On the behaviour of the short Kratky-Porod chain

Using the exact computation of a large number of moments of the distribution function of the end-to-end distance G(r,N) of the worm-like chain, we have established the analytical form of the coefficients in Taylor expansions of the moments for short chain lengths N. The knowledge of these coefficients enabled us to resum the moment expansion of G(r,N) by taking into account consecutively the deviations of the moments from their stiff rod limit. Within this procedure we have derived the short-chain expansion for G(r,N), the scattering function, and the extension-force relation, which take into account the deviations of the moments from their stiff rod limit to the seventh order in N