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We calculate the screening corrections to the electron capture rates in densestars by the relativistically degenerate electron liquid. In order to calculatethe screening corrections we adopt the linear response theory which is widelyused in the field of solid state physics and liquid metal physics. Inparticular, we use the longitudinal dielectric function for therelativistically degenerate electron liquid derived by Jancovici. We calculatethe screening potential at the position of the nucleus. By using this screeningpotential one can calculate the screening corrections to the electron capturerates. We will present accurate analytic fitting formulae which summarize ournumerical results. These fitting formulae will facilitate the application ofthe present results. The screening corrections to the electron capture ratesare typically a few percent.Comment: uses AAS LaTeX macro package (Ver. 5.0), 8 pages, 2 tables, 4  figures, 2 subroutines, published in ApJ 579, 380-385 (2002

Screening Corrections to the Electron Capture Rates in Dense Stars by the Relativistically Degenerate Electron Liquid