  We study secondary electron emission from metallic surfaces due to Auger
de-excitation of diatomic metastable molecules. Our approach is based on an
effective model for the two active electrons involved in the process -- a
molecular electron described by a linear combination of atomic orbitals when it
is bound and a two-center Coulomb wave when it is not and a metal electron
described by the eigenfunctions of a step potential -- and employs Keldysh
Green's functions. Solving the Dyson equation for the retarded Green's function
by exponential resummation we are able to treat time-nonlocal self-energies and
to avoid the wide-band approximation.Results are presented for the
de-excitation of \NitrogenDominantMetastableState\ on aluminum and tungsten and
discussed in view of previous experimental and theoretical investigations. We
find quantitative agreement with experimental data for tungsten indicating that
the effective model captures the physics of the process quite well. For
aluminum we predict secondary electron emission due to Auger de-excitation to
be one to two orders of magnitude smaller than the one found for resonant
charge-transfer and subsequent auto-detachment.
