Inelastic electron scattering off of simple atoms for large-momentum-transfer collisions

Inelastic electron scattering off of simple atoms is studied for collisions where the momentum transferred ($q$) from the incident electron to the atom is larger than the normal momenta of the bound electrons. We discuss the direct part of the scattering for collisions where the atom is excited to another bound state. In lowest order the second Born term, which dominates the scattering amplitude, factors into two parts. One part ($\frac{1}{q^2}$) displays a Rutherford-like scattering off the nucleus; the other factor gives the response of the atom to the presence of the impinging electron. The second Born scattering amplitudes for $1s\to 2s$ and $1s\to 2p$ electron-hydrogen scattering and $1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\to 2{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ electron-helium scattering for large-momentum-transfer collisions are calculated.