THE FRIEDRICHS-MODEL WITH FERMION-BOSON COUPLINGS

Abstract

In this work we present an extended version of the Friedrichs Model (FM), which includes fermions. The standard FM describes the coupling between discrete and continuous components of a boson field. It is an exactly solvable model which allows for a clear identification of Gamow Resonances. In this extended version a set of fermion bound states is coupled to the boson field. As a result of the coupling some of the fermion states become resonant states. The structure of the solutions of the model is discussed analytically. The contact with nuclear structure calculations, where the model can be used to grasp basic features of the solutions of purely numerical treatments, is established by introducing realistic couplings constants.