Does the Time-Dependent Close-Coupling Approximation Predict Symmetric Single Differential Cross Sections for Electron Ionization of Hydrogen?

The single differential cross section (SDCS) for electron-impact single ionization should be symmetrical about half the total energy of the system. However, numerical results for the convergent close-coupling approximation do not exhibit this symmetry. Consequently, a controversy has arisen as to whether this is characteristic for all fully converged time-independent close-coupling calculations or whether this indicates a lack of convergence. In this paper, the behaviour of the SDCS is examined for time-dependent close-coupling calculations and it is found that a fully converged calculation would be symmetrical about half the total energy.