Angular momentum diatomic rigid rotor

Here is the reduced mass of the coUisional system, B is the rotational constant of the diatom (rigid rotor approximation assumed), j and J are the operators for rotational angular momentum of the diatom and total angular momentum, respectively, and V is the interaction potential. The BF z-axis is chosen to lie along the ion-diatom center of mass vector R, such that Q is the projection of both J and j along the BF z-axis. 

The coordinate system used in the close-coupling method is the space-fixed frame. For simplicity we consider the atom-diatom scattering. The wave function iM(.R,r,R) for an atom-rigid rotor system corresponding to the total energy E, total angular momentum J, and its projection M on the space-fixed z axis can be written as an expansion,... 

Simple as they may appear, the classical Hamiltonians developed for rigid rotors in the preceding section are conceptually new. In our discussion of diatomic rotations in Chapter 3, the rotational states JM> were obtained as eigenfunctions of the space-fixed angular momentum operators and P =P 4-Jl + P. The space-fixed angular momentum components J, Jy, p obey the familiar commutation rules... 

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