3: Magnetic Interaction Energy (Anomalous Zeeman Effect)
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- 66538
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The interaction energy of the magnetic moments of the atom, with the external field is given by
- ---------------[45]
With the help of relation , where , the equation (45) is simplified to
- ---------------[45']
With projection of on , i.e. component of along , relation (45') reduces to
- (in mks units)
- (in cgs units) with ---------------[46]
Finally, in terms of Bohr magneton,
- ---------------[47]
Or ---------------[47']
- is Lorentz unit ---------------[48]
gives the change in energy for each of from the original line. Obviously, apart from the dependence on , the Landeʹg factor plays an important role to find the relative separations of the Zeeman levels. The value of the g-factor depends on , and ; consequently, value of and therefore the energy differences, is different for different terms i.e. different values. This results in the appearance of the several lines in accordance with the selection rule . Further, when spin is disregarded , value of turns out to be one; in such a case, the differences between the Zeeman levels again reduce to , that is the equation reduces to Lorentz’s classical formula.
Levels in Anomalous Zeeman levels split into equidistant levels for a given but with a magnitude times , the separation observed in the normal Zeeman Effect. In the absence of anomalous behaviour of the spin, is expected to be equal to would have been in line with resultant mechanical moment; consequently
A relation similar to the one obtained for orbital motion except that is replaced by . Magnetic interaction energy (in ) then is given by
- or ---------------[49]
Separations between Zeeman lines (because ) would have again been same like in the case of normal Zeeman Effect.
Zeeman patterns for yellow sodium lines (first member of the Principal series) are derived as an
factor for are
Similarly, g- factor for and are and 2 respectively. Self explanatory figure (8) shows splitting of Zeeman levels, transitions in accordance with the selection rules , and finally pattern of expected anomalous Zeeman spectrum. Dotted horizontal line on the left side represents the centre of gravity of the levels, dotted vertical transitions indicate forbidden transitions and the heights of the expected spectral lines (shown at the bottom of the Fig. 8) indicate relative intensities.
Fig.8 Anomalous Zeeman pattern of Sodium lines.
Electromagnetic waves that have undergone Zeeman Effect get polarized; nature of polarization as mentioned in the beginning of the section 3 depends on the direction (with respect to the magnetic field) of the field of view. Polarization rules can be derived both from the classical theory as well as from the quantum mechanics. These are summarised below:
Transverse View (viewed perpendicular to the direction of magnetic field, )
1. Transitions with yield plane polarized light having its electric vector oscillating perpendicular to , termed as - components.
2. Transitions with yield plane polarized light having its electric vector oscillating parallel to , termed as - components.
Longitudinal View (viewed parallel to the direction of magnetic field, )
1. Transitions with yield circularly polarized light, termed as - components.
2. Transitions with are forbidden.
Problem: Discuss the Anomalous Zeeman spectra of the green and violet lines of mercury.