Asymptotic properties of H q

The properties of H(q) for large q are directly related to the singularities of p(r) and this fact is a consequence of (E.4). In particular, for a random structure, or a structure with a random position, the asymptotic behaviour of H(q) depends mainly on the singularities of p(r) at the origin. 

we aim at showing how the asymptotic behaviour of H(q) depends, for large q, on the properties of the corresponding structure. 

In particular, it will be shown that a solid D-dimensional body with a random orientation in a d-dimensional space (d D) has a form function whose asymptotic behaviour is not at all the same when d D and when d = D. 

we shall illustrate this remark by studying the form function of a rigid rod in various cases then, afterwards, we shall consider the form factors associated with convex solid bodies of dimension D. Finally, we shall determine the asymptotic behaviour of the form factor of critical continuous polymer chains (Brownian chains and Kuhnian chains). 

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