  The valence level photoemission spectra in the Anderson impurity model for Ce
compounds at zero temperature are studied as a function of the photon energy
$\omega$. Most of former studies on Ce compounds are based on the sudden
approximation, which is valid in high energy region. For the photoemission in
the adiabatic limit of low energy region, one should consider the dipole matrix
elements and the hole-induced photoelectron scattering potential. We can manage
it by combining the time-evolution formalism and the $1/N_f$ scheme in a large
$f$-level degeneracy $N_f$. This gives the exact results as $N_f\to\infty$. In
view of experiments on the valence photoemission, two contributions of $4f$-
and band emissions are mixed. We study the separate $4f$ and band contributions
(from Ce $5d$) and total emission including the interference between two on an
equal footing with varying the photon energy. In the $4f$-emission case, we
also explore the effects of hole-induced scattering potential of the
photoelectron with respect to $\omega$. Its effects are found very similar to
the core level photoemission in shake down case with a localized charge
transfer excitation. Additionally, we examine the adiabatic-sudden transition
in valence level photoemission for the present localized system through the
simplified two-level model.
