Longitudinal cross-relaxation rate

The longitudinal cross-relaxation rate (see Eq. (13)) originates solely from the terms in the dipolar Hamiltonian involving both spins, namely those terms corresponding to zero-quantum and double-quantum transitions so that... 

Concerning these cross-relaxation rates, an important point is that the longitudinal cross-relaxation rate a// can go through zero at relatively high measurement frequencies and therefore become non-observable, whereas this... 

In small molecules, these artifacts are rarely observed because crossrelaxation rates are small. However, in biological macromolecules, crossrelaxation rates become competitive with the rate of Hartmann-Hahn transfer, because they increase with the correlation time or molecular weight. Fortunately, in large molecules it is possible to suppress contribitu-ions from cross-relaxation, based on the opposite signs of transverse and longitudinal cross-relaxation rates and (Griesinger et al.,... 

The symbols Rauto and Rcross within the relaxation matrix are the auto- and cross-relaxation rates, respectively. and (l2Z) are the longitudinal magnetizations of spin 1 and 2, respectively, and the brackets indicate averaging over the whole ensemble of spins. Rcross in terms of the spectral densities is given by... 

Fig. 12. Comparison of longitudinal and transverse cross-relaxation rates as a function of the measurement frequency (vq) for a pair of protons and a normalized spectral density of the form 2tc/(1 -I- (see Eqs. (58) and (59)).

The last point is about equivalent spins (or like spins as the two protons of the water molecule). Referring to Solomon equations (see (13)), we can notice that, because of this equivalence, the effective longitudinal relaxation rate is obtained by adding the cross-relaxation rate to the specific longitudinal relaxation rate ... 

Based on Eq. (139), a relationship between A and the contribution of of longitudinal cross-relaxation to the effective cross-relaxation rate [see Eq. (131)] can be derived. For two spins with the same offset v, = Vj, the invariant trajectories are identical [n j Kt) = and the... 

This equation shows that perturbation of 5 affects the z magnetization of / at a rate ajs, known as the cross-relaxation rate. In contrast to this, relaxes back to its equilibrium magnetization at a rate pjs, known as the dipolar longitudinal relaxation rate (which is similar to the spin-lattice relaxation rate 1/Ti). 

When l l, the above gives the so-called cross-correlation functions and the associated cross-correlation rates (longitudinal and transverse). Crosscorrelation functions arise from the interference between two relaxation mechanisms (e.g., between the dipole-dipole and the chemical shielding anisotropy interactions, or between the anisotropies of chemical shieldings of two nuclei, etc.).40 When l = 1=2, one has the autocorrelation functions G2m(r) or simply... 

---