An ultrasimple classical model

We consider the photofragmentation of a triatomic molecule, ABC — A + BC(j), within the model outlined in Section 3.2. The vibrational coordinate of BC is fixed and the total angular momentum is zero. According to (5.23), the classical approximation of the partial photodissociation cross section for producing BC in rotational state j is given by 

As in Section 6.1 we set the initial momenta, Pq and jo, to zero and with the help of (2.57) we eliminate Ro as initial variable. The (unnormalized) final rotational state distribution for a given energy is thus transformed into a one-dimensional integral, 

Re and 7e specify the equilibrium of the electronic ground state and the exponents an and o 7 are related to the frequencies according to (5.16). Throughout this section we will assume that the parent molecule is in its lowest bending state before the excitation takes place. The summation in (6.22) extends over all trajectories which start with initial angle 70O ) and end with a specified final angular momentum j, i.e., which solve the 

In principle, j can be any real number in order to make contact with quantum mechanics and experiment, however, j is confined to the integers 

For simplicity, let us assume that the weighting function is identical to the square of the bending wavefunction 7(7) and secondly, that J(70) 

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