Zeeman relaxation

Proton n.m.r. measurements of Zeeman relaxation for the same coal showed (Jurkiewicz,A., Colorado State University, personal communication, 1988) that mobile protons represent 32% of all protons. Assuming that the content of hydrogen in the mobile and immobile phases of the coal is approximately the same, the relaxation measurements indicate that the coal mobile phase content is app. 32 wt % of organic material. 

Figure 8.8 The ratios of the cross sections for elastic scattering and Zeeman relaxation in NH- NH collisions as functions of the magnetic field at different collision energies 10" cm" ...

P. A. Beckmann, M. Bloom and E. E. Burnell, Deuteron Zeeman relaxation of CD4 in the isotropic liquid, the liquid crystalline, and the solid state of several substances.. Chem. Phys., 1986, 54(10), 5898-5905. 

While Tp the Zeeman relaxation time, is sensitive to motions occurring at the Larmor speed in the large applied field, the dipolar relaxation time is sensitive to fluctuations occurring at the Larmor speed in the local field which is three to five orders of magnitude smaller. The former might be in the range of 5-300 MHz while the latter will be in the few kHz range. 

Ihese FC Txd results lead to two important conclusions by contrasting the data with pertinent theoretical expressions. Making use of the well-established finding that order fluctuations (OF) of the nematic director dominate the Zeeman relaxation time, Tiz, in the kHz region up to typically 1 MHz, one can simplify equations (lb), (3a) and (4a) for frequendes <10 kHz to the spedal forms ... 

Translational energy thermalization of molecules in buffer-gas-cooling experiments is mediated by elastic collisions with helium atoms. In order to estimate the efficiency of buffer-gas-cooling experiments, it is necessary to understand the mechanism of Zeeman relaxation and evaluate the cross-sections for elastic scattering and... 

Figure 4.2 illustrates that the probability of Zeman relaxation in NH-He collisions is very small and extremely sensitive to the magnitude of an external magnetic field at low collision energies. The efficiency of Zeeman relaxation in collisions of molecules in the E electronic states is determined by the magnitude of the spin-rotation and spin-spin interactions giving rise to the molecular fine-structure [13]. The results of Figure 4.2 indicate that the fine-structure interactions in the NH molecule are weak. 

FIGURE 4.2 Ratio of cross-sections for elastic scattering and Zeeman relaxation in colli-... 

The mechanism of Zeeman relaxation in collisions of molecules in electronic states with nonzero electronic orbital angular momenta is different from that in collisions of E-state molecules. The response of non-E-state molecules to a magnetic field is determined by both the electron spin and the orbital angular momentum of the electrons in the open electronic shell. The orbital motion of the electrons induces electronic anisotropy, which gives rise to multiple adiabatic interaction potentials between the collision partners [20]. Consider, for example, the collision system of a hydrogen atom in an excited P state and a structureless atom, such as He. The interaction between the atoms can be described by an effective potential as a function of the interatomic distance and an angle between the direction of the electronic F-orbital and the interatomic separation line. The angular dependence of this potential is the electronic anisotropy. An alternative description of the interatomic interaction can be... 

FIGURE 4.4 Zero-temperature rate eonstant for Zeeman relaxation in collisions of rotation-ally ground-state NH( S) moleeules in the maximally stretched spin level with He atoms. Such field dependence is typical for Zeeman or Stark relaxation in ultracold collisions of atoms and molecules without hyperfine interaction. The variation of the relaxation rates with the field is stronger and extends to larger field values for systems with smaller reduced mass. (Adapted from Krems, R.V., Int. Rev. Phys. Chem., 24, 99, 2(X)5. With permission.)... 

Both Zeeman and Stark relaxation in collisions of molecules are determined by the anisotropy of intermolecular interactions. The mechanisms of Zeeman and Stark transitions in collisions of E-state molecules are, however, different. For example, Zeeman relaxation in collisions of CaH molecules with He atoms is induced by an interplay of the atom-molecule interaction anisotropy coupling different rotational states of the molecules and the spin-rotation interaction coupling the rotational... 

Hutson, J.M., Feshbach resonances in ultracold atomic and molecular collisions threshold behaviour and suppression of poles in scattering lengths. New. J. Phys., 9,152,2007. Maussang, K., Egorov, D., Helton, J.S., Nguyen, S.V., and Doyle, J.M., Zeeman relaxation of Cap in low temperature coUisions with heUum, Phys. Rev. Lett., 94, 123002, 2004. 

FIGURE 13.5 Trapped molecule lifetime vs. buffer-gas density (note semilog scale) for two hypothetical molecular species. For the dashed curve, the helium-induced Zeeman relaxation cross-section has been increased by a factor of 10. 

A significant drawback of trapping via a LFS Zeeman sublevel is that this opens an exothermic inelastic collision channel. During a collision, a stretched-state [76] LFS molecule can undergo a Zeeman transition to a less-trapped or even HFS state. This process is referred to as either spin relaxation [77] (as in Figure 13.5) or collision-induced Zeeman relaxation. To utilize buffer-gas loading to trap a species, this process must be sufficiently unlikely that the external motion of the molecule can be thermalized and the experiment carried out before the Zeeman state changes. 

Zeeman Relaxation Collisions between Molecules and Helium... 

All of the mechanisms described above for atoms can and do lead to helium induced Zeeman relaxation of diatomic molecules. There are, however, additional pathways leading to trap loss that are unique to molecules. Figure 13.8c shows a hypothetical electron charge density for a diatomic molecule in the rest frame of the molecule. Comparison to Figure 13.8a,b suggests that a similar argument of... 

State, which exhibits significant anisotropy in the lab frame. It is the manipulation of the rotational wavefunction by the helium interaction that governs collision-induced Zeeman relaxation of molecules. 

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