Lower branch of the spectrum of a fermion interacting with a bosonic gas (polaron)

The lower single-particle bound state of a fermion interacting with a bosonic gas is studied. In the case of a small coupling constant, the employed method makes it possible to improve significantly the accuracy of the previously known results on the polaron branch of the spectrum. The results give a hint that in one-and two-dimensional systems there may exist an excited polaron state with small value of the momentum.