  Numerically determined ionization rates for the field ionization of atomic
hydrogen in strong and short laser pulses are presented. The laser pulse
intensity reaches the so-called "barrier suppression ionization" regime where
field ionization occurs within a few half laser cycles. Comparison of our
numerical results with analytical theories frequently used shows poor
agreement. An empirical formula for the "barrier suppression ionization"-rate
is presented. This rate reproduces very well the course of the numerically
determined ground state populations for laser pulses with different length,
shape, amplitude, and frequency.
  Number(s): 32.80.Rm
