Zeeman effect normal

Paschen-Back effect spect An effect on spectral lines obtained when the light source is placed in a very strong magnetic field the anomalous Zeeman effect obtained with weaker fields changes over to what is, in a first approximation, the normal Zeeman effect. pash-on bak i,fekt ... 

Zeeman displacement spect The separation, in wave numbers, of adjacent spectral lines in the normal Zeeman effect in a unit magnetic field, equal (in centimeter-gram-second Gaussian units) to e/4innc, where e and m are the charge and mass of the electron, or to approximately 4.67 x 10 (centimeter) (gauss) . za man di.splas-mant ... 

Figure 14.14—Normal Zeeman effect. Illustration of the oscillating field method (path 1 without field B noise plus element, path 2 with field B noise only).

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... 

Figure 2 Normal Zeeman effect on a 1P-1S transition. The Zeeman splitting is not drawn to scale.

The g = 2 Puzzle. When an atom vapor passes through a magnetic field, the "normal" Zeeman effect splits an optical absorption or emission line into an odd number of lines for example, in a P state the normal Zeeman effect splits the optical spectrum of an atom into three lines, which argues for Mi = —l, 0, +1 states, whence L = 1, and gL = 1. 

Pieter Zeeman was the first to study the effect of an applied magnetic field on atomic emission spectra. Since a perpendicular applied field was subsequently typically used within Zeeman (excited state emission) spectroscopy the normal Zeeman effect is usually described in terms of parallel (II) and perpendicular (J.) plane polarized bands (Figure 1). It should be noted, however, that Zeeman also studied the parallel magnet alignment used within MCD spectroscopy. In Zeeman s words during his Nobel prize lecture in 1902 describing results obtained for emission from the 5d orbital of Cd to the 5p orbital,. But let us first consider the rays... 

Figure 1 The normal Zeeman effect. The emission from an atomic lamp source placed within a magnet observed perpendicular (a) and parallel (b) to the lines of force. It should be noted that when 5 = 0 and the Russell-Saimders spin coupling mechanism is applicable, J = L, and Mj = Ml as shown here. (Reprinted from Mack, Stillman and Kobayashi, Elsevier 2007)...

In a magnetic field, E depends on m also, indeed the extra term mvjh occurs as an addition to the energy, exactly as in Bohr s theory. Wave mechanics, so far as we have developed it up to the present, yields only the normal Zeeman effect (as above, 2, p. 110). To the directional quantisation of Bohr s theory there corresponds here the finite number of values of m, i.e. of energy levels in the magnetic field there are in fact 2Z + 1 of these, in place of each term which occurs when there is no magnetic field. The splitting of the terms in an electric field (Stark effect) is correctly reproduced by wave mechanics, qualitatively and quantitatively. 

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. 

We may briefly recall the explanation of the normal Zeeman effect. The revolution of the electron produces a mechanical moment j>i of the orbital motion, and this is quantised by known rules ... 

Fig. 3.—Precession of the orbital angular momentum, round the direction of the magnetic field (in the absence of the spin it would always lead to the normal Zeeman effect).

Fig. 7.—Vector model for the Paschen-Back effect (transition to the normal Zeeman effect). Since the energy of the orbital moment and spin-moment in the magnetic field is greater than the magnetic interaction between orbit and spin, the orbital and spin-moments process separately round the field direction.

We therefore in this case obtain a term-splitting with the term-separation corresponding to the normal Zeeman effect. Thus when the magnetic field is steadily increased, a gradual transition takes place from the anomalous to the normal Zeeman effect the transitional zone is referred to as that of the Paschen-Back effect. The nomen-... 

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. 

In the two following diagrams we collect the values of the separations of the terms, taking the separation for the normal Zeeman effect as unit. That is, we write down the values mg for the upper and lo ver terms of the two lines. The values of m, like j, must be halves of odd numbers, as they are equal to —j, —j + I,, . . , j. 

These selection rules at once determine the positions of the components in the Zeeman splitting of the D lines. We measure their displacements on either side from a central zero posi-tion, as before taking the separation in the normal Zeeman effect, i.e. in the frequency scale, as unit. The tt com- horizontal axis and the o- components below. We thus obtain the splitting diagram of fig. 6,... 

Figure 13.15 Normal Zeeman effect. Pictoral explanation of the rotating polarizer method.

Since the separation between the levels is the same in the term as in the D2 term, and since the selection rule requires AMj = 0, 1, it follows that each line in the spectrum is split into three lines. The middle line is at the original frequency, while the other two lines are spaced equally on either side of the original frequency. This is the normal Zeeman effect. 

Splitting of the spectral lines into three components according to the normal Zeeman effect occurs only for atoms with singlet lines (terms with A = 0). Singlet lines are the main resonance lines of the alkaline earth metals (Be, Mg, Ca, Sr, Ba) and the Zinc group metals (Zn, Cd, Hg). 

For the normal Zeeman effect the energy levels are expressed as ... 

Figure 10 The normal Zeeman effect splitting of a spectral line in a magnetic field...

The mechanism of the anomalous Zeeman effect is exactly the same as that of the normal Zeeman effect, but it exhibits more than three components. For the anomalous Zeeman effect it is characteristic that the n -compon-ent also splits into several lines and thus no longer coincides exactly with the original resonance line. In this case the Landen factor, g will vary for various terms which is the reason for the splitting of the spectral lines into the several components (Figure 12). 

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