Resonances and chaos in the collinear collision system (He,H<inf>2</inf>⁺) 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 predominantly irregular for collinear (He,HD+) and predominantly regular for collinear (He,DH+). These findings are reinforced by a significantly larger "correlation hole" in ensemble averaged survival probability 〈〈P(t)〉〉 value for collinear (He,HD+) than for collinear (He,DH+). In addition we have also examined masurement of classical chaos through the dependence of the final vibrational action, nf, on the initial vibrational phase φi of the diatom, and Poincaré surfaces-of-section. They show that (He,HD+) collisions are partly chaotic over the entire energy range (0-2.78eV) while (He,DH+) collisions, in contrast, are highly regular at collision energies below the classical threshold for reaction. Above the threshold, the scattering remians regular for initial vibrational states v = 0 and 1 of DH+.