Triply-differential cross sections for ionisation of hydrogen atoms by electrons and positrons

A derivation is given of the exact form of the three-body Coulomb wavefunction in the asymptotic region where the separation of all particles tends to infinity. Using a modification of the method of Pluvinage (1951), an approximate three-body scattering wavefunction is derived that satisfies this boundary condition. Triply-differential cross sections (TDCS) for electron impact ionisation of atomic hydrogen calculated with this scattering wavefunction, which contains no free parameters, show excellent agreement with measurements at impact energies greater than 150 eV. The corresponding TDCS for positron impact ionisation are also presented.