Resonances and chaos in the collinear collision system (He, H ₂⁺) and its isotopic variants

Abstract

The collinear atom-diatom collision system provides one of the simplest instances of chaotic or irregular scattering. Classically, irregular scattering is manifest in the sensitive dependence of post-collision variables on initial conditions, and quantally, in the appearance of a dense spectrum of dynamical resonances. We examine the influence of kinematic factors on such dynamical resonances in collinear (He, H₂⁺) collisions by computing the transition state spectra for collinear (He, HD⁺) and (He, DH⁺) collisions using the time-dependent quantum mechanical approach. The nearest neighbor spacing distribution P(s) and the spectral rigidity Δ₃(L) for these resonances suggest that the dynamics is predominantlyirregular for collinear (He, HD⁺) and predominantlyregular for collinear (He, DH⁺). These findings are reinforced by a significantly larger "correlation hole" in ensemble averaged survival probability «P(t)» values for collinear (He, HD⁺) than for collinear (He, DH⁺). In addition we have also examined measures of classical chaos through the dependence of the final vibrational action, n_f, on the initial vibrational phase φ_i of the diatom, and Poincaré surfaces-of-section. They show that (He, HD⁺) collisions are partly chaotic over the entire energy range (0-2.78 eV) while (He, DH⁺) collisions, in contrast, are highly regular at collision energies below the classical threshold for reaction. Above the threshold, the scattering remains regular for initial vibrational states ν=0 and 1 of DH⁺.