Zeeman-splitting

Figure 16.1. (a) Simplified scheme of EPR phenomenon, showing the energy-level splitting (Zeeman effect) for the electron spin S = 1/2 (Ms = +1/2) as a function of applied magnetic field (H), (b) the EPR absorption line, and (c) first derivative of absorption line, indicating the g value and line width (AH), normally detected in the EPR spectra. 

Spin system, 157, 159 Splitting, Zeeman, 154 Stability study, accelerated, 260 Standard potential, 254, 359 Standard reaction, 315 Standard state, 253 selection of, 208 Stationary-state hypothesis, 101 Statistical analysis, 40 Statistical analysis of solvent effects,... 

For an understanding of ESR in crystals, a detailed discussion of the molecular fundamentals is necessary. We deal with this primarily in Sections 7.2 and 7.3. There, the spin quantisation in triplet states, magnetic dipole-dipole couphng, zero-field splitting, Zeeman spHtting and fine structure are explained. These fundamentals apply both to isolated molecules and to excitons (Sects. 7.4 and 7.5). In the two later Sects. 7.6 and 7.7 of this chapter, the so called optical spin polarisation in excited triplet states and dynamic nuclear spin polarisation will be treated. 

Figure 7.3 Energy level splittings (Zeeman energies) of a muon in a magnetic field. Also indicated are the common notations used for these levels [12].

From the optically pumped atomic or molecular Rydberg levels neighbouring levels can be reached by microwave transitions, as was mentioned above. This "triple resonance" (two-step laser excitation plus microwave) is a very accurate method to measure quantum defects, fine-structure splittings, Zeeman and Stark splittings in Rydberg states [10.75]. 

Of the NMR-active nuclei around tluee-quarters have / > 1 so that the quadnipole interaction can affect their spectra. The quadnipole inter action can be significant relative to the Zeeman splitting. The splitting of the energy levels by the quadnipole interaction alone gives rise to pure nuclear quadnipole resonance (NQR) spectroscopy. This chapter will only deal with the case when the quadnipole interaction can be regarded as simply a perturbation of the Zeeman levels. 

Fig. 51. Zeeman splitting of the lowest AE octet of the CHj group. Levels of the E state with m = +1/2 are twice degenerate.

In spin relaxation theory (see, e.g., Zweers and Brom[1977]) this quantity is equal to the correlation time of two-level Zeeman system (r,). The states A and E have total spins of protons f and 2, respectively. The diagram of Zeeman splitting of the lowest tunneling AE octet n = 0 is shown in fig. 51. Since the spin wavefunction belongs to the same symmetry group as that of the hindered rotation, the spin and rotational states are fully correlated, and the transitions observed in the NMR spectra Am = + 1 and Am = 2 include, aside from the Zeeman frequencies, sidebands shifted by A. The special technique of dipole-dipole driven low-field NMR in the time and frequency domain [Weitenkamp et al. 1983 Clough et al. 1985] has allowed one to detect these sidebands directly. 

For electron spin resonance (ESR) measurements, the sample is placed in a resonant microwave cavity between the pole pieces of an electromagnet. The magnetic field is gradually increased, which induces a Zeeman splitting of the excila-... 

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. 

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...

Zeeman energies of the ground and the excited states, respectively. The splitting of the 7 = 3/2 state Into two dotted lines In the middle panel indicates the effect of quadrupole splitting discussed earlier... 

Fig. 4.10. The left side of the scheme represents the starting situation of pure Zeeman splitting, as described by (4.48) and shown before in Fig. 4.9. In this example, the field B = (0,0,B), which defines the quantization axis, is chosen as the z-direction. The additional quadrupole interaction, as shown on the right side of Fig. 4.10, leads to a pair-wise shift of the Zeeman states with mj = 3/2 and mi = 1/2 up- and down-wards in opposite sense. In first order, all lines are shifted by the same energy as expected from the m/-dependence of the electric...

Ml = 3/2 than for mj = 1/2. Moreover, the ground state experiences pure Zeeman splitting A M.g 4s given by (4.48) (recall, the nuclear g factor of the 7g = 1/2 ground state is different from that of the L = 3/2 excited state). 

If the electric quadrupole splitting of the 7 = 3/2 nuclear state of Fe is larger than the magnetic perturbation, as shown in Fig. 4.13, the nij = l/2) and 3/2) states can be treated as independent doublets and their Zeeman splitting can be described independently by effective nuclear g factors and two effective spins 7 = 1/2, one for each doublet [67]. The approach corresponds exactly to the spin-Hamiltonian concept for electronic spins (see Sect. 4.7.1). The nuclear spin Hamiltonian for each of the two Kramers doublets of the Fe nucleus is ... 

Fig. 4.15 Effective nuclear g values for the excited I = 3/2 state of Fe in units of the corresponding nuclear g factor (g e = —0.10317). The left panel shows the Zeeman splitting of the 7 = 3/2 manifold with large quadrupole slitting under the influence of a weak field, and the two panels on the right show the 77-dependence of the corresponding effective nuclear g values for the I m/ = 1/2 and m/ = 3/2) doublets with the field oriented along the x, y, and z principal axes of the EFG...

---