Numerical simulation of the double-to-single ionization ratio for the helium atom in strong laser fields

Abstract

We present calculations on the ratio between double and single ionization of helium by a strong laser pulse at a wavelength of 780 nm using the quantitative rescattering (QRS) model. According to this model, the yield for the doubly charged ion $\mathrm{He}^{2+}$ can be obtained by multiplying the returning electron wave packet (RWP) with the total cross sections (TCSs) for electron impact ionization and electron impact excitation of $\mathrm{He}^{+}$ in the singlet spin channel. The singlet constraint was imposed since the interaction of the helium atom with the laser and the recollision processes both preserve the total spin of the system. An $R$-matrix (close-coupling) code is used to obtain accurate TCSs, while the RWPs, according to the QRS, are calculated by the strong-field approximation for high-energy photoelectrons. The laser field, which lowers the required energy for the electron to escape from the nucleus at the time of recollision, is also taken into account. The simulated results are in good agreement with the measured $\mathrm{He}^{2+}\text{/}\mathrm{He}^{+}$ ratio over a broad range of laser intensities. The result demonstrates that the QRS approach based on the rescattering model is fully capable of quantitatively interpreting nonsequential double ionization processes.