科研之友
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摘要
The moments of truncated dynamic magnetic resonance spectra, M-n(L), are expanded in terms of power series of the integration range -L to +L. The expansion consists of three contributions: 1) an L-independent term that, for the first three moments (n=1 to 3), is independent of the motion and equals the corresponding moment, M-n, of the rigid powder spectrum; 2) a limited number of (positive) terms, diverging as L-k (k<n, odd), reflecting the broadening effect due to motion; these terms vanish for the first three moments and become nonzero, with motion-dependent coefficients, only from the fourth moment on; and 3) an infinite series of converging (negative) terms, in powers of 1/L-k (k is odd), reflecting the reduction of the moments due to the truncation of the spectra; these terms are motion dependent for all moments. The convergence properties of this series are discussed and expressions for the lower (truncated) moments in the slow and fast motion limits of a secular Hamiltonian are derived. For the slow motion limit, it is shown how the L-dependence of the moments can be used to estimate the magnetic and dynamic parameters. The procedure is demonstrated using computer-simulated spectra. In the fast motion regime, closed expressions are obtained in a similar form to those of the relaxation equations. The effect of natural line width and strong-collision dynamics on the various moments as well as that of nonsecular terms in the Hamiltonian are also briefly discussed.
- 出版日期2014-2
