  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.
