  Adiabatic potential energy curves of the 3sSigma+, 3tSigma+, 2sPi and 2tPi
states correlating for large internuclear distance with the K(4s) + Li(2p)
atomic asymptote were calculated. Very good agreement between the calculated
and the experimental curve of the 2sPi state allowed for a reliable description
of the dissociation process through a small (20 cm-1 for J = 0) potential
energy barrier. The barrier supports several rovibrational quasi-bound states
and explicit time evolution of these states via the time-dependent nuclear
Schroedinger equation, showed that the state populations decay exponentially in
time. We were able to precisely describe the time-dependent dissociation
process of several rovibrational levels and found that our calculated spectrum
match very well with the assigned experimental spectrum. Moreover, our approach
is able to predict the positions of previously unassigned lines despite their
low intensity
