Stern-Gerlach magnets

Figure 14. Molecular beam intensity profiles of a Na molecular beam, without (A) and with (B) Stern-Gerlach magnetic field on. The undisplaced beam is Na f+ traces of the displaced...

The Stark effect and the Zeeman effect of molecules in an inhomogeneous external field serve to select molecules due to their different rotational quantum states and are thus used to produce molecules with well defined preferential orientations in a beam molecules with different orientation are differently deflected in these fields. With regard to state selectors one can distinguish between simple deflection devices like Stern-Gerlach magnets (and their electrical analogues) and multipole fields where molecules with a well-defined Stark or Zeeman-effect are focused into the detector. In both cases the state selector works as a filter enhancing the relative number of molecules in a certain quantum state. 

The Stern-Gerlach experiment demonstrated that electrons have an intrinsic angular momentum in addition to their orbital angular momentum, and the unfortunate term electron spin was coined to describe this pure quantum-mechanical phenomenon. Many nuclei also possess an internal angular momentum, referred to as nuclear spin. As in classical mechanics, there is a relationship between the angular momentum and the magnetic moment. For electrons, we write... 

Orbital angular momentum of an electron in an atom can be measured by the same type of Stern-Gerlach experiment described before for the measurement of electron spin. In this case it will be assumed to use a metal such as magnesium whose atoms have a total electron spin of zero. The magnetic moment... 

Let us consider this case in some detail. If collisions are eliminated in a molecular beam, it is possible to orient molecules (their figure axis) by removing the particles possessing unwanted orientation (analogous to the Stern-Gerlach experiment with a magnetic field). Then, classically, the interaction energy with external electric field is simply... 

This degeneracy is lifted in a magnetic field, for instance in a Stern-Gerlach experiment. 

The spinor that describes the spherical rotation satisfies Schrodinger s equation and specifies two orientations of the spin, colloquially known as up and down (j) and ( [), distinguished by the allowed values of the magnetic spin quantum number, ms = . The two-way splitting of a beam of silver ions in a Stern-Gerlach experiment is explained by the interaction of spin angular momentum with the magnetic field. 

The results of the Stern-Gerlach experiment were in complete contradiction to the classical interpretation and its predictions. Silver atoms turned out to possess a magnetic moment, but instead of a single, smeared-out distribution, two spots centered around Mup and Mdown were observed. Thus the magnetic moment of a silver atom is space-quantized by an inhomogeneous magnetic field, and this magnetic moment can adopt only two values, hz Hhl ... 

From our present standpoint, we know that the deflection of a silver atom in the Stern-Gerlach experiment is caused by the interaction of its electronic spin angular momentum S with an inhomogeneous magnetic field. The projection of S on the direction of this field, Ms, is quantized. For a silver atom, Ms can take two values +vjh and — h, where h is Planck s constant h over 2ji and adopts a value of 1.054571596 x 10-34 Js in cgi units. 

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... 

There have been a couple of studies on triple decker benzene complexes of scandium and related transition metals M2(C6H6)3 (M = Sc, Ti, V). Stern-Gerlach measurements have shown that the magnitudes of their magnetic moments are reduced from their spin-only values by a factor of 1/4 for M = Sc and Ti, and 3/5 for V.87 Ab initio calculations have given insight into... 

Shortly after the results of the Stern-Gerlach experiment appeared in the scientific literature. Stern received an invitation to join the faculty at the University of Hamburg, where, over the period 1922 to 1933, he continued his experimental work. In 1932, Stern decided to adapt the molecular beam method to a daunting experiment to measure the magnetic moment of the proton, the nucleus of the hydrogen atom. Joining him is this endeavor was Otto Robert Frisch. 

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