QUADRUPOLE DISSOCIATION DYNAMICS OF MOLECULAR HYDROGEN

Abstract

Studies are reported of the quadrupole excitation and dissociation cross sections of molecular hydrogen in its ground electronic state. Explicit solutions of the time-dependent Schr\""{o}dinger equation constructed with stable second-order time propagation and finite-difference expanding-lattice-grid methodology are employed in obtaining the appropriate auto-correlation functions and discrete and continuum cross sections. The precise numerical wave functions obtained in both position and momentum representations verify explicitly the formation of a quadrupole-prepared state and the classical Bethe front in the short- and long-time limits. Aspects of the Ehrenfest force driving the excitation and dissociation processes are indicated. The calculated cross sections exhibit Cooper-minimum-like variations with photon energy, particularly for the higher-lying vibrational levels. Some general comments are provided on connections between static and explicitly time-dependent developments for constructing discrete and continuum molecular eigenstates and related properties.