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A comment on powder averaging in wide line NMR
T Iwaniec1, R Kopiecki2, S Szymanski3
1Department of Mathematics, Syracuse University, 900 South Crouse Ave, Syracuse, NY 13244, USA.
Abstract:
Computer calculations of wide line NMR spectra of powders usually involve numerical evaluation of double integrals over two Euler angles. Practice confirms intuition-based expectations that the integration results should be independent from the choice of the crystal-fixed (or molecule-fixed) coordinate system used in the calculations. However, a closer inspection of the relevant integration formulas may make one wonder why this is so. The present paper provides a rigorous mathematical proof of the validity of these intuitive predictions, by formulating the problem in terms of surface integrals on a sphere, which has presumably no precedence in the NMR literature.
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