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

A trial wavefunction, Psi 1 , which contains both linear and nonlinear parameters is constructed using an approximate target wavefunction, Psi 1 is related to a quantity, a v , which becomes the Kohn scattering length if the target wavefunction is exact, through an integral expression corresponding to a slight modification of the usual Kohn variational method. It is conjectured that if the values of a v display a local minimum when all the nonlinear parameters of Psi 1 are varied, then this local minimum value of a 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 wavefunction are analysed using this criterion. 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.