Equivalence of population-flow and quantum-mechanical derivations of quadrupolar multiplet intensities
File(s)
Published version
Author(s)
Kuchel, Philip W
Elliott, Stuart J
Eykyn, Thomas R
Type
Journal Article
Abstract
In a previous article (Concepts Magn. Reson. Part A, 40A, 90–99, 2012) a simple explanation for the relative intensities of the components of quadrupolar-split nuclear magnetic resonance (NMR) multiplets was presented. The derivation avoided angular-momentum operator algebra and instead used a population-flow argument based on Boltzmann statistics and relaxation from magnetic saturation. Some colleagues subsequently suggested that the agreement between this intuitive derivation and the standard quantum-mechanical result might be coincidental. In this paper, we show explicitly that the two approaches are mathematically equivalent. The excess-spin construction used previously corresponds directly to the diagonal elements of the deviation density matrix, and the recursive population-flow relations map onto the same quadratic dependence that arises from the matrix elements of the transverse spin operator. Thus, the derivation is neither heuristic, approximate, nor accidental: it is an alternative representation of the same underlying quantum-mechanical structure. The presented work gives an intuitive understanding of the NMR peak intensities observed for quadrupolar nuclear spins embedded in anisotropic materials.
Date Issued
2026-06-01
Date Acceptance
2026-05-01
Citation
Journal of Magnetic Resonance Open, 2026, 27
ISSN
2666-4410
Publisher
Elsevier BV
Journal / Book Title
Journal of Magnetic Resonance Open
Volume
27
Copyright Statement
© 2026 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
License URL
Publication Status
Published
Article Number
100219
Date Publish Online
2026-05-05