Preparation of the initial state

An important ingredient in our analysis was the characterization of the initial state of the system 11) as a nonstationary state. Otherwise, if 11 was an eigenstate oiH, its time evolution would satisfy (Z) = = e / l, and Ci(Z) = 

The answer is not unique, but a general statement can be made A short time external perturbation exerted on a system in a stationary state (i.e. an eigenstate of the system s Hamiltonian) will generally move the system into a nonstationary state provided that the duration of this perturbation is short relative to h/ E, where E is a typical spacing between the system s energy levels in the spectral range of interest. In what follows we describe a particular example. 

Consider a molecule in its ground state tj/g, an exact eigenstate of the molecular Hamiltonian, subjected to the very short external perturbation M S (Z) (such as caused by a very short radiation pulse, in which case M is proportional to the dipole moment operator). From Eq. (2.74) truncated at the level of first-order perturbation theory 

Therefore, the excited component in the resulting state arises from Now, if, because of selection rules, (1 M g f 0 but (Z M g) = 0 for all I, the excited state of the system following this sudden excitation will be the non stationary state 11). 

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Coherent preparation of the initial state (—) thermal preparation of the initial state, (see Ref. 25 for more details). (From Ref. 25.)... 

A previous review provides a description of the theory of electronic relaxation in polyatomic molecules with particular emphasis on the vibronic state dependence of radiationless transition rates. A sequal review considers the general question of collisional effects on electronic relaxation, while the present one covers only the special phenomenon of collision-induced intersystem crossing. It departs from the other collisional effects review in presenting only a qualitative description of the theory the full theoretical details can be obtained from the previous review and the original papers.As a review of the basic concepts of radiationless transitions theory is necessary as a prelude to a discussion of collision-induced intersystem crossing, considerable overlap exists between this section and Section II of the previous collision effects review. However, since many concepts from radiationless transition theory, such as the nature and criteria for irreversible decay, the role of the preparation of the initial state, the occurrence of intramolecular vibrational relaxation, etc. pervade the other papers on laser chemistry in these volumes, it is useful to recall the primary results of the theory of electronic relaxation in isolated molecules and its relevance to the material in the present volume as well as to this review. 

The computation now proceeds in three stages The preparation of the initial state, the subsequent application of local unitary transformations to obtain a suitable final state, and the measurement on the final state to get the solution. 

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