Exciton Rydberg series

For both weak and strong coupling an infinite number of bound states exist for 1/r interactions for an infinite polymer. As a result of the discreteness of the lattice, and the restrictions on the exciton wavefunctions in one-dimension, the progression of states does not follow the Rydberg series. 

Fig. E.2. The zero-momentum exciton binding energies in units of Ej in the weak-coupling limit for a regularized Coulomb potential versus a/aj. Even parity (odd n) states (solid curves) and odd (even n) parity states (dashed curves). The energies of the odd parity solutions approach the Rydberg series as a/aj 0, while the energy of the n = 1 solution diverges.

We can then calculate, on the basis of a hydrogenic series, an exciton Rydberg of R = 14.7 0.4 meV. The corrections are given to meV accuracy, but the experimental data do not correspond to the assumed difference between the ionization potential and the electron affinity. Thus, even a calculation yielding the exact I - A would not coincide with the experimental result. 

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