  In this article, we revisit the heteronuclear Efimov effect in a Bose-Fermi
mixture with large mass difference in the Born-Oppenheimer picture. As a
specific example, we consider the combination of bosonic $^{133}\mathrm{Cs}$
and fermionic $^6\mathrm{Li}$. In a system consisting of two heavy bosons and
one light fermion, the fermion-mediated potential between the two heavy bosons
gives rise to an infinite series of three-body bound states. The intraspecies
scattering length determines the three-body parameter and the scaling factor
between consecutive Efimov states. In a second scenario, we replace the single
fermion by an entire Fermi Sea at zero temperature. The emerging interaction
potential for the two bosons exhibits long-range oscillations leading to a
weakening of the binding and a breakup of the infinite series of Efimov states.
In this scenario, the binding energies follow a modified Efimov scaling law
incorporating the Fermi momentum. The scaling factor between deeply bound
states is governed by the intraspecies interaction, analogous to the Efimov
states in vacuum.
