The self-trapping by the nondiagonal particle-phonon interaction between tw
o quasidegenerate energy levels of the excitonic system is studied. We prop
ose this is realized in the charge-transfer exciton, where the directions o
f the polarization give the quasidegeneracy. It is shown that this mechanis
m, unlike the conventional diagonal one, allows a coexistence and resonance
of the free and self-trapped states even in one-dimensional systems and a
quantitative theory for the optical properties (light absorption and time-r
esolved luminescence) of the resonating states is presented. This theory gi
ves a consistent resolution for the long-standing puzzles in quasi-one-dime
nsional compound A-PMDA.