We study light absorption by nearly monodisperse PbS nanocrystals
grown in a glass matrix. The absorption spectra demonstrate a well-resolved
structure at energies above the first absorption peak. The absorption cross sections are calculated with an empirical tight-binding model accounting for the quantum confinement, the band anisotropy, and valley splittings. Absorption spectra measured at 4 K quantitatively agree with the atomistic calculations. This allows us to unambiguously ascribe the much-debated second absorption peak to the p−p optical transition and directly measure the splitting of excited p states.