Coherence levels and coherence pathways in NMR. A simple way to design phase cycling procedures |
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| Affiliation: | 1. CLST NMR Facility, RIKEN, Yokohama, Kanagawa 230-0045, Japan;2. JEOL RESONANCE Inc., Musashino, Akishima, Tokyo 196-8558, Japan;3. Biophysics and Department of Chemistry, University of Michigan, Ann Arbor, MI 48109-1055, USA;1. Institut für Physik - NMR, Martin-Luther-Universität Halle-Wittenberg, Betty-Heimann-Str. 7, D-06120 Halle, Germany;2. Institut für Chemie – Organische Chemie, Martin-Luther-Universität Halle-Wittenberg, Kurt-Mothes-Str. 2, D-06120 Halle, Germany;1. Univ. Lille, CNRS, Centrale Lille, Univ. Artois, UMR 8181 – UCCS – Unité de Catalyse et Chimie du Solide, Lille 59000, France;2. Univ. Lille, CNRS, INRAE, Centrale Lille, Univ. Artois, FR 2638 – IMEC – Fédération Chevreul, Lille 59000, France;3. Nano-Crystallography Unit, RIKEN-JEOL Collaboration Center, Yokohama, Kanagawa 230-0045, Japan;4. Bruker Biospin, 34 rue de l''industrie, Wissembourg 67166, France;1. Chemical Physics, Lund University, Sweden;2. Institute of Molecular Biosciences, Goethe University Frankfurt, Germany;3. Cavendish Laboratory, University of Cambridge, United Kingdom |
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| Abstract: | The paper presents a simple way of calculating what a phase cycling procedure in a pulse NMR experiment does. This is done by exploiting the fact that if a pulse is phase shifted by angle φ and if it changes the coherence level by Δm, then the effect on the coherence is a multiplication by eiΔmφ The coherence level is a fundamental quantum number of the system-the z component of the Liouville space angular momentum—and is a generalization of the number of quanta in a multiple-quantum transition. The sequence of coherence levels that a signal passes through between the first pulse and the time it reaches the receiver is the coherence pathway. This pathway, combined with the above formula, provides a powerful method for analyzing pulse NMR experiments. |
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