Few-cycle laser-pulse-assisted electron-atom potential scattering
$S$-matrix theory of electron-atom scattering assisted by a few-cycle laser pulse is introduced. The result obtained in the first Born approximation corresponds to the direct or single scattering, while the result in the second Born approximation corresponds to the rescattering or double scattering contribution to the laser-assisted scattering process. The rescattered electrons may acquire high energies while moving in the laser pulse. The dependence of the energy spectrum on the value of the carrier-envelope phase and the duration of the laser pulse is investigated. The abrupt cutoffs of the plateau structures in the energy spectra of the process are explained by the classical analysis. It is shown that the height of both the single and double scattering plateaus can be increased by orders of magnitude by choosing the heavier atomic targets.