We report a full theoretical calculation of the rovibrational structur
e of the Na-2 O-g(-) state, including hyperfine structure. The purely
long-range O-g(-) state has been observed in the photoassociation spec
troscopy of ultracold trapped alkali-metal atoms. For the lighter alka
li-metal atoms (Li, Na, and K), the purely long-range states are compl
etely characterized by atomic data since the inner turning point of th
e potentials are at internuclear separations where exchange interactio
ns are still negligible.