  The properties of impurities immersed in a large Fermi sea are naturally
described in terms of dressed quasiparticles: attractive and repulsive
polarons, and dressed molecules. Motivated by recent experiments on narrow
Feshbach resonances, we analyze here how the quasiparticle properties are
affected by a non-zero resonance range. We find two interesting analytic
results. For large range, the ground state energy close to resonance is shown
to become perturbative in the inverse range. In the limit of broad resonance
instead, we provide a new Tan's relation linking the impurity ground state
energy $E_\downarrow$ to the number of atoms in its dressing cloud $\Delta N$.
As a corollary, at unitarity one finds $\Delta N=-E_\downarrow/\epsilon_F $,
with $\epsilon_F$ the Fermi energy of the bath.
