Complex effective Hamiltonian approach for ir multiphoton dissociation

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Abstract
A complex effective Hamiltonian (CEH) approach is formulated in the semiclassical (quantum-molecule–classical-field) representation for the study of ir multiphoton-dissociation processes. This formulation enables one to evaluate the dissociation dynamics in terms of the discrete states only. The effects of the bound–continuum-state interactions are manifested in the CEH matrix by the addition of level shifts and imaginary decay widths to the unperturbed bound-state energies and bound-bound dipole-coupling elements. The periodicity of the CEH matrix in time is preserved, allowing the use of Floquet theory to exactly evaluate the time development of the system. This CEH formulation requires that transitions between continuum states can be safely ignored, that the bound-continuum dipole couplings vary slowly with the continuum state energy ɛ, and that time t is sufficiently long. High field intensities also tend to make these requirements more stringent. It is found that the CEH matrix in the semiclassical representation can be asymmetric with respect to the level shifts and decay widths. For the ir multiphoton dissociation of a nonrotating model diatomic molecule in the ground electronic state, a rather truncated form of the CEH is tested against a discretized continuum plus optical potential method. Despite the high field intensity and relatively short laser pulse used in these tests, the results indicate that this CEH method works well provided the bound-continuum dipole-coupling elements vary slowly with ɛ. As can be expected, the validity of the CEH is limited when the bound-continuum dipole couplings vary strongly with ɛ, which is the case with our model diatomic molecule. The nature of the bound-continuum interactions can apparently have considerable effect on the dissociation dynamics.

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