  In this article we study the interaction between an impurity and the gas of
Bogoliubov excitations of a Fermi superfluid by mapping it on the polaron
problem for an impurity in a BEC. The description of the Fermi superfluid
across the BEC-BCS crossover regime is based on a recently developed effective
field theory presented in [Eur. Phys. J. B 88, 122 (2015)] and provides us with
the interaction-dependent dispersion relations for the Bogoliubov excitations.
The behavior of the polaronic coupling constant $\alpha$ and of the effective
mass of the polaron is examined in a broad window of the BEC-BCS crossover.
