An Analytical Formulation of CPMAS

Details An Analytical Formulation of CPMAS An Analytical Formulation of CPMAS

2002-03-02

arxiv.org/abs/physics/0203003v1

Physics

Chemical Physics

12 pages, 4 figures

Scientific paper

An exact expression for the cross polarization between two spin-1/2 particles is derived from the quantum Liouville equation. This is given in the form of two integrodifferential equations. These can be solved exactly in the static case (no sample spinning) and a powder average performed numerically. With magic angle spinning, the neglect of certain interference terms simplifies the numerical calculation. A further assumption decoupling the calculation of the sidebands gives a very simple formula that is capable of giving a qualitative interpretation of all experimental observations. Examples are given illustrating typical buildup curves and CPMAS matching profiles.

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