Partial wave dispersion relations: application to electron-atom scattering

In this letter we propose the use of partial wave dispersion relations (DRs) as the way to solve the longstanding problem of correctly incorporating exchange in a valid DR for electron-atom scattering. In particular, a method is given for effectively calculating the contribution of the discontinuity and/or Doles of the partial wave amplitude which occur in the negative E plane. The method is successfully tested in three cases: (i) the analytically solvable exponential potential, (ii) the Hartree potential and (iii) the S-wave exchange approximation for electron-hydrogen scattering. The latter is the first successful DR which includes exchange.