Yukawa fluids in the mean scaling approximation: III New scales

In recent work a general solution of the Ornstein Zernike equation for a general Yukawa closure for a single component fluid was found. Because of the complexity of the equations a simplifying assumption was made, namely that the main scaling matrix $\bGamma$ had to be diagonal. While in principle this is mathematically correct, it is not physical because it will violate symmetry conditions when different Yukawas are assigned to different components. In this work we show that by using the symmetry conditions the off diagonal elements of $\bGamma$ can be computed explicitly for the case of two Yukawas, and that although the solution is different than in the diagonal case, the excess entropy is formally the same as in the diagonal case. Analytical expressions for the Laplace transforms of the pair distribution functions are derived.