Close-coupling approach for rotational excitation

If we fix the intramolecular distance of the diatom, the system is described by the two Jacobi coordinates R and 7, where R is the distance from A to the center-of-mass of BC and 7 is the orientation angle of the diatom with respect to the scattering vector R. The appropriate Hamiltonian is given by (see Section 11.1 for a more detailed discussion) 

In the limit R — 00, hrot goes over into the rotational energy of the free fragment. The eigenfunctions of hrot are the rotor wavefunctions, i.e., 

The partial dissociation wavefunctions (R, 7 -E1, j), which describe dissociation into A+BC(j), are now expanded in terms of the Yju(7,0) according to  

Inserting (3.19) into the Schrodinger equation and proceeding as described in Section 3.1 yields the set of coupled equations 

The product of the ground-state wavefunction and the transition dipole function is also expanded in terms of spherical harmonics, 

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