  The influence of inner electrons on the ionization dynamics in strong laser
fields is investigated in a wavelength regime where the inner electron dynamics
is usually assumed to be negligible. The role of inner electrons is of
particular interest for the application of frozen-core approximations and
pseudopotentials in time-dependent density functional theory (TDDFT) and the
single-active-electron (SAE) approximation in strong-field laser physics.
Results of TDDFT and SAE calculations are compared with exact ones obtained by
the numerical ab initio solution of the three-electron time-dependent
Schr\"odinger equation for a lithium model atom. It is found that dynamical
anti-screening, i.e., a particular form of dynamical core polarization, may
substantially alter the ionization rate in the single-photon regime.
Requirements for the validity of the approximations in the single and
multiphoton ionization domain are identified.
