In this paper the Na-2 X(1) + Sigma(g)(+) and (1)(1) IIg elect tronic states long range tail functional behavior is analysed in the light of multipolar expansion theory combined with damping functions. The experimental data used here is the one reported by Barrow et al. . In the present paper this experimental data is used in a nonlinear reduction to van der Waals C-n constants using the multipolar expansion Sigma(n) C-n/r(n). Since the internuclear distance reached by the biggest part of the data is still out of the Le Roy's region (where the internuclear distance must be grater than r(lim): r(lim) = 2((r(A)(2)) (1/2) + (r(B)(2)) (1/2)), being the outermost electron orbital radii for the (r(A)) and (r(B)) two atoms), the exchange energy must be taken into account. Due to the fact that the 1/r(n) expansion diverges when r-->0, the damping functions has been included in order to prevent this. The obtained values for the C-n coefficients, as well as the exchange energy constants, show a good agreement with the theoretical available data, for both electronic states.