Low-energy electron-impact laser-assisted ionization of atomic hydrogen

We have studied the influence of a linearly polarized laser field on the dynamics of low $(e,2e)$ collisions in atomic hydrogen. The influence of the laser on the target states is treated using a first-order perturbation approach. The continuum states of the scattered and ejected electrons are described respectively by Volkov and Coulomb-Volkov wave functions. The second Born approximation is used to calculate triple differential cross sections for laser-assisted ionization by low-energy electron impact. The required scattering amplitudes are evaluated by using the Sturmian basis expansion. The influence of the laser parameters (photon energy, intensity, and direction of polarization) on the triple differential cross sections is analyzed, and several illustrative examples are discussed. Our second Born approximation results agree very well with those obtained in the first-order Born approximation at larger incident energies. The margins between the second and first Born approximation results are large at low incident energies in the vicinity of the recoil peaks.

Figure 1

Triple differential cross sections corresponding to the laser-assisted electron-impact ionization process of atomic hydrogen as a function of the incident electron energy. The laser frequency is 1.17 eV, the electric field strength is ${10}^7$ V/cm. The ejected electron energy is $E_{k_b}=5$ eV, and the scattering angle is ${\theta }_a=5^{\circ }$. The laser polarization of the field is set parallel to the incident momentum ${\mathit{k}}_i$. Solid lines: second Born approximation results. Dashed lines: first Born approximation results. Dotted lines: results obtained by neglecting the dressing of the target. Dashed dotted lines: field-free results.

Figure 2

Triple differential cross sections corresponding to the laser-assisted electron-impact ionization process of atomic hydrogen as a function of the amplitude vector. The laser frequency is 1.17 eV, the incident electron energy is $E_{k_i}=30$ eV, and the ejected electron energy is $E_{k_b}=5$ eV. The scattering angle is ${\theta }_a=5^{\circ }$, and the emission angle of the ejected electron is ${\theta }_b={130}^{\circ }$. The laser polarization of the field is set parallel to the incident momentum ${\mathit{k}}_i$. Solid lines: second Born approximation results. Dashed lines: first Born approximation results. Dotted lines: results obtained by neglecting the dressing of the target.

Figure 3

All the parameters are the same as Fig. 2, while the laser polarization is perpendicular to the incident momentum ${\mathit{k}}_i$.

Figure 4

Triple differential cross sections corresponding to the laser-assisted electron-impact ionization process of atomic hydrogen as a function of the ejected angle ${\theta }_b$. The laser frequency $\omega =1.17$ eV and the electric field strength is ${10}^7$ V/cm. The incident electron energy is $E_{k_i}=30$ eV, the ejected electron energy is $E_{k_b}=5$ eV, and the scattering angle is ${\theta }_a=5^{\circ }$. The laser polarization of the field is set parallel to the incident momentum ${\mathit{k}}_i$. Solid lines: second Born approximation results. Dashed lines: first Born approximation results. Dotted lines: results obtained by neglecting the dressing of the target.

Figure 5

Same as Fig. 4, but with the laser frequency $\omega =2.34$ eV.

Figure 6

Same as Fig. 4, but with the laser frequency $\omega =6.42$ eV.