The Anomalous Zeeman Effect

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  

On the other hand, the revolving electron acts like a circular current of strength I = e oj/27r), where co is the frequency of revolution, and so generates a magnetic field. But the magnetic field of a circular current I is, as we know, equivalent to that of a magnetic dipole of moment M = Aljc, where A is the area enclosed by the circuit, and 

The value e /(47rjiic) therefore represents the smallest unit for the magnitude of a magnetic orbital moment in the atom it is called the Bohr magneton. 

If a homogeneous magnetic field is applied, the atom is set into processional motion (fig. 3) about the direction of the field, as has been explained above (p. 109) consequently the component m of U in this direction must be a whole number (quantisation of direction). As for the supplementary 

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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 ... 

The origin of this magnetic moment was not clear in 1922. In its electronic ground state, a silver atom does not possess a spatial angular momentum, and the concept of an intrinsic electronic angular momentum (the electron spin) was yet to be created. In 1925, Goudsmit and Uhlenbeck introduced a fourth (spin) electron degree of freedom—in addition to the three spatial coordinates (x, y, z)—as a model to ease the explanation of the anomalous Zeeman effect.3,4... 

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. 

Carrying on the investigation of the anomalous Zeeman effect and the Paschen-Back effect on the spectra of the alkali atoms, Pauli postulated that an electron in an external magnetic field has to be described by four independent quantum numbers. Moreover, in order to justify the Bohr-Sommerfeld Aufbau (building-up) principle of the periodic system of the elements, he came up with his famous exclusion principle (Ausschliefiungsprinzip). In its original formulation it reads 10... 

In contrast, electron spin caused an early conundrum, the "anomalous" Zeeman effect Atoms with an odd number of electrons, placed in a magnetic field, showed a complicated number of lines. If L = 0, two lines were seen,... 

Bohr s theory leaves some questions unexplained. Why must the pendulum orbits be excluded The reason given, which points to the collision with the nuchius, is hardly cogent moreover, it is outside the bounds of Bohr s theory. How does the anomalous Zeeman effect come about The explanation of this, as we shall see (p. 140), requires us to use the fact that the el( ctron possesses in itself mechanical angular momentum and magnetic moment. Finally, the calculation of the simplest problem of the type involving more than one body, viz. the lielium problem, h .ads to difficulties, and to results contrary to exjKvrimental facts. 

The anomalous Zeeman effect, however, can be explained completely by assuming that the magnetic spin-moment is got from the mechanical, not by multiplying by e/2/xc, as with orbital moments, but by multiplying by ejfjiC, so that... 

It is just this difference between the orbital and the spin-moments which is responsible for the anomalous Zeeman effect. The result of it is that the vector sum of the magnetic moments, i.e. the total magnetic moment M, is not in general in the same direction as the total... 

Fig. 4.— Vector model for the anomalous Zeeman effect. The direction of the total angular momentum does not coincide with the direction of the resultant magnetic moment only the component M parallel to / is magnetically effective the other component Mj disappears when avei aged, on account of the rotation of the vector figure about j (the total angular momentum).

Fig. s.— Transitions in the anomalous Zeeman effect since the splitting is different in the various term groups, we get in general just as many separated lines as there are possible transitions altogether. 

The splitting np of a line in the anomalous Zeeman effect is therefore essentially determined by the Lande factors for the upper and lower states. These factors, as will now be shown, can be ascertained with comparative ease from the developments already given with regard to the vector model. ... 

Fig. 6.—Splitting of the sodium D lines in the anomalous Zeeman effect. I he splitting (> /,) in the normal cfFect is...

Abstract. This chapter is relative to the calculation in other external fields, limited here to a weak magnetic field, giving one of the most important phenomena associated with the Dirac theory, the anomalous Zeeman effect. 

They considered an increasing spin perturbation H2 that may reduce the original symmetry to only the second operation, or in other words, the irreducible structure of subspaces for II are decomposed into smaller non-decomposing components of H +H2. This theory, then, also explained the splitting of spectral terms by a perturbation that produces spin differences naturally. Empirically, such a phenomenon has been observed in the anomalous Zeeman effect, as spectral... 

In 1926 it was realized that there is a property of the electron other than the charge which must be taken into account, namely, the magnetic moment associated with intrinsic spin. It was shown by Goudsmit and Uhlenbeck [53] that this property, which represents an extra degree of freedom and therefore demands a fourth quantum number, could account for the doublet structure of the alkali spectra and the anomalous Zeeman effect. If was necessary and sufficient that the extra quantum number he two-valued. 

For systems other than singlets, g is not equal to 1. In this case, a more complicated splitting occurs the anomalous Zeeman effect. For example, consider the doublet system in hydrogen and the alkali metals. The lowest term is 5 /2 For this term, L = 0, J = S = therefore Mj = i, — i and g = 2. The product gMj = 2( ) = 1. Using this value in Eq. (24.49) we obtain... 

The experimental spectrum of atomic H shows good agreement with this model, except when it is subjected to a magnetic field, which results in a splitting of the spectrum lines. This phenomenon, also known as the anomalous Zeeman effect, can be explained by assuming that, in addition to its orbital momentum, an electron possesses an intrinsic angular momentum, p, with value p = [s(s + l)y h, where s is the spin quantum... 

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). 

In strong magnetic fields the magnetic energy of an atom will be higher than the splitting of the lines. Then the L-S interaction will become negligible and the anomalous Zeeman effect resembles the Zeeman triplet (the Paschen-Back effect). 

Figure 12 The anomalous Zeeman effect splitting and the allowed transitions...

The sensitivity obtained by transverse AC Zeeman AAS for the elements with the normal Zeeman pattern is good and often nearly the same as for the conventional AAS. In addition, for many elements with the anomalous Zeeman effect such as Ni, Mn, Sb, Tl, and Ag,... 

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