  Our exact theory for continuous harmonic perturbation of a one dimensional
model atom by parametric variations of its potential is generalized for the
cases when a) the atom is exposed to short pulses of an external harmonic
electric field and b) the forcing is represented by short bursts of different
shape changing the strength of the binding potential. This work is motivated
not only by the wide use of laser pulses for atomic ionization, but also by our
earlier study of the same model which successfully described the ionization
dynamics in all orders, i.e. the multi-photon processes, though being treated
by the non-relativistic Schr\"odinger equation. In particular, it was shown
that the bound atom cannot survive the excitation of its potential caused by
any non-zero frequency and amplitude of the continuous harmonic forcing. Our
present analysis found important laws of the atomic ionization by short pulses,
in particular the efficiency of ionizing this model system and presumably real
ones as well.
