-hole pair and the condensate of ⁴He. We also investigate the ³He-⁴He vertex corrections in the ladder approximation, and show that the third branch, the combined mode of fermionic particle-hole pair and the third sound quanta, provides a unique correction to the Landau f function. Some implications for a fermion-boson mixture of alkali atoms in a potential trap are discussed.