Hyperfine relaxation

Figure 8.4 Magnetic field dependence of the Zeeman (the full curves) and hyperfine relaxation (the dashed curves) cross sections at zero electric field (a), = 10 kV/cm (b), and E = 10 kV/cm (c). The symbols in the upper panel are the results of the calculations without the spin-rotation interaction. The collision energy is 0.1 K x kg. Adapted with permission from Ref. [86].

The present Chapter deals with the hyperfine shifts which are only due to the average electron induced magnetic moment and therefore are related to (Sz). Chapter 3 will deal with nuclear hyperfine relaxation which, as discussed above, depends on both average electron induced magnetic moment (Curie relaxation) and on the full electron magnetic moment (dipolar and contact relaxation). 

Thus measuring the SLR time as a function of temperature gives a simple diagnostic tool for assessing, whether the hyperfine relaxation is dominant in the system. Similarly, the plot of relaxation rate (1/Ti) as a function of Larmor frequency (a>) gives information about the dimensionality of conduction. 

Continuous wave operation of COIL is facilitated by the hyperfine structure of the atom. Iodine has a nuclear spin of, so the P /2 and Pz/2 levels are split by hyperfine interactions. Figure 8 shows the allowed transitions between the hyperfine sublevels and a high resolution emission spectrum. The F = 3 — F" = 4 transition is most intense, and this is the laser line under normal conditions. Collisional relaxation between the hyperfine sub-levels of Pz 2 maintains the population inversion, while transfer between the Fi/2 levels extracts energy stored in the F = 2 level. Hence, if it is not sufficiently rapid, hyperfine relaxation can limit power extraction. 

Collisions between I and closed-shell collision partners (He, Ar, and N2) did not relax the nonequilibrium hyperfine distribution to any measurable degree. But, in accord with the theoretical picture outlined above, hyperfine relaxation was observed for collisions with 02(A). For example, the shift towards equilibrium can be seen in Fig. 9 by comparing traces recorded in the absence and presence of O2. Hyperfine transfer induced by collisions with O2 was examined at the temperatures T = 295, 150, and 10 K. For T > 150 K, I quenching and hyperfine transfer occurred at simUar rates. Hence, both processes were considered in the kinetic model used to extract the rate constants. At the lowest temperature (10 K) quenching was negligible. The hyperfine transfer rate constants were found to be independent of temperature, within the experimental errors. Values oi k F = 2 F = 3) = (2.3 0.5) X 10- and fc(F = 3 -> F = 2) = (1.6 0.5) x 10" cm s... 

Currently the experiment is limited by sample heating effects on the hyperfine relaxation time of the spins, as evidenced by an apparent T] time which varies by up to 20% on timescales of order 5 min. This seems to indicate that too much excess heat is being generated inside the sample volume by the pump pulse, causing temperature fluctuations. In addition, there are various mechanical and electronic problems that limit our ability to take reproducible data over the timescales necessary to do the measurement. 

Hyperfine Interaction (dipolar and scalar) 2,0 Electron relaxation, may be complicated Paramagnetic systems and Impurities [17-191... 

The tliree-line spectrum with a 15.6 G hyperfine reflects the interaction of the TEMPO radical with tire nitrogen nucleus (/ = 1) the benzophenone triplet caimot be observed because of its short relaxation times. The spectrum shows strong net emission with weak E/A multiplet polarization. Quantitative analysis of the spectrum was shown to match a theoretical model which described the size of the polarizations and their dependence on diffrision. 

For example, if the molecular structure of one or both members of the RP is unknown, the hyperfine coupling constants and -factors can be measured from the spectrum and used to characterize them, in a fashion similar to steady-state EPR. Sometimes there is a marked difference in spin relaxation times between two radicals, and this can be measured by collecting the time dependence of the CIDEP signal and fitting it to a kinetic model using modified Bloch equations [64]. 

The value of the magnetic hyperfine interaction constant C = 22.00 kHz is supposed to be reliably measured in the molecular beam method [71]. Experimental data for 15N2 are shown in Fig. 1.24, which depicts the density-dependence of T2 = (27tAv1/2)-1 at several temperatures. The fact that the dependences T2(p) are linear until 200 amagat proves that binary estimation of the rotational relaxation rate is valid within these limits and that Eq. (1.124) may be used to estimate cross-section oj from... 

OIDEP usually results from Tq-S mixing in radical pairs, although T i-S mixing has also been considered (Atkins et al., 1971, 1973). The time development of electron-spin state populations is a function of the electron Zeeman interaction, the electron-nuclear hyperfine interaction, the electron-electron exchange interaction, together with spin-rotational and orientation dependent terms (Pedersen and Freed, 1972). Electron spin lattice relaxation Ti = 10 to 10 sec) is normally slower than the polarizing process. 

In addition to the standard constraints introduced previously, structural constraints obtainable from the effects of the paramagnetic center(s) on the NMR properties of the nuclei of the protein can be used (24, 103). In iron-sulfur proteins, both nuclear relaxation rates and hyperfine shifts can be employed for this purpose. The paramagnetic enhancement of nuclear relaxation rates [Eqs. (1) and (2)] depends on the sixth power of the nucleus-metal distance (note that this is analogous to the case of NOEs, where there is a dependence on the sixth power of the nucleus-nucleus distance). It is thus possible to estimate such distances from nuclear relaxation rate measurements, which can be converted into upper (and lower) distance limits. When there is more than one metal ion, the individual contributions of all metal ions must be summed up (101, 104-108). If all the metal ions are equivalent (as in reduced HiPIPs), the global paramagnetic contribution to the 7th nuclear relaxation rate is given by... 

Thus, the starting parameters for the computer-simulation of spectrum IB were chosen to agree with the value of hyperfine fields at 613 K as measured by Rlste and Tenzer, using neutron scattering measurements (36). In addition, the magnetic relaxation rate depends on temperature, as discussed in the Theory section of this paper. 

Fig. 6.2 Theoretical Fe Mossbauer relaxation spectra for longitudinal relaxation with the indicated relaxation times and with a hyperline field that can assume the values 55 T. The symmetry direction of the axially symmetric EFG is assumed parallel to the magnetic hyperfine field. (Reprinted with permission from [9] copyright 1966 by the American Physical Society)...

When, however, phonons of appropriate energy are available, transitions between the various electronic states are induced (spin-lattice relaxation). If the relaxation rate is of the same order of magnitude as the magnetic hyperfine frequency, dephasing of the original coherently forward-scattered waves occurs and a breakdown of the quantum-beat pattern is observed in the NFS spectrum. 

Fig. 9.24 Theoretical calculations of nuclear forward scattering for the relaxation rates as indicated for a system with electron spin S = 1/2, hyperfine parameters A y jg fi = 50 T, and AF.q = 2 mm s in an external field of 75 mT applied perpendicular to k and O . The transition probabilities co in ((9.8a) and (9.8b)) are expressed in units of mm s , with 1 mm corresponding to 7.3 10 s. (Taken Ifom [30])...

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