We Calculate the Coulomb pseudopotential $μ^*$ for the simple hexagonal phase of Si at a pressure of 14 GPa using a full dielectric matrix approach within the local-density approximation. We investigate the dielectric screening effects such as crystal potential, local-field, and exchange- correlation effects. With the full screening effects, $μ^*$ is estimated to be 0.104. Considering only the crystal potential, $μ^*$ is very close to that of the free electron gas. The local-field effect, which results from the covalent bonds, reduces $μ^*$. However, the exchange-correlation effect is more important, which gives rise to a large enhancement of $μ^*$.
