Using the most accurate potential curves available for the a (3)Sigma(u)(+)
and X (1)Sigma(g)(+) states of lithium molecules, we compute the positions
of shape resonances. We also calculate the deexcitation probability from a
bound level upsilon' with rotational number N' to the continuum of the low
er state, and conclude that a shape resonance should be measurable for the
transition 2 (3)Pi(g) --> a (3)Sigma(u)(+). Such a shape resonance has been
identified from the spectra of the transition from the upsilon' = 2,N' = 4
level of 2 (3)Pi(g) into the N " = 4 continuum of a (3)Sigma(u)(+). Its po
sition is in good agreement with the theoretical prediction. [S1050-2947(99
)09909-6].