  The macroscopic dielectric function in the random-phase-approximation without
local field effect has been implemented using the local density approximation
with an all electron, full-potential linear muffin-tin orbital basis-set. This
method is used to investigate the optical properties of the semiconductors Si,
Ge, and GaAs under hydrostatic pressure. The pressure dependence of the
effective dielectric function is compared to the experimental data of Go\~ni
and coworkers, and an excellent agreement is found when the so called
``scissors-operator'' shift (SOS) is used to account for the correct band gap
at $\Gamma$. The effect of the $3d$ semi-core states in the interband
transitions hardly changes the static dielectric function, $\epsilon_\infty$;
however, their contribution to the intensity of absorption for higher photon
energies is substantial. The spin-orbit coupling has a significant effect on
$\epsilon_\infty$ of Ge and GaAs, but not of Si. The $E_1$ peak in the
dynamical dielectric function is strongly underestimated for Si, but only
slightly for Ge and GaAs, suggesting that excitonic effects might be important
only for Si.

Condensed Matter;Materials Science