Zeeman effects

As mentioned above, in the case of Kramers ions with non-integer value of J, the crystal field does not completely lift the degeneracy of the / levels. This degeneracy can however 

f wrsLWu lWrs L ) (iPrsi i7Vk/ 5 i ) PrstWu lWrs L ) 

Pb is the Bohr Magneton B is the magnitude of the external magnetic field and g is Lande s factor (Equation 1.36) in the LS coupling scheme. 

If the applied magnetic field is parallel to the z-axis of a crystal, the splitting energy Ez is given by 

Mz is the quantum number associated with this perturbation. If, on the other hand, the Zeeman interaction is anisotropic, the Hamiltonian in Equation 1.35 should be rewritten as 

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Sutter D FI and Flygare W FI 1976 The molecular Zeeman effect Topics Curr. Chem. 63 89... 

Not only can electronic wavefiinctions tell us about the average values of all the physical properties for any particular state (i.e. above), but they also allow us to tell us how a specific perturbation (e.g. an electric field in the Stark effect, a magnetic field in the Zeeman effect and light s electromagnetic fields in spectroscopy) can alter the specific state of interest. For example, the perturbation arising from the electric field of a photon interacting with the electrons in a molecule is given within die so-called electric dipole approximation [12] by ... 

Magnetic circular dicliroism (MCD) is independent of, and thus complementary to, the natural CD associated with chirality of nuclear stmcture or solvation. Closely related to the Zeeman effect, MCD is most often associated with orbital and spin degeneracies in cliromophores. Chemical applications are thus typically found in systems where a chromophore of high symmetry is present metal complexes, poriihyrins and other aromatics, and haem proteins are... 

From accurate measurements of the Stark effect when electrostatic fields are applied, information regarding the electron distribution is obtained. Further Information on this point is obtained from nuclear quadrupole coupling effects and Zeeman effects (74PMH(6)53). 

Another legacy of the late nineteenth century was identification of the electron by an appropriate interpretation of the Pieter Zeeman effect in 1896, and more especially by J. J. Thomson s experiments the... 

In the previous section it has been shown that the measured sample absorbance may be higher than the true absorbance signal of the analyte to be determined. This elevated absorbance value can occur by molecular absorption or by light scattering. There are three techniques that can be used for background correction the deuterium arc the Zeeman effect and the Smith-Hieftje system. 

In practice, the emission line is split into three peaks by the magnetic field. The polariser is then used to isolate the central line which measures the absorption Ax, which also includes absorption of radiation by the analyte. The polariser is then rotated and the absorption of the background Aa is measured. The analyte absorption is given by An — Aa. A detailed discussion of the application of the Zeeman effect in atomic absorption is given in Ref. 51. 

This adiabatic principle was one of the corner-stones of the old quantum theory. It allowed one to find the quantum conditions when an adiabatic change was imposed on a system. It was used successfully to account for the Stark and Zeeman effects in the spectrum of atomic hydrogen, resulting from the application of an electric and magnetic field respectively (Schwartzchild [1916] Epstein [1916]). 

The number of energy levels found to date, with the aid of the Zeeman effect and the isotope shift data, is 605 even and 586 odd levels for Pu I and 252 even and 746 odd for Pu II. The quantum number J has been determined for all these levels, the Lande g-factor for most of them, and the isotope shift for almost all of the Pu I levels and for half of those of Pu II. Over 31000 lines have been observed of which 52% have been classified as transitions between pairs of the above levels. These represent 23 distinct electron configurations. 

First-order means that we consider nothing beyond that described here. In second-order , we would include the effects of mixing between ground and excited states brought about by the magnetic field. This is briefly discussed under second-order Zeeman effects later. 

Microwave spectra obtained from PHgD and PHDa in a magnetic field of about 25 kG showed Zeeman effects, from which molecular g values were calculated. They were 20 times smaller than those for ammonia. The molecular quadrupole moments of phosphine and ammonia were approximately the same. Magnetic susceptibilities and molecular quadrupole moments were also compared. 

A nucleus in a state with spin quantum number 7 > 0 will interact with a magnetic field by means of its magnetic dipole moment p. This magnetic dipole interaction or nuclear Zeeman effect may be described by the Hamiltonian... 

Fig. 4.9 Magnetic dipole splitting (nuclear Zeeman effect) in pe and resultant Mossbauer spectrum (schematic). The mean energy of the nuclear states is shifted by the electric monopole interaction which gives rise to the isomer shift 5. Afi. g = Sg/tN and A M,e = refer to the...

The nuclear Zeeman effect is not a very strong interaction as compared to electric quadrupole splitting because of the relatively weak nuclear magneton. A field of B... 

Au dissolved in ferromagnetic hosts of Fe, Co, Ni as sources versus Au metal absorber Nuclear Zeeman effect in Au atoms, super-transferred hf fields, // at Au sites... 

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