Introduction to Fiber Diffraction

Helix Selection Rule

For more complicated helices which repeat after two or more turns n and l are related by the helix selection rule

l = tn + um

The selection rule is an integer equation which makes use of an alternative definition of helix symmetry: there are t subunits in u turns of a repeat. m can take all positive and negative integer values. As an example, for an [alpha] helix t=5 and u=18 i,e, there are 18 subunits arranged on 5 turns per repeat. Solutions to the selection rule tell you which Bessel functions will turn up on which layer lines. Bessel functions with very large orders can be forgotten since they will occur so far out in the diffraction pattern (at such high resolution) that they will not be visible. Converseley, if one can figure out which Bessel functions turn up on which layer lines one knows the symmetry. The effects helical symmetry are in fact very useful for an analysis of fiber diffraction patterns. Without helical symmetry all Bessel functions would turn up on all layer lines, which would be a mess. The helical symmetry limits the allowed Bessel to one or two per layer-line which renders such problems tractable.