In the framework of four-band envelope-function formalism, developed earlier for spherical semiconductor nanocrystals, we study the electronic structure and optical properties of quantum-confined lead-salt (PbSe and PbS) nanowires (NWs) with a strong coupling between the conduction and the valence bands. We derive spatial quantization equations, and calculate numerically energy levels of spatially quantized states of a transverse electron motion in the plane perpendicular to the NW axis, and electronic subbands developed due to a free longitudinal motion along the NW axis. Using explicit expressions for eigenfunctions of the electronic states, we also derive analytical expressions for matrix elements of optical transitions and study selection rules for interband absorption. Next we study a two-particle problem with a conventional long-range Coulomb interaction and an interparticle coupling via medium polarization. The obtained results show that due to a large magnitude of the high-frequency dielectric permittivity of PbSe material, and hence, a high dielectric NW/vacuum contrast, the effective coupling via medium polarization significantly exceeds the effective direct Coulomb coupling at all interparticle separations along the NW axis. Furthermore, the strong coupling via medium polarization results in a bound state of the longitudinal motion of the lowest-energy electron-hole pair (a longitudinal exciton), while fast transverse motions of charge carriers remain independent of each other.
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