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## Magic angle (EELS)This article is about the ## Additional recommended knowledgeThe The "magic" angle depends on both the incoming electron
energy (which is typically fixed) and on the energy-loss suffered by the electron. The
ratio of the magic-angle θ ## Mathematical definitionIn the non-relativistic case the "magic" angle is defined by the equality of two different functions
(denoted below by
and
where β is the speed of the incoming electron divided by the speed of light (N.B., the symbol β is also often used in the older literature to denote the collection-angle instead of α). Of course, the above integrals may easily be evaluated in terms of elementary functions, but they are presented as above because in the above-form it is easier to see that the former integral is due to momentum-transfers which are perpindicular to the beam-direction whereas the latter is due to momentum-transfers parallel to the beam-direction. Using the above definition it is then found that ## References- Daniels H, et al. (2003). "Experimental and theoretical evidence for the magic angle in transmission electron energy loss spectroscopy".
*Ultramicroscopy***96**: 523-534.
- Schattschneider P, et al. (2005). "Anisotropic relativistic cross-sections for inelastic electron scattering, and the magic angle".
*Phys. Rev. B***72**: 045142.
- Jouffrey B, et al. (2004). "The Magic Angle: a solved mystery".
*Ultramiscoscopy***102**: 61-66.
Categories: Materials science | Spectroscopy | Radiology | Magnetic resonance imaging |

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Magic_angle_(EELS)". A list of authors is available in Wikipedia. |