Excitation-manifold basis

We consider a model for the pump-probe stimulated emission measurement in which a pumping laser pulse excites molecules in a ground vibronic manifold g to an excited vibronic manifold 11 and a probing pulse applied to the system after the excitation. The probing laser induces stimulated emission in which transitions from the manifold 11 to the ground-state manifold m take place. We assume that there is no overlap between the two optical processes and that they are separated by a time interval x. On the basis of the perturbative density operator method, we can derive an expression for the time-resolved profiles, which are associated with the imaginary part of the transient linear susceptibility, that is,... 

On the assumption of the identity of their 19.8 kK. band with the 21 kK. band of Brown et al., Allen, El-Sharkawy, and Warren rejected the ZT ig -+ zEg assignment on the basis of comparisons with the isoelectronic Os(IV) species, and attributed all the bands below 20 kK. as arising from transitions within the t g manifold. Thus the rather indistinct absorption at 12.9 kK. was assigned as the nearly coincident zT g - -lEt and ZT iff lTZg excitations, and the well defined peak at 19.8 kK. as... 

Figure 3. Dressed state basis for atomic collisions. A - The square of the transfer matrix between the excitation Fock state and the dressed state bases for N = M = 100. Darker areas correspond to larger probability. B - Damping spectrum between the N = M = 5000 manifold and the N = 4999, M = 5000 manifold. Dashed line k = 3.2, dotted line k = 1.6 and solid line k = 0.7, q = k/ /2. Inset energy-conserving surfaces for the two center frequencies of the solid line and for elastic damping from mode k (dashed line). The splitting in the spectrum is due to the nonlinear population oscillations due to three-wave mixing of the modes in the time domain. This behavior is analogous to that of a strongly driven two level atom (Mollow splitting).

In Section 9.3 we have used this truncated dressed state picture to discuss photoabsorption and subsequent relaxation in a model described by a zero-order basis that includes the following states a molecular ground state with one photon of frequency doorway state with no-photons, l, 0), and a continuous manifold of states /) that drives the relaxation. This model is useful for atomic spectroscopy, however, in molecular spectroscopy applications it has to be generalized in an essential way—by accounting also for molecular nuclear motions. In the following section we make this generalization before turning to consider effects due to interaction with the thermal environment. 

As the unperturbed Hamiltonian, we choose the same HF Hamiltonian as was employed in the above EP development, and we use a basis set of real orthonormal spin-orbitals. We develop an approximation to the PP that yields the primary excitation energies and the corresponding transition moments (and the frequency-dependent polariziibility) consistent through second order in the residual electronic repulsion (Nielsen et ai, 1980). To determine the poles belonging to the principal excitation energies, the corresponding transition moments, and the frequency-dependent polarizability through second order, it proves sufficient to consider the truncated projection manifold... 

---