Statistical Average of a Product of Phase Sums Arising in the Study of Disordered Lattice. II

This recurrence formula, derived in a previous paper [J. Math. Phys. 10, 2263 (1969)] to evaluate 〈S(k 1)S(k 2) ⋯ S(kn )〉,is extended here, for the case when k 1 + k 2 + ⋯ + kn = 0 but no other partial sum of the set k 1, k 2, ⋯, kn is zero. The average is of O(N) as compared to the O(1) when k 1 + k 2 + ⋯ + kn ≠ 0. Formulas are then proposed for the situations when more than one partial sum of the set vanish. 〈S(k)S(−k)〉 is considered for a parabolic probability distribution s(r) with a cutoff which shows striking similarity with x‐ray diffraction pattern of liquids.