Exchange effects and second-order Born corrections in laser-assisted $(e,2e)$ collisions with helium atoms

The triple differential cross section for laser-assisted ionization of a helium target by slow electrons is analyzed within the framework of the second Born approximation. We evaluate the $S$-matrix elements using Volkov and Coulomb-Volkov wave functions for describing the continuum states of the scattered and the ejected electrons, respectively. The required scattering amplitudes are performed by expanding the atomic wave functions onto a complex-scaled Sturmian basis, which allows us to exactly take into account the contribution of the continuous spectrum to the dressing of the atomic states. Our results have been improved by taking into account exchange effects. Furthermore, the second-order Born correction is seen to be important and significantly affects the magnitudes of the binary and recoil peaks.

Figure 1

Selected orientations of laser polarization for electron-impact ionization in the presence of a linearly polarized laser field: (a) $\widehat{\varepsilon }\parallel \mathit{\Delta }$ and (b) $\widehat{\varepsilon }\perp \mathit{\Delta }$.

Figure 2

Triple differential cross sections corresponding to the laser-assisted electron-impact ionization process of a helium atom as a function of the ejected angle ${\theta }_b$ with no net exchange of photons $(\ell =0)$. The laser frequency is 1.17 eV and the electric field strength is $1\times {10}^7$ V/cm. The incident electron energy is $E_{k_i}=40$ eV, the ejected electron energy is $E_{k_b}=5$ eV, and the scattering angle is ${\theta }_a=4^{\circ }$. The laser polarization in (a) is parallel to the momentum transfer $(\widehat{\varepsilon }\parallel \mathit{\Delta })$ and in (b) perpendicular to the momentum transfer $(\widehat{\varepsilon }\perp \mathit{\Delta })$. Solid lines, second Born approximation results with including exchange effects; dashed lines, second Born approximation results without including exchange effects; dash-dotted lines, first Born approximation results; dotted lines, field-free results in the second Born approximation.

Figure 3

All the parameters are the same as in Fig. 2, but with the absorption of one photon $(\ell =1)$.

Figure 4

All the parameters are the same as in Fig. 2, but with the emission of one photon $(\ell =-1)$.