The magic angle is a precisely defined angle, the value of which is approximately 54.7356°. The magic angle is a root of a second-order Legendre polynomial, and so any interaction which depends on this second-order Legendre polynomial vanishes at the magic angle. This property makes the magic angle of particular importance in magic angle spinning solid-state NMR spectroscopy.
Read more about Magic Angle: Mathematical Definition, Magic Angle and Nuclear Magnetic Resonance, Application To Medical Imaging: The Magic Angle Artifact
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