  We investigate a single impurity interacting with a free two-dimensional
atomic Fermi gas. The interaction between the impurity and the gas is
characterized by an arbitrary attractive short-range potential, which, in two
dimensions, always admits a two-particle bound state. We provide analytical
expressions for the energy and the effective mass of the dressed impurity by
including the two-body bound state, which is crucial for strong interactions,
in the integral equation for the effective interaction. Using the same method
we give also the results for the polaron parameters in one and three dimensions
finding a pretty good agreement with previous known results. Thus our relations
can be used as a simple way to estimate the polaron parameters once the
two-body bound state of the interaction potential is known.
