A Formalism for Scattering of Complex Composite Structures: 2 Distributed Reference Points

Recently we developed a formalism for the scattering from linear and
acyclic branched structures build of mutually non-interacting sub-units.[C.
Svaneborg and J. S. Pedersen, J. Chem. Phys. 136, 104105 (2012)]
We assumed each sub-unit has reference points associated with it.
These are well defined positions where sub-units can be linked together.
In the present paper, we generalize the formalism to the case where
each reference point can represent a distribution of potential link
positions. We also present a generalized diagrammatic representation
of the formalism. Scattering expressions required to model rods, polymers,
loops, flat circular disks, rigid spheres and cylinders are derived.
and we use them to illustrate the formalism by deriving the generic
scattering expression for micelles and bottle brush structures and
show how the scattering is affected by different choices of potential
link positions.