Fermi polarons with the finite-range fermion-impurity interactions

We study a problem of an infinitely heavy impurity introduced into a polarized Fermi gas, which can be solved exactly with the help of Fumi's theorem. We consider the regime of finite-range fermion-impurity interactions beyond the standard $s$-wave scattering regime and investigate how this affects the energy of the polaron. We show how one can account for the effective range effects as well as the contribution from higher angular momentum channels, which are important for the study of ionic and Rydberg polarons. Our findings have relevance for atomic gas mixtures with a large mass imbalance and for the impurities trapped inside the optical tweezers.