This work describes an extension of the Reproducing Kernel Hilbert Space (RKHS) method, in conjunction with the Tikhonov regularization, for constructing potential energy surfaces, with correct asymptotic forms, from high quality experimental measurements. The method is applied to the construction of new, global potential energy curves of the two lowest states X (1)Sigma(g)(+) and a (3)Sigma(u)(+) of the sodium dimer using rovibrational spectral measurements. The exchange interaction of Na-2 at intermediate and long ranges is accordingly derived and adopted for determining the ionization energy of the corresponding valence electron. It is found that the resulting ground-state X (1)Sigma(g)(+) dissociation energy 6022.025 (+/-0.049) cm(-1) of Na-2 agrees within the experimental errors with the most recent experimental value [6022.0286 (+/- 0.0053) cm(-1), Jones , Phys. Rev. A 54, R1006 (1996)]. The well depth of the a (3)Sigma(u)(+) state is determined to be 174.96 (+/-1.18) cm(-1), compared to the Rydberg-Klein-Rees (RKR) value of 174.45 (+/- 0.36) cm(-1) [Li , J. Chem. Phys. 82, 1178 (1985)]. Moreover, the equilibrium positions of both RKHS potential curves, 3.0796 (+/- 0.0010) Angstrom for the X (1)Sigma(g)(+) state and 5.089 (+/- 0.062) Angstrom for the a (3)Sigma(u)(+) state, are in excellent agreement with previously determined RKR results of 3.079 53 Angstrom [Babaky and Hussein, Can. J. Phys. 67, 912 (1989)] and 5.0911 Angstrom (Li ), respectively. The experimentally determined values of the equilibrium position and well depth for the a (3)Sigma(u)(+) state differ from recent theoretical values of 5.192 Angstrom and 177.7 cm(-1) obtained by highly accurate ab initio calculations [Gutowski, J. Chem. Phys. 110, 4695 (1999)]. Finally, both RKHS potential curves at large distances reproduce very recent theoretical dispersion coefficients within 1.0x10(-5) percentage errors. (C) 2000 American Institute of Physics. [S0021-9606(00)00114-8].