Reexamination of over-the-barrier and tunneling ionization of the hydrogen atom in an intense field

Ionization of the hydrogen atom in an intense laser field is calculated using the classical-trajectory Monte Carlo method with allowance of tunneling at the classical turning points. With an initial condition of zero angular momentum, excellent agreement with an accurate quantum-mechanical calculation is obtained. The usually mentioned classical threshold for ionization at field strength 0.0625e/a₀² is shown to be irrelevant to realistic pulses; the effective classical thresholds for an adiabatically ramped dc pulse are found to be 0.080e/a₀² in one dimension and 0.130e/a₀² in three dimensions.