An extension of the analytical solution of the Ornstein-Zernike equation with the Yukawa closure

The analytical solution of the Ornstein-Zernike equation with one Yukawa closure of the factorizable-coefficient case is extended from the scalar-factorization case to the vector-factorization case. As a result, the scaling parameter is extended from a scalar quantity to a matrix quantity, and the scaling matrix <(Gamma)over cap> is given by the physical solution of the matrix equation: <(Gamma)over cap>(2) + z<(Gamma)over cap> + pi (D) over cap (K) over cap = 0.