Effective Electron and Hole Interactions in a Polarizable Field;

The problem of exciton states is considered in the presence of the interactions of the electron and the hole with optical phonons. In the two limits exciton Bohr radius $r_{\mathrm{ex}}$ much smaller and much larger than the polaron radii $r_{e,h}^{}{}_{}{}^{*}$, the problem can be solved exactly. An interpolation scheme for obtaining results for intermediate values of the parameter $\frac{r_{\mathrm{ex}}}{r_{e,h}^{}{}_{}{}^{*}}$ is proposed. An effective nonlocal electron-hole potential is obtained which reduces to the physically expected results in various limits.