Rotational angular momentum of the nuclei

The angular momentum 0 then combines with the angular momentum O due to the rotation of the molecule to give a total angular momentum (apart from nuclear spin) J. (In the older literature, the rotational angular momentum of the nuclei is called N instead of O.) The magnitude of J is... 

We see from the way in which the effective rotational Hamiltonian is constructed that it is naturally expressed in terms of the angular momentum operator N. In the scientific literature, however, it is frequently written in terms of the vector R (which represents the rotational angular momentum of the nuclei) rather than N. While R = N — L occurs in the fundamental Hamiltonian (7.71), its use in the effective Hamiltonian is not satisfactory because R has matrix elements (due to L) which connect different electronic states and so is not block diagonal in the electronic states. In practice, authors who claim to be using R in their formulations usually ignore any matrix elements which they find inconvenient such as those of Lx and Ly. We shall return to this point in more detail later in this chapter. 

Atomic nuclei possess nuclear spin, the angular momentum of the nucleus, which is due to rotation. Sinee nuclei contain an electric charge, in the form of protons, their rotation often produces an electric current which creates a magnetic field. Like an electromagnet, therefore, the nucleus has a magnetic moment. 

Let us summarize the Hund coupling scheme [5, 6, 7] that is given in Table 1 together with the quantum numbers of the quasimolecule for each case of Hund coupling. We denote by L the total electron angular momentum of the molecule, S is the total electron spin, J is the total electron momentum of the molecule, n is the unit vector along the molecular axis, K is the rotation momentum of nuclei, A is the projection of the angular momentum of electrons onto the molecular axis, H is the projection of the total electron momentum J onto the molecular axis, 5 is the projection of the electron spin onto the molecular axis, Lyv, Si, Jn are projections of these momenta onto the direction of the nuclear rotation momentum N. Below we will take this scheme as a basis. 

As regards the angular momentum of the electrons in diatomic molecules, we have seen in the previous paragraph that it has no influence on the rotational motion of the nuclei, and gives rise only to an additive term in the energy if its axis is parallel to the line joining the nuclei. The same must be true when the nuclei perform oscillations in this direction we shall therefore restrict ourselves here to this case. 

If we also allow for the possibility of rotation of the nuclei, this leads to the addition of a positive term proportional to 1/p, originating in the centrifugal forces, to the function Vo(p) which determines the nuclear vibration. This term is larger if the molecule rotates faster. For a molecule without angular momentum of the electrons around the internuclear axis, which behaves like a simple rotator, this term is... 

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