Zeeman energy levels

Figure 5. Energy level diagram for a spin 5/2 nucleus showing the effect of the first-order quadrupolar interaction on the Zeeman energy levels. The (m V2 m = -V2) transition (shown in bold) is independent of the quadrupolar interaction to...

Figure 8.5 (a) Zeeman energy levels of the CaD( H) molecule. The dashed line shows the energy... 

Fig. 5.2. Zeeman energy level pattern for the OD A2T,+, v = 0, IV = 1, J = 3/2 level as a function of magnetic field.

This equation means that the spin populates the two Zeeman energy levels according to the Boltzmann distribution. 

Figure 11.16. Zeeman energy level diagram for the N = 1 level of para- H2 in the 3nu, v = 1 state, and the transitions responsible for the spectrum shown in figure 11.15.

In the presence of a strong magnetic field, a nucleus possessing spin I > 0 is in one of 21 +1 equally spaced Zeeman energy levels. Each nucleus is also exposed to the influence of other nuclei, which modify the local magnetic field. Thus, the total Hamiltonian is expressed by the sum of the six individual interactions. The units for the Hamiltonians are given elsewhere.14... 

Chemical Shifts. In Exp. 32, the Zeeman energy levels of a nucleus in an external applied field were given as... 

Fig. 11. Zeeman energy levels of atomic oxygen in the P states.

Transitions between Zeeman energy levels, and hence nuclear magnetic relaxation, are caused by fluctuations (time variations) in the local interactions at the nucleus that can cause transitions. The transition rates between these energy levels that cause nuclear spin relaxation depend on two factors ... 

The quadrupolar interaction shifts each of the three Zeeman energy levels by an amount... 

Figure 2. Zeeman energy levels of positronium in its ground state.

ESR studies as applied to micellar systems rely on the sensitivity of a free radical probe to its microenvironment. Molecular species with a free electron posses labeled intrinsic angular momentum (spins), which in an external magnetic field undergoes Zeeman splitting. For a system with 5 = 1/2, two Zeeman energy levels are possible whose energy gap (AE) is given by ... 

Fig. 2. Zeeman energy levels for electron spin 5 and nuclear spin / (a) scalar coupling, dominant relaxation transition S / (b) dipolar coupling, dominant relaxation transition S-1+. ...

Originally the three-spin effect was postulated to explain the positive enhancements observed for certain fluorine nuclei in solvents also containing protons.The possibility arose that the fluorine nuclei were being influenced by the proton polarization as well as by the direct coupling to the electron spins. The basic idea behind the three-spin effect can be seen by considering the transitions among the Zeeman energy levels shown in Fig. 20. Since the electron—proton interaction is of the dipolar kind, the predominant coupled transition will be an... 

Fig. 20. Zeeman energy levels for electron open S, proton H and fluorine F. The dominant relaxation mechanisms are S-H and H+F+. ...

Figure 2. Effect of the quadrupole interaction on the Zeeman energy levels of an 1 = 1 nucleus with axial symmetry. I is the total spin, m its component, and 6 is the angle between the applied magnetic field and the principal (z) axis of the quadrupole splitting tensor.

The sensitivity of conventional nuclear magnetic resonance (NMR) is rather poor compared with other spectroscopic techniques like EPR or optical spectroscopy. This is a result of the small population difference between the nuclear Zeeman energy levels even in the highest magnetic fields currently available in the laboratory. At room temperature, and in a magnetic field of 9.4 T, the polarisation of the protons is less than 4 x 10. In order to overcome this inherent limitation, methods to improve the signal to noise ratio (SNR) in magnetic resonance experiments have been the subject of active research since the discovery of NMR. 

Figure 5. Energy level diagram for a spin 5/2 nucleus showing the effect of the first-order quadrupolar interaction on the Zeeman energy levels.

Fig. 5. Zeeman energy level diagrams for (nn ) benzophenone in canonical orientations. Allowed (A, B) and forbidden (C) transitions are shown for a frequency of 9.6 GHz (Mucha, 1974).

Figure 8 shows the Zeeman energy level diagrams for the two possible zf schemes of (nn ) benzophenone with the magnetic field parallel to the / axis of D. It is known that 90% of the radiative activity to the (0,0) band originates in the sublevel (Yamauehi and Pratt, 1979a). Since the application of a field parallel to / mixes with (Table 8), the -l-l> and I — 1 > sublevels are radiative in hf whereas the 0> sublevel is dark. At low temperatures (< 4.2 K), both hf ODMR transitions of triplet benzophenone are detected as increases in the phosphorescence intensity in this orientation. Thus, o > under our excitation conditions, in agreement with... 

---