Hyperspherical coordinates 10 Transition amplitudes 6 Wave functions 6 Calculations 4 Dinger equation 4 Hyperspherical 4 Sturmian 4 Analytic expressions 2 Analytical expressions 2 Asymptotic limits 2 Atoms 2 Basis sets 2 Closed form solutions 2 Collision process 2 Confined atoms 2 Discrete functions 2 Discretization scheme 2 Double ionization 2 Electric dipole oscillators 2 Electric fields 2 Electron-electron interactions 2 Electron-impact ionization 2 Electrons 2 First Born approximation 2 Fragmentation process 2 Hamiltonians 2 Helium 2 High-energy electron 2 Hyperspherical harmonics 2 Impact ionization 2