Transition amplitudes 16 Wave functions 8 Dinger equation 6 Hyperspherical coordinates 6 Impact ionization 6 Sturmian 6 Atoms 4 Double ionization 4 First Born approximation 4 Helium 4 Hyperspherical 4 Non-homogeneous 4 Projectile target interaction 4 Scattering process 4 Single-differential cross sections 4 TRANSITION AMPLITUDES 4 ADIABATIC EFFECTS 2 Analytic expressions 2 Analytical results 2 Asymptotic analysis 2 Asymptotic behaviors 2 Asymptotic behaviour 2 Asymptotic limits 2 Basis functions 2 Basis sets 2 Bound state 2 CRYSTAL DEFECTS 2 Calculations 2 Charged particles 2 Closed form solutions 2