Adiabatic theory of ionization of atoms by intense laser pulses: One-dimensional zero-range-potential model

As a first step toward the adiabatic theory of ionization of atoms by intense few-cycle laser pulses, here we consider the simplest one-dimensional zero-range-potential model. The theory for this model is developed. This theory rests on a single parameter epsilon giving a ratio of the atomic and laser time scales and becomes exact in the limit epsilon -> 0 uniformly with respect to the amplitude of the laser pulse. We construct the asymptotics of the solution to the time-dependent Schroodinger equation and photoelectron spectrum. The factorization formula for the photoelectron spectrum near its classical boundary, first suggested by T. Morishita et al. [Phys. Rev. Lett. 100, 013903 (2008)] on the basis of ab initio calculations, is derived. The theory is illustrated by numerical calculations. Its comparison with the strong-field approximation is discussed.