A time-dependent quantum mechanical investigation of dynamical resonances in three-dimensional HeH₂⁺ and HeHD⁺ systems

Abstract

Bound and quasibound states of HeH₂⁺ and HeHD⁺ in three dimensions, for zero total angular momentum, have been computed using a time-dependent quantum mechanical approach. Time evolution of a carefully chosen wave packet in the interaction region is followed and the time correlation function evaluated and its Fourier transform obtained. The resulting eigenvalue spectrum and the corresponding eigenfunctions are examined to characterize the nature of the dynamical resonances for the system. It becomes clear that at low energies the quasibound states can be assigned readily in terms of local modes. While some of the higher energy state eigenfunctions resemble the hyperspherical modes, a large number of them cannot be assigned easily, suggesting irregular dynamics, in keeping with a large number of unstable periodic orbits known for the system.