Intense-field photodissociation of H2+: Comparison of time-dependent and time-independent calculations.

Abstract

The decay of the initial bound-state population and the fragment kinetic-energy distribution produced by the intense-field photodissociation of ${\mathrm{H}}_{2}^{+}$ are calculated using both a time-dependent and a time-independent method. The time-dependent method calculates the time evolution of the wave function describing ${\mathrm{H}}_{2}^{+}$ interacting with a classical time-dependent laser field by repeated application of a short-time propagator. The time-independent method constructs a wave packet using the energy eigenstates of the total molecule-plus-field Hamiltonian with the field expressed as a superposition of quantized photon number states. Specifically, the wave packet represents an initial bound-state wave function of the field-free molecule subjected to a coherent photon state that simulates the classical radiation field at t=0. The subsequent decay of this nonstationary state can be viewed as a laser-induced predissociation of field-dressed bound states into field-dressed continuum states with various numbers of photons absorbed from the field. For very rapid dissociation, the decays of the initial bound-state population calculated by both methods are in good agreement if a square pulse shape is used and the initial phase of the time-dependent interaction is averaged over. The fragment kinetic-energy distributions calculated by the two methods are in good agreement if they are compared at times when there is unit probability for dissociation. For slow to moderately rapid dissociation, averaging over the initial phase of the field is unnecessary because there is no rapid decay component. However, this also implies that the wave function must be propagated over many time steps before complete dissociation is achieved. To avoid this, we describe a procedure for fitting a short-time line-shape function, which represents incomplete dissociation of the initial state, to the nondepletion-limit fragment kinetic-energy distribution. A parametric fit to the calculated distributions allows us to extract very accurate estimates of decay rates, ac Stark shifts, and branching ratios.