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 SchrSdinger 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.
Two-dimensional （2D） electron momentum distributions and energy spectra of a hydrogen in an intense laser field are calculated by solving the time-dependent SchrSdinger equation combined with the window-operator technique. Compared with the standard projection technique, the window-operator technique has the advantage that the continuum states of atoms can be avoided in the calculation. We show that the 2D electron momentum distributions and the energy spectra from those two techniques accord quite well with each other if an appropriate energy width is used in the window operator.
