Sudden approximation, appropriate for rotational excitation

As opposed to the adiabatic limit, we assume in the sudden approximation that the internal motion is slow compared to the external (i.e., translational) motion. Most familiar is the rotational sudden approximation which is frequently exploited in energy transfer studies in full collisions (Pack 1974 Secrest 1975 Parker and Pack 1978 Kouri 1979 Gianturco 1979 ch.4). Its application to photodissociation is straightforward and will be outlined below for the model discussed in Section 3.2. 

Within the rotational sudden approximation we assume that the interaction time is much smaller than the rotational period of the fragment molecule so that the diatom BC does not appreciably rotate from its original position while the two fragments separate. In terms of energies, this requires the rotational energy, Erot, to be much smaller than the total available energy. If that is true, the operator for the rotational motion of BC, hrot, can be neglected in (3.16). The partial differential equation thus becomes an ordinary differential equation, 

One readily proves, using the completeness of the spherical harmonics, that the radial functions Xj (R Ef,j) defined by 

If we assume, in analogy to (3.40), a separable ground-state wavefunc-tion of the form 

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