  We present a first principle study of the electron-phonon (e-p) interaction
at the Be(0001) surface. The real and imaginary part of the e-p self energy are
calculated for the surface state in the binding energy range from the
$\bar{\Gamma}$ 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 real part of
the self-energy presents a strong temperature and energy variation close to
$E_{F}$, making it difficult to measure its value just at $E_{F}$.

Materials Science;Superconductivity