The Friedrichs-Model with fermion-boson couplings

Abstract

In this work we present an extended version of the Friedrichs Model, which includes fermion-boson couplings. The set of fermion bound states is coupled to a boson field with discrete and continuous components. As a result of the coupling some of the fermion states may become resonant states. This feature suggests the existence of a formal link between the occurrence of Gamow Resonant States in the boson sector, as predicted by the standard Friedrichs Model, with similar effects in the set of solutions of the fermion central potential (Gamow fermion resonances). The structure of the solutions of the model is discussed by using different approximations to the model space. Realistic couplings constants are used to calculate fermion resonances in a heavy mass nucleus.