V-Particle Decay in the Lee Model

Abstract

The formalism developed previously for scattering of wavepackets is applied to the N + θ sector of the Lee model. A single analysis suffices to discuss both the stable and unstable case. The rate at which N and θ particles are produced and the number of V particles produced are calculated as a function of time assuming that the incident wave is initially a semi‐infinite, plane‐wave train. An unstable V‐particle state is constructed from the |N, θ〉 state by requiring agreement with the scattering analysis. Its dependence on the production process is explicitly shown. The state can be made independent of the production process by requiring normalization. The time dependence of each channel is also calculated for this case. It is shown that both the unstable and stable V‐particle states can be generated from the mathematical V‐particle state, the only difference being the location of the pole which describes the resonance state or the bound state.