Special directions for surface integrals in cubic lattices with application to the evaluation of the COMPTON profile of copper

Several sets of special directions are presented which allow the integration of functions with full cubic symmetry over a solid angle. These sets yield a higher accuracy than those published up to now. The sets corresponding to N = 2, 3, 4, 6 and 7 directions satisfy the criteria of the best choice rather well. But even for N = 8, 10, 12, 24 and 48 the sets proposed allow an approximation by a finite series of cubic harmonics with high precision. These sets are useful both for experimentalists and theoreticians. Extensive measurements e.g. experiments needing large exposure time are suitably done with a small set whereas theoreticians will prefer the big sets due the large CPU capacities now available. The power of these considerations is illustrated by evaluation of the spherical average of the Compton profile of Cu. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)