Self-intersecting Regge trajectories in multi-channel scattering

Abstract

We present a simple direct method for calculating Regge trajectories for a multichannel scattering problem. The approach is applied to the case of two coupled Thomas-Fermi type potentials, used as a crude model for electron-atom scattering below the second excitation threshold. It is shown that non-adiabatic interaction may cause formation of loops in Regge trajectories. The accuracy of the method is tested by evaluating resonance contributions to elastic and inelastic integral cross sections.

Complex angular momentum theory of state-to-state integral cross sections: resonance effects in the F + HD → HF(v′ = 3) + D reaction

“…In a similar way, a pole of S in the complex J-plane at a fixed E determines the angular momentum and the mean angle of rotation before the decay (lifeangle) of the complex formed at this energy. These complex angular momentum (CAM) or Regge poles [22][23][24][25][26][27] are more useful for quantifying the resonance effects in observables, such as the ICSs, which are given by sums over partial waves at a given energy. This was first realised by Macek and co-workers, who related low-energy oscillations in the ICS to single-channel proton scattering by hydrogen atoms 28 and inert gases, 29 and gave a simple expression (known as the Mulholland formula 30 ) for the resonance contribution to an ICS.…”

“…For a single-or few-channel scattering problem, Regge poles can be found numerically by integrating the Schroedinger equation for complex-valued J's [23,27,28,32,33], or by semiclassical methods [29]. This is no longer the case for a realistic reactive system with dozens of open channels, where evaluating the scattering matrix for physical integer values of J is already a challenging task.…”

Numerical Regge pole analysis of resonance structures in state-to-state reactive differential cross sections

“…Relevant information on the Regge poles can be found in Refs. [11]- [16]. Some applications of the poles to the angular scattering and integral cross sections are discussed in Refs.…”