Nuclear Larmor frequency

Often the electronic spin states are not stationary with respect to the Mossbauer time scale but fluctuate and show transitions due to coupling to the vibrational states of the chemical environment (the lattice vibrations or phonons). The rate l/Tj of this spin-lattice relaxation depends among other variables on temperature and energy splitting (see also Appendix H). Alternatively, spin transitions can be caused by spin-spin interactions with rates 1/T2 that depend on the distance between the paramagnetic centers. In densely packed solids of inorganic compounds or concentrated solutions, the spin-spin relaxation may dominate the total spin relaxation 1/r = l/Ti + 1/+2 [104]. Whenever the relaxation time is comparable to the nuclear Larmor frequency S)A/h) or the rate of the nuclear decay ( 10 s ), the stationary solutions above do not apply and a dynamic model has to be invoked... 

A similar approach, also based on the Kubo-Tomita theory (103), has been proposed in a series of papers by Sharp and co-workers (109-114), summarized nicely in a recent review (14). Briefly, Sharp also expressed the PRE in terms of a power density function (or spectral density) of the dipolar interaction taken at the nuclear Larmor frequency. The power density was related to the Fourier-Laplace transform of the time correlation functions (14) ... 

It differs from the equation for R2M for the substitution of the non-dispersive term with an coits dependent term, where a>i is the nuclear Larmor frequency in the B field. Since the latter frequency is always such that >i rc 1, R pm... 

Plots of J o>) versus oj for different values of Tc are shown in Fig. 8.1. The values of rc should be compared with the reciprocal of the nuclear Larmor frequency w0. For either a very short or very long rc the value of J 0 is relatively small. J(to) reaches its maximum when rc = l/o)0, that is, when the average molecular tumbling frequency is equal to the nuclear precession... 

Dynamic nuclear polarization experiments consist of observing the proton NMR signal (at the nuclear Larmor frequency o)n/2tt — 107 s-1), while pumping with microwave power near the ESR Larmor frequency (x>e/2TT — 1010 s 1 (Fig. 7). Two limiting results may occur according to whether the electron nuclear coupling is static or dynamic. In the static case, the elec-... 

Figure 6.24 shows the temperature dependence of the frequency-derivative ENDOR spectra of an unstretched C-enriched c/s-rich sample. Spectra show a clear temperature dependence, where the structures of the lineshape become more prominent as the temperature is lowered. Some structures clearly show the feature of single resonance lines. The spectral lineshapes at higher temperahires are close to those reported in [116]. The detailed measurements of the frequencies of these signals have revealed that the frequencies of the structures are given by the multiple or fractional sum or difference of free proton and C nuclear Larmor frequencies, Vp and v., as marked in the figure. 

The nuclear Larmor frequency v increases with magnetic field and thus with the microwave frequency of the EPR spectrometer, whereas A" and F" are molecular parameters and thus are independent of the field (although, as described below, they are dependent on the g value, or position within the EPR spectrum). This typically means that when the ENDOR transitions from two different types of nuclei (e.g., H, N) are overlapping for one microwave frequency range, they may be resolved by changing to a different microwave frequency, as shown in Fig. 5. 

Practically, the SE requires the use of polarizing agents with a homogeneous EPR line width and an inhomogeneous spectral width smaller than the nuclear Larmor frequency. These agents can ensure that only one of the forbidden transitions is excited at a time. However, the Differential Solid Effect (DSE, [17]) simultaneously exists and leads to partial or complete cancellation of the polarization effect. 

Integrated Solid Effect (ISE) was first introduced by Henstra et al. [17]. It can overcome the low efficiency of SE when the homogeneous width is much larger than the nuclear Larmor frequency (A (Uo v)> in which the polarization effect could be canceled by simultaneous saturation of the forbidden transitions at ct)o fflow-The ISE can preserve the polarization in the case of A coow by inverting a forbidden EPR transition prior to saturation of an allowed transition. This effect can be achieved by using a selective inversion pulse after the irradiation on resonance at cooe i (Oon, or applying CW microwave irradiation at a fix frequency... 

In practice, modem NMR instruments are designed to deliver high-power 90 pulses closer to 10 ps, rather than the hundreds predicted from the above arguments. This is to suppress the undesirable effects that arise when the pulse rf frequency is off-resonance, that is, when the transmitter frequency does not exactly match the nuclear Larmor frequency, a situation of considerable practical significance that has been ignored thus far. 

If solids are irradiated with ultrasound having a frequency below the nuclear Larmor frequency, reference to the discussion of the Raman phonon relaxation process indicates that relaxation emission... 

---