Static and dynamic scattering from fractals

A scaling form for the pair correlation function of random fractals is combined with the scaling form of the percolation distribution of cluster sizes to obtain expressions for the static structure factor S(q) and first cumulant $K_1$ of the dynamic structure factor S(q,t) at the gel point. We find S(q)∼$q^{\mathrm{-}\mu }$ and $K_1$∼$q^3$ with μ=D(3-τ), where D is the fractal dimension and τ is the exponent for the distribution of cluster sizes. Special forms are suggested for the scaling functions to obtain results for the nonscaling regime.