  Unique optical properties of semiconductor nanoparticles (SN) make them very
promising in the multitude of applications including lasing, light emission and
photovoltaics. In many of these applications it is imperative to understand the
physics of interaction of electrons in a SN with external electromagnetic
fields on the quantitative level. In particular, the strength of
electron-photon coupling determines such important SN parameters as the
radiative lifetime and absorption cross section. This strength is often assumed
to be fully encoded by the so called Kane momentum matrix element. This
parameter, however, pertains to a bulk semiconductor material and, as such, is
not sensitive to the quantum confinement effects in SNs. In this work we
demonstrate that the quantum confinement, via the so called band mixing, can
result in a significant suppression of the strength of electron interaction
with electromagnetic field. Within the envelope function formalism we show how
this suppression can be described by introducing an effective energy-dependent
Kane momentum. Then, the effect of band mixing on the efficiencies of various
photoinduced processes can be fully captured by the conventional formulae
(e.g., spontaneous emission rate), once the conventional Kane momentum is
substituted with the renormalized energy-dependent Kane momentum introduced in
here. As an example, we evaluate the energy-dependent Kane momentum for
spherical $\rm{PbSe}$ and $\rm{PbS}$ SNs (i.e., quantum dots) and show that
neglecting band mixing in these systems can result in the overestimation of
absorption cross sections and emission rates by a factor of $\sim$2.
