Unitarisation of the eikonal-Born series method for electron-atom and positron-atom collisions

A systematic study is made of the unitarisation method which the authors recently proposed for the eikonal-Born series approximation, in the case of fast electron-atom and positron-atom collisions. The authors' unitarisation procedure is based on a generalisation of the potential scattering eikonal expansion of Wallace to the multiparticle case, suitably modified to take the long-range polarisation effects and absorption effects at small angles into account correctly. They also develop a new non-perturbative approximation for the exchange scattering amplitude, which is appropriate to use with the authors' unitarised EBS direct scattering amplitude for electron-atom collisions. The authors' then apply their unitarised EBS method to the elastic scattering of electrons and positrons by atomic hydrogen in the energy range 100-400 eV. A detailed comparison is made with other related theoretical methods and with recent absolute measurements of (e - -H) elastic differential cross sections. Total (integrated) elastic and total (complete) cross sections for both electron and positron impact are also discussed.