  We calculate the screening corrections to the electron capture rates in dense
stars by the relativistically degenerate electron liquid. In order to calculate
the screening corrections we adopt the linear response theory which is widely
used in the field of solid state physics and liquid metal physics. In
particular, we use the longitudinal dielectric function for the
relativistically degenerate electron liquid derived by Jancovici. We calculate
the screening potential at the position of the nucleus. By using this screening
potential one can calculate the screening corrections to the electron capture
rates. We will present accurate analytic fitting formulae which summarize our
numerical results. These fitting formulae will facilitate the application of
the present results. The screening corrections to the electron capture rates
are typically a few percent.
