Effects of fermion-boson interaction in neutral atomic systems

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