VΘ-Bound State and Uniqueness in the Three-Particle Sector of the Lee Model

Abstract

If the coupling constant is large enough, but still smaller than its critical value, there exists a Vθ‐bound state in the Lee model. We find the bound‐state wavefunction via the solution of the homogeneous Källen‐Pauli equation. The condition for the existence of a Vθ‐bound state is seen to give a statement about the uniqueness of the scattering solutions of both the Vθ‐ and N2θ‐integral equations. There exists no N2θ‐bound state if the V particle is unstable.