Structure of atoms from the (e,2e) reaction

A model is derived for the differential cross section for ($e,2e$) reactions on atoms, leaving the residual ion in an excited state. The eigenstates of the ion are described by the shell model with configuration interaction. In the case of argon, $3s^{-1\mathrm{}}$ spectroscopic factors are independently determined. They describe the probability that each of the three ion eigenstates whose ($e,2e$) angular correlation has the $3s^{-1\mathrm{}}$ shape, contain the $3s^{-1\mathrm{}}$ configuration. Two Hartree-Fock single-particle models are compared. The spectroscopic factors add to 1 for both, but only one correctly predicts the experimental single-hole energy level.