Multiphoton and tunneling ionization of atoms in an intense laser field

We study the ionization probabilities of atoms by a short laser pulse with three different theoretical methods,i.e.,the numerical solution of the time-dependent Schro¨dinger equation(TDSE),the Perelomov-Popov-Terent’ev(PPT) theory,and the Ammosov-Delone-Krainov(ADK) theory.Our results show that laser intensity dependent ionization probabilities of several atoms(i.e.,H,He,and Ne) obtained from the PPT theory accord quite well with the TDSE results both in the multiphoton and tunneling ionization regimes,while the ADK results fit well to the TDSE data only in the tunneling ionization regime.Our calculations also show that laser intensity dependent ionization probabilities of a H atom at three different laser wavelengths of 600 nm,800 nm,and 1200 nm obtained from the PPT theory are also in good agreement with those from the TDSE,while the ADK theory fails to give the wavelength dependence of ionization probability.Only when the laser wavelength is long enough,will the results of ADK be close to those of TDSE.