Centrifugal coupling

After making these adjustments to allow for the fact that the analysis line cannot be located in the region of space where the centrifugal coupling in the body-fixed coordinates is negligible, and also for the fact that the analysis of Ref. 75 did not account for the long-range analytic form of the spherical Bessel functions, the space-fixed S matrix of Eq. (4.47) must be transformed back to the body-fixed axes and Eq. (4.46) must be used to compute the state-to-state differential cross sections [136,160]. 

For a non-linear polyatomic molecule, again with the centrifugal couplings to the vibrations evaluated at the equilibrium geometry, the following terms form the rotational part of the nuclear-motion kinetic energy ... 

As described by Schweizer and Chandler [123] and also by Myers and Mar-kel [124], the effective potential for the vibration-rotation centrifugal coupling is the rotational kinetic energy which is given by... 

The vibrations and rotations are coupled via the Hv, term in Eq. (4). This coupling can be divided into two contributions. The first includes those terms that are proportional to JJp, which is the difference between the second term in Eq. (1) and Hr. These are referred to as centrifugal coupling. The second includes those terms that are linear in Ja. These contributions are referred to as a-axis Coriolis coupling and consist of the third term in Eq. (1). 

With the above approach we can combine the use of curvilinear normal coordinates with the Eckart frame. When we do so, the harmonic oscillator, rigid rotor, and, to lowest order, the Coriolis and centrifugal coupling contributions to H have exactly the same form as those found for the more commonly used Watson Hamiltonian (58). 

J is a good quantum number. This means that it is a strictly conserved quantity and that calculations can be carried out separately for each J quantum number. A is the quantum number for the projection of the total angular momentum on the body-fixed z axis. This is not a good quantum number in the sense that the dissociation dynamics of the system mixes up, or couples, different A values. The different A values are coupled by the centrifugal coupling terms in the hamiltonian operator, eq. (5.1). 

In (5.88), terms are centrifugal coupling terms that are independent... 

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