The fluorescence spectrum of Na2 induced by the 4726.87 Å line of an Argon ion laser has been analyzed with special emphasis on determination of accurate relative intensities. This work extends previous observations on Na2 by using this excitation line. We have observed eight fluorescence series for the B1Piu --> X1Sigma+g band system corresponding to the excitation transitions v' = 9, J' = 38 <-- v" = 1, J" = 37; v' = 14, J' = 46 <-- v" = 4, J" = 47; v' = 14, J' = 81 <-- v" = 3, J" = 80; v' = 15, J' = 65 <-- v" = 4, J" = 66; v' = 12, J' = 36 <-- v" = 3, J" = 36; v' = 12, J' = 40 <-- v" = 3, J" = 39 v' = 17, J' = 45 <-- v" = 6, J' = 45 and v' = 18, J' = 63 <-- v" = 6, J" = 63. The seven latter series are reported for the first time. Optically pumped laser transitions obtained in Na2 vapor by using this excitation wavelength have been assigned. The radiative transition probabilities for the observed fluorescence series were calculated using hybrid potential energy curves for the B1Piu and X1Sigma+g states constructed up to last vibrational levels and an ab initio transition dipole moment function. Radiative lifetimes for the rovibrational levels of the upper states pumped by the laser line have also been calculated. The transition probabilities and lifetimes agree with the corresponding observed measurements, usually within the experimental uncertainty. From the rotational satellite structure with DeltaJ' = +/-1 and +/-2 of some bands, for the most intense fluorescence series, collision-induced transition rates and average cross sections have been obtained. Copyright 1998 Academic Press.