Unstable states produced in multiparticle reactions

Normalized wavefunctions for unstable-particle states are constructed to meet the following physically plausible specifications. The wavefunctions of such states should enter into the theoretical production cross section in the same manner as the boundstate wavefunctions of stable particles. The cross section for the production of an unstable particle should be equal to the breakup cross section integrated over the resonance minus the background. For this purpose the multiparticle reaction cross section is brought into a form such that final-state resonances and interference corrections can be exhibited explicitly. The present theory is limited to unstable particles that decay into one or several two-body channels. For heuristic purposes, rearrangement and breakup scattering for three simple particles is treated numerically. For two particles interacting via a local potential, the wavefunction of the unstable state and the scattering phase shifts are computed with a simple algebraic technique. In order to treat complex multiparticle systems, we extend the resonance theory of simple two-particle systems to resonances in multiparticle two-body channels.