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Coupling of Angular Momentum

An electron in a diatomic molecule has a variety of angular momenta, associated with different electronic states and energy levels. For diatomic molecules, it is quite common to express the angular momenta in terms of projections along the internuclear axis, as these are better quantum numbers than the value of the angular momentum itself. The different types of angular momenta which are important to this study and their projections onto the internuclear axis are given in Table 3.1.


Table 3.1: Angular momenta in diatomic molecules
Angular Quantum Projection along
Momentum Number Molecular axis
Total J $\Omega = \Lambda +\Sigma$
Electronic Orbital L $\Lambda$
Electronic Spin S $\Sigma$
Nuclear rotation R -
Total less spin N= R + L $\Lambda$


As angular momentum is not a scalar quantity, it is necessary to consider the addition of various angular momenta in terms of vector addition. The coupling of the momenta with the nuclear rotational angular momentum R, gives rise to the different Hund's cases:

Figure 3.3: Coupling of angular momenta for Hund's case (c)
\includegraphics{figures/hundc.eps}

Due to the large spin-orbit coupling in GeH+ , which arises from the large coupling in the atomic Ge+ of 1,767 cm-1, the molecule should strictly be treated using Hund's case (c). However, for the purposes of this work, it can be treated adequately within a Hund's case (a) formalism, as is the case for the isovalent CH+ and SiH+.


next up previous contents
Next: Lambda doubling Up: Spectroscopic theory Previous: Spectroscopic theory   Contents
Tim Gibbon
1999-09-06