  Exciton effects on conjugated polymers are investigated in soliton lattice
states. We use the Su-Schrieffer-Heeger model with long-range Coulomb
interactions. The Hartree-Fock (HF) approximation and the single-excitation
configuration- interaction (single-CI) method are used to obtain optical
absorption spectra. The third-harmonic generation (THG) at off-resonant
frequencies is calculated as functions of the soliton concentration and the
chain length of the polymer. The magnitude of the THG at the 10 percent doping
increases by the factor about 10^2 from that of the neutral system. This is
owing to the accumulation of the oscillator strengths at the lowest exciton
with increasing the soliton concentration. The increase by the order two is
common for several choices of Coulomb interaction strengths.
