Disagreements between empirical and ab initio potential curves of the Na-2 a (3)Sigma(u)(+) state are examined. These disagreements are explained mainly by the influence of spin-rotation-type interactions with the effective constant gammacongruent to-5.6.10(-3) cm(-1). A new potential energy function of this state is determined from the joint analysis of the continuous 2 (3)Sigma(g)(+)-->a (3)Sigma(u)(+) and the discrete 3 (3)Pi(g)--> a(3)Sigma(u)(+) experimental spectra. The new potential function is able to reproduce all the available spectroscopic data within experimental accuracy, and is closer to the modern high quality ab initio potentials than all the earlier reported empirical potential functions. (C) 2003 American Institute of Physics.