Characteristics of the SAS correlation function of long cylinders with oval right section

An approximation for the small-angle scattering (SAS) correlation function (CF) β₀(r) of a plane oval domain X is discussed. The approach is based on two parameters, the perimeter u and the surface area S_RS, of X. The function β₀(r) fixes the correlation function γ₀(r) of the oval homogeneous rod with constant right section X. The mean chord length l₁ of such a rod is the root of the equation γ₀(l₁) = 1 − 8/(3π). For a dilute rod arrangement, the Porod length l_p and γ′(l₁), the value of the derivative of the sample CF at r = l₁, are related by γ′(l₁) = −4/(3πl_p).