New observations of the 39K2 a3Σu+ state are reported. The results include ro-vibrational term values and intensity distributions of the transitions from excited triplet states to this lowest triplet state. The new and previous experimental data are analyzed to obtain the multi-parameter [modified Lennard-Jones] description of the a3Σu+ state potential function in a range including both attractive and repulsive limbs. The same description is applied to the K2 33Πg and 43Σg+ states. © 2005 Elsevier Inc. All rights reserved.