We present a first principle study of the electron-phonon (e-p) interaction at the Be(0001) surface. The real and imaginary parts of the e-p self-energy (Sigma) are calculated for the (&UGamma;) over bar surface state in the binding energy range from the (&UGamma;) over bar point to the Fermi level. Our calculation shows an overall good agreement with several photoemission data measured at high and low temperatures. Additionally, we show that the energy derivative of ReSigma presents a strong temperature and energy variation close to E-F, making it difficult to measure its value just at E-F.
