Franck-Condon distribution

Let us make this more quantitative using the time-independent quantum mechanical theory outlined in Section 3.1. Because the interaction potential is independent of r the potential matrix V defined in (9.2) is diagonal, i.e., different vibrational fragment states do not mutually couple. As a result, the matrix of radial wavefunctions Xri (A, r E, n), which solve the coupled equations (3.5), is diagonal as well, i.e., Xri E,n) o firm - If we assume, in order to simplify the subsequent discussion, that the nuclear wavefunction in the ground electronic state factorizes as pr R) / r(r) [see Equation (3.40)] the dissociation amplitudes t(E,n) in Equation (3.14) reduce to a single term for each final state n and the unnormalized final state distribution becomes 

If the radial overlap integrals g(E, n) are considered as functions of the translational energy Etrans = E — en, where the en are the vibrational energies of the product molecule, they do not depend on the vibrational quantum number n because the radial functions Xn Etrans,n) all solve 

The photodissociation of HONO — HO + NO via the A state produces OH radicals predominantly in the lowest vibrational state (Vasudev, Zare, and Dixon 1984). Although the lifetime of the excited complex amounts to several NO and OH vibrational periods, there is no appreciable restoring force which could change the O-H bond distance during the fragmentation. The calculated two-dimensional PES of Suter and Huber (1989) clearly elucidates this particular aspect of the dissociation dynamics of HONO which is otherwise more complex.  

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Franck-Condon distribution Electron-impact ionization high kinetic-energy ion beam... 

H2+(Jf2S,+ ) Franck-Condon distribution Merging ion-neutral beams electron-impact ionization... 

Studies of electron-impact ionization of molecular nitrogen and oxygen near threshold [141, 142] have demonstrated that a Franck-Condon distribution of vibrational levels is not obtained because many ions are formed indirectly, via autoionizing states. The importance of autoionization can be seen in the case of where the Franck-Condon factors for transitions... 

Fixed at ab initio values [4], The value of A9q, agrees well with the Franck-Condon distribution of band intensities. 

The initial wave packet is provided by a vertical transfer of the vibrational ground state of the neutral molecule to the potential energy curve of the ground electronic state of the D2. This Franck-Condon distribution of the vibrational states of the ion has been employed. To obtain back the vibrational ground state of the neutral molecule one has to assume the initial wave packet on the curve as the superposition of all the vibrational states of the D J ion. 

From rotational analysis of HCCI and DCCI and from the Franck-Condon distribution of the intensities of the vibrational bands in the photoelectron spectmm. 

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