Zeeman spectroscopy

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 

Let us compare the spectral pattern of a Zeeman-split 1P-1S transition with the Zeeman effect on an electronic transition between an atomic singlet 

Since electric dipole transitions alter the ML quantum number by at most one unit 

Much more interesting and informative than Zeeman spectroscopy on atoms with zero electronic spin is the Zeeman effect on electric dipole transitions between states with a nonzero electronic spin moment. For historical reasons, this is called the anomalous Zeeman effect. 

For their interactions with the external field to be equal, the proportionality constant between the spin angular momentum and the associated magnetic moment must be twice as large as for the angular momentum. More precisely, this ratio amounts to 2.0023 the deviation from the value of 2, predicted by Dirac theory, is mainly caused by radiative corrections explainable in the framework of quantum field theory. 

Finally, we can relate the magnetic dipole to another quantity of quantum-mechanical importance the angular momentum. Consider a particle with a charge of q moving around in a circle. It induces a magnetic dipole. If the particle has a linear velocity v in meters per second and is traveling in a circle having radius r meters, then the time necessary for one circular orbit is 

Because current is defined as charge passing a point per second, the current I at any point in the particle s orbit is 

Remember that the definition of the angular momentum L is L = mr X v, or in our magnitude formalism, L = L = m v r = mvr. Substituting, we find that 

For a single electron, the charge is -e, which equals —1.602 X 10 C. In this case, we have expressly included the minus sign on e because the electron is negatively 

Do not confuse the magnetic dipole, /a, for the symbol for the Bohr magneton, /ab- Th Bohr magneton has a value of about 9.274 X 10 J/T (joules per tesla). It (or similarly defined constants) is a necessary constant for almost all magnetic spectroscopies. 

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Molecular electric quadrupole moments are more elusive animals, and they are not particularly easy to determine experimentally. Prior to 1970, the only direct routes to these quantities were from the Kerr and Cotton-Mouton effects. They can now be obtained from microwave Zeeman spectroscopy, to fair accuracy. It is fair to say that direct calculation offers a faster and more reliable route to this property than experiment. 

The 1.7% Co2+ ZnO DMS-QDs in Figure 34 were also examined by Zeeman spectroscopy in transmission mode. An average band-edge Zeeman shift of 53 cm 1/7 over the range of 0-7 T ( Fig. 35) was measured. The Zeeman data were analyzed in the mean-field approximation using Eq. 11, where x is the dopant mole fraction and (Sz) is the expectation value of the Sz operator of the spin Hamiltonian. 7/oa and iVop quantify the exchange interactions between the dopant and unpaired spins in the conduction (CB) and valence bands (VB), respectively (19, 159-161). 

An investigation of the complete NQR spectrum using single-crystal Zeeman spectroscopy results in the knowledge of... 

The number of different orientations of the EFG tensor due to the symmetry operations of the Laue group is lower if the nuclei occupy special crystallographic sites (special point positions). Information about such special sites of nuclei can be found from NQR single-crystal Zeeman spectroscopy. This is... 

In order to identify the location of the carbon sources, Zeeman spectroscopy has turned out to be a valuable tool. The principles of the influence of the magnetic field on carbon and oxygen ions in the fusion edge plasma (B = 1 to 10 T) have been outlined in [19,20]. The method works well when the Zee-man (Paschen-Back) effect plays an important, or dominant, role in relation to other broadening mechanisms. In general the line splitting is given by ... 

Metalloporphyrins Optically detected ESR, 87, 88 microwave induced delayed phosphorescence, 87, 89 Zeeman spectroscopy, 94 MCD, 95 resonance Raman spectra, 97, 100, 101 ESR, 88,96 photolysis 142 ... 

M. Quack, D. A. Ramsay, L. Veseth, R. N. Zare, Remarks on the signs of g factors in atomic and molecular Zeeman spectroscopy. Mol. Phys. 98 (2000) 1597-1601. 

Af fhe end of the 1960s and 1970s, all spectroscopists agreed upon the fact that MCD was very powerful and a beautiful technique as it describes the ultimate intrinsic electronic properties of matter the characterization of a Zeeman level by a signal fhat has a sign. This is not the case in EPR or classical Zeeman spectroscopy which measure the energy difference between two states (e.g., AM = 1) but which cannot tell which one is... 

Verhoevan, J., and A. Dymanus, Magnetic properties and molecular quadrupole tensor of the water molecule by beam-maser Zeeman spectroscopy. J. Chem. Phys., 1970. 52 3222-3233. 

Fri Friedrich, B., Weinstein, J.D., deCarvalho, R., Doyle, J.M. Zeeman spectroscopy of CaH molecules in a magnetic trap, J. Chem. Phys. 110 (1999) 2376-2383. 

M. Dubs, J. Muhlbach, H. Bitto, R Schmidt, J.R. Huber, Hyperfine quantum beats and Zeeman spectroscopy in the polyatomic molecule propynol CHOCCHO. J. Chem. Rhys. 83,3755 (1985)... 

There are several recent experimental studies on the CeO diatomic molecule. Schall et al. (1986) have studied CeO using the sub-doppler Zeeman spectroscopy. Again, the ligand-field model is so successful in explaining the observed spectra due to the ionic nature of the diatomic lanthanide oxide. Linton et al. (1979, 1981, I983a,b) as well as Linton and Dulick (1981) have studied the electronic spectrum of CeO using absorption, emission as well as laser spectroscopic method. There are many 0-0 bands for... 

One of the most straightforward and simple types of magnetic spectroscopy is called Zeeman spectroscopy. Its existence was proposed in 1890 by the Dutch physicist Hendrik Lorentz. If atoms were composed of electrical charges, Lorentz said, these charges should be affected by a magnetic field and a change would be noted in the atomic spectrum. In 1896 a student of Lorentz s, Pieter Zeeman, verified this prediction experimentally. For their work, Lorentz and Zeeman shared a 1902 Nobel Prize. 

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