Resonances and chaos in the collinear collision system (He, H₂⁺) 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 distributionP(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,nf, on the initial vibrational phaseφi 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 v=0 and 1 of DH⁺.