Quantum chaos in collinear (He, H₂⁺) collisions

Abstract

The quasibound spectrum of the transition state in collinear (He, H₂⁺) collisions is obtained from time-dependent wave packet calculations. Examination of short- and long-, and the spectral rigidity, Δ₃(L), reveals signatures of quantum chaotic behavior. Analysis in the time domain is carried out by computing the survival probability <<P(t)>> averaged over initial states and Hamiltonian. All these indicators show intermediate behavior between regular and chaotic. A quantitative comparison of <<P(t)>> with the results of random matrix theory provides an estimate of the fraction of phase space exhibiting chaotic behavior, in reasonable agreement with the classical dynamics. We also analyse the dynamical evolution of coherent Gaussian wave packets located initially in different regions of phase space and compute the survival probability, power spectrum and the volume of phase space over which the wave packet spreads and illustrate the different behaviors.