The small-angle scattering correlation function for packages of hard long parallel homogeneous circular cylinders

Expressions are given which define the isotropized small-angle scattering correlation γ(r) function and the isotropized set covariance C(r) of an arrangement of homogeneous, parallel, infinitely long circular cylinders of constant diameter d in terms of the pair correlation function g(s) of the random distance s between two cylinder axes. This type of model is useful for describing geometric arrangements of parallel cylinders, which form a cylinder package, where many packages are isotropically uniformly randomly arranged in space. es of the result in terms of the function g(s) are discussed. The derived expressions for the real space structure functions are exemplified for selected models of the pair correlation g(s):(1) mensional dead leaves model of disks with constant diameter, d and d three cylinders whose z-axes are separated by a fixed distance, s=s0. nctions γ(r) and C(r) are in use in materials science and closely connected with the scattering pattern of selected arrangements of microparticles. Thus, the article is the basis for deriving isotropic small-angle scattering intensities in a new case, namely, for tightly packed isotropic uniform random (homogeneous) cylinders.