Abstract
Direct and resonant ionisation of atoms are considered for the case of an intense electromagnetic wave with any smooth envelope. The JWKB method (over time) is used along with other approaches to solve this problem. Various ranges of light pulse and atomic parameters lead to physically different regimes of resonant ionisation. The resonance curves describing the dependence of the ionisation probability w on the detuning parameter epsilon are obtained. A general expression for the resonance width Gamma is given which is valid for light pulses of arbitrary intensity, duration and shape.

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