We studied the reversible transitions between two levels of excited mo
lecule stimulated by encounters with other solutes. The inter-system c
rossing results in either quenching or trapping of excitation dependin
g on the relationship between the lifetimes of the levels. In the part
icular case of an immobile excited molecule and equal lifetimes, an ex
act solution of the problem was given which is valid for arbitrary con
centration of solutes. We compared the fluorescence quantum yield obta
ined with this solution, superposition approximation and integral enco
unter theory. Our main conclusion is that for equal lifetimes the latt
er has an advantage, even in small concentration limits and is out of
competition when the lifetime of the primary excited level is shorter
than another. (C) 1998 American Institute of Physics.