A complex T-matrix derivation of a resonance amplitude

Time-dependent perturbation-theory techniques are used to derive a compact expression, valid to arbitrary order and displaying time dependence explicitly, for a quantum-mechanical transition amplitude applicable to the description of resonances. A solution representing a complex-energy generalization of the usual real-energy (nonresonant) amplitude is obtained and generalized to all orders by introducing a complex-energy T matrix. Applications to physical problems such as the extension of the Fermi golden rules to resonances (Norbury and Deutchman, 1984); pion production in relativistic nucleus-nucleus collisions (Norbury et al., 1985); and the determination of resonant cross sections for nuclear, atomic, or molecular processes involving the formation and decay of intermediate discrete or continuum states are indicated.