We reconsider the influence of two-particle final state interactions (
FSI) on two-particle Bose-Einstein interferometry. We concentrate in p
articular on the problem of particle emission at different times. Assu
ming chaoticity of the source. we derive a new general expression for
the symmetrized two-particle cross section. We discuss the approximati
ons needed to derive from the general result the Koonin-Pratt formula.
Introducing a less stringent version of the so-called smoothness appr
oximation we also derive a more accurate formula. It can be implemente
d into classical event generators and allows us to calculate FSI corre
cted two-particle correlation functions via modified Bose-Einstein ''w
eights.''