Lorentz Zeeman effect

With most lines, however, an anomalous Zeeman effect is observed and the number of components is greater, in some cases reaching twelve or fifteen. They arc symmetrically arranged and symmetrically polarized. The displacements, as in the simpler case, are proportional to the magnetic field intensity H, and are always expressible, in wave numbers, as rational multiples of the displacemenl in the normal effect, which is 4.67 x I0 57f (reciprocal centimeter), a quantity known as the Lorentz unit. The Zeeman effects observed in sun spots give valuable information as to the magnetic conditions in those areas. 

Abstract. Following a suggestion of Kostelecky et al. we have evaluated a test of CPT and Lorentz invariance from the microwave spectrosopy of muonium. Precise measurements have been reported for the transition frequencies U12 and 1/34 for ground state muonium in a magnetic field H of 1.7 T, both of which involve principally muon spin flip. These frequencies depend on both the hyperfine interaction and Zeeman effect. Hamiltonian terms beyond the standard model which violate CPT and Lorentz invariance would contribute shifts <5 12 and <5 34. The nonstandard theory indicates that P12 and 34 should oscillate with the earth s sidereal frequency and that 5v 2 and <5 34 would be anticorrelated. We find no time dependence in m2 — vza at the level of 20 Hz, which is used to set an upper limit on the size of CPT and Lorentz violating parameters. 

We shall now show that the electron s own magnetic moment, which is bound up with its mechanical moment, supplies the explanation of the anomalous Zeeman effect, i.e. the observed phenomenon that in a (weak) magnetic field a spectral line is split up into a considerable number of lines (fig. 2, Plate VII) while, according to classical theory, and also according to wave mechanics when spin is not taken into account, we can only have the normal Zeeman effect, i.e. the splitting up of every spectral line into a Lorentz triplet. 

These theoretical statements can be tested directly in the case of the normal Zeeman effect. As is well Imown, on transverse observation (at right angles to the magnetic field) we see the normal Lorentz triplet, i.e. a splitting-up into three components. Of these the central one, which corresponds to the transition m -> m and is therefore not displaced, is polarized in the direction of the magnetic field, while the two other components, corresponding to the transitions m i 1 are transversally polarized. In longitudinal observations the undisplaced component disappears and we see only the two displaced components, which, as theory requires, are circularly polarized. 

Fig. III. 14. The effect of the translational Zeeman effect on the absorption spectra of symmetric top molecules moving at different velocities perpendicular to the exterior magnetic field is shown for the J = - J = 2, K =l rotational transition of methylacethylene (l Oj. = 0, 100, 200,. 800 m/sec). With increasing velocity the aligning force of the Lorentz cross field...

Fig. III. 16. In light symmetric top molecules with reasonably large electric dipole moments such as for instance methylfluoride the change of the absorption spectrum due to the translational Zeeman effect occurs at comparatively low perpendicular velocities. The spectrum shown here corresponds to the absorption of a group of molecules moving at 267 m/sec (maximum of the Maxwell-Boltzmann probability distribution) perpendicular to the magnetic field. The dotted line gives the spectrum calculated neglecting the translational Zeeman effect. The Lorentz cross field has caused considerable mixing of Mj substates resulting in considerable changes in the selection rules...

This result is the same as in the classical theory of H. A. Lorentz. It is verified experimentally for such lines of the other elements as are simple (singlets). This simple theory (which is analogous to the classical theory of Lorentz), does not suffice for the explanation of the complicated Zeeman effects which occur in the case of multi-plets. The theory of these anomalous Zeeman effects lies outside the scope of this book.1... 

Stark effect The splitting of lines in the spectra of atoms due to the presence of a strong electric field. It is named after the German physicist Johannes Stark (1874-1957), who discovered it in 1913. Like the normal Zeeman effect, the Stark effect can be understood in terms of the classical electron theory of Lorentz. The Stark effect for hydrogen atoms was also described by the Bohr theory of the atom. In terms of quantum mechanics, the Stark effect is described by regarding the electric field as a perturbation on the quantum states and energy levels of an atom in the absence of an electric field. This application of perturbation theory was its first use in quantum mechanics. 

The discovery of the Zeeman effect at the close of the nineteenth century proved to be the first essential step in the study of extraterrestrial magnetism. The classical derivation is based on Lorentz electron theory. An electron spirals about a magnetic-field fine due to the Lorentz force. 

Extensions allowing CPT and Lorentz invariance violations [23] lead to atomic models that reflect the symmetry violations as shifts in the atomic energy levels. It has been argued that such effects can be discovered in the fine-structure of Is — 2s transitions and also in the hyperfine structure of Zeeman transitions. 

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