Angular momentum Zeeman effect

When the magnetic field is along the axis of quantization, the Zeeman interaction splits the Sj = j and = states but does not mix them. The splitting is just /SH g S there is little contribution from orbital angular momentum as there are no low-lying excited states to be mixed in by the spin-orbit coupling. Therefore, along the z direction the effective g value is about 2. 

Such splitting is called zero field splitting and indicated as ZFS. It adds up to the Zeeman energy. In the spin-Hamiltonian formalism, i.e. when the effects of the orbital angular momentum are parameterized, it is indicated as... 

The origin of this magnetic moment was not clear in 1922. In its electronic ground state, a silver atom does not possess a spatial angular momentum, and the concept of an intrinsic electronic angular momentum (the electron spin) was yet to be created. In 1925, Goudsmit and Uhlenbeck introduced a fourth (spin) electron degree of freedom—in addition to the three spatial coordinates (x, y, z)—as a model to ease the explanation of the anomalous Zeeman effect.3,4... 

Let us first consider the normal Zeeman effect, which applies to transitions between electronic states with zero total spin magnetic moment, so-called singlet states. Like the projection Ms of S in the Stern-Gerlach experiment, the projection Ml of the spatial angular momentum L is space quantized in the external magnetic field. We shall describe the quantization of the spatial angular momentum by means of quantum mechanical methods in detail later. Suffice it to say that each state with spatial angular momentum quantum number L splits into 2L + 1 components, i.e., a P state (L = 1) splits into three components with... 

This term describes the rotational Zeeman effect, that is, the coupling between the external field and the magnetic moment of the rotating nuclei. We note that there is no corresponding vibrational contribution since R a k is zero. The physical reason for this lack is that it is not possible to generate vibrational angular momentum in a diatomic molecule because it possesses only one, non-degenerate, vibrational mode. 

A recent paper [32] has suggested that the primary g-factors, gs and g L, should be defined as negative quantities so that they reveal the alignment of the magnetic dipole moment relative to the angular momentum. If this convention is adopted, the signs of the two contributions to the effective Zeeman Hamiltonian, given above, must be reversed. 

We have already shown the importance of the Zeeman effect, both in identifying the J quantum numbers involved in each line, and in providing effective g-factors for the levels. These g-factors serve as additional labels for each level, and provide information concerning the best angular momentum coupling scheme. We now develop the theory of the Zeeman effect in Hund s case (c). 

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