Application of the eikonal amplitude to rotational excitations of diatomic molecules by electron impact

The eikonal amplitude is used in the framework of the adiabatic approximation to obtain the rotational excitations of homonuclear diatomic molecules by intermediate-energy electron impact. The formalism is simple and may be extended to collision processes in which heteronuclear molecules are used as the target, or positrons as projectiles. The results for the differential cross section of the $J=1\mathrm{}\to 3$ rotational excitation of hydrogen molecules by 40-eV electron impact are in qualitative agreement with the recent experimental findings.