Primary Extinction in Cylinders and Spheres

By transforming the Takagi equations into a representation using angular coordinates, it is in principle possible to obtain analytical expressions for the coefficients in a series expansion for the primary extinction factor in perfect crystals with a circular diffraction plane. In practice, it has been possible to obtain the first five terms in the expansion. This involves establishing recurrence relations for the families of Bragg and Laue boundary-value Green functions combined with integrations over the entrance and exit surfaces. The calculations, which cover the whole range of values for the scattering angle, , are performed using the mathematical software systems Mathematica and Maple.