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O. Gunnarsson (a), V. Meden (b) and K. Schönhammer (b)
(a) Max-Planck-Institut für Festkörperforschung, Stuttgart
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*
(b) Institut für Theoretische Physik, Universität Göttingen,Göttingen, Germany
*

The electron spectral function is calculated for a model including
electron-phonon coupling to Einstein phonons. The spectrum is studied
as a function
of the electronic band width and the energy epsilon_{k} of the level
from which the electron is removed.
A cumulant expansion is used for the time-dependent Green's function,
and the second and fourth order cumulants are studied. This approach
is demonstrated to give accurate results for an exactly solvable
two-level
model with two electronic levels coupling to local phonons.
For a one-band, infinite, three-dimensional model
the cumulant expansion gives one satellite in the large band width limit.
As the band width is reduced, the spectrum calculated
with the fourth order cumulant develops multiple satellites, if
epsilon_k is close to the Fermi energy E_{F}, and as the
band width
becomes small results similar to the two-level model are obtained.
If epsilon_{k} is more than a phonon energy below E_{F},
the spectrum instead shows a very broad peak, due to the decay
of the hole into a hole closer to E_{F} and a phonon.
If the spin degeneracy of the electrons is taken into account,
the broadening due to the deacy of a hole into a hole closer to E_{F}
and an electron-hole pair becomes important, even if epsilon_{k}
is closer to E_{F} than the phonon energy.
The validity of Migdal's theorem for A_{3}C_{60}
(A=K, Rb) is discussed.
The inter sub band electron-phonon coupling is appreciable for
A_{3}C_{60}, and it may be argued that the
effective band width is large. It is shown that Migdal's theorem
is, nevertheless, not valid for A_{3}C_{60}.

Phys. Rev. B **50**, 10462 (1994).

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