Calculation of NMR line shapes in calcium fluoride from modified moment expansions

G. W. Parker and F. Lado
Phys. Rev. B 9, 22 – Published 1 January 1974
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Abstract

Theoretical second, fourth, sixth, and eighth moments of nuclear-magnetic-resonance absorption lines in calcium fluoride are used to examine the convergence of two different modified moment expansion for free-induction-decay (fid) curves. These expansions provide a systematic method of obtaining corrections to two initial approximations to a line shape which are obtained from either the local-field model, which gives a Gaussian fid curve, or the Abragam function. In the former case one obtains the Fourier transform of the Gram-Charlier expansion and in the latter case a Neumann expansion. These expansions may also be applied to the memory function, a local-field correlation function, rather than the fid function since, in general, the functional form of a memory function is insensitive to the form of a line shape and, in particular, these two curves are similar in shape for dipolar-broadened resonance lines. In analyzing the results of these expansions we are led to formulate a condition for oscillations in an fid curve. This condition is that local-field correlations persist for a time T2** which is at least of the order of the mean beat period M212. Here M2 is the second moment of the resonance line and T2** is the relaxation time of the memory function. Also, a new trial function is proposed for CaF2 fid curves which gives the proper behavior at both long and short times.

  • Received 23 July 1973

DOI:https://doi.org/10.1103/PhysRevB.9.22

©1974 American Physical Society

Authors & Affiliations

G. W. Parker and F. Lado

  • Department of Physics, North Carolina State University, Raleigh, North Carolina 27607

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Issue

Vol. 9, Iss. 1 — 1 January 1974

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