Calculation of electron or positron-atom scattering lengths using approximate target wavefunctions

Results of calculations on the positron-hydrogen and electron-hydrogen scattering systems at zero energy using distorted hydrogen-like target wavefunctions are presented. A trial wavefunction, PSIsub(t), which contains both linear and nonlinear parameters is constructed using an approximate target wavefunction. PSIsub(t) is related to a quantity, asub(v), which becomes the Khon scattering length if the target wavefunction is exact, through an integral expression corresponding to a slight modification of the usual Kohn variational method. On comparing the results obtained with the definitive values for these systems, it is conjectured that if the values of asub(v) display a local minimum when all the nonlinear parameters of PSIsub(t) are varied, then this local minimum value of asub(v) is an upper bound on the exact scattering length. Calculations on the Zero-energy positron-helium scattering system using Hylleraas-type approximations to the helium ground-state wave-function are analysed using this criterion. It is concluded that the use of either a six-parameter or a ten-parameter Hylleraas-type approximation to the helium ground-state wavefunction can give good results in scattering calculations for the positron-helium system at zero energy. (author)