INTEGRAL EXPRESSIONS OF THE SMALL-ANGLE SCATTERING CORRELATION-FUNCTION DERIVATIVES

The integral expression of the nth derivative of the SAS correlation-function (gamma(r)) is reported. It is the average, throughout the sample interface, of the loop integral of a vectorial field A(n) over arrow pointing right (r(j)(l)). All the A(n) over arrow pointing right (r(j)(l))'s, with n greater-than-or-equal-to 3, are recursively obtained by appropriate differentiation of A(2) over arrow pointing right (r(j)(l)), whose explicit expression is given in terms of the parametric equations of the interface. For very smooth interface it results that all the CF even-derivatives are null at the origin.