A Hartree Self Consistent Method for the Scattering of Positrons by Hydrogen Atoms #268868

Our aim has been to develop a method whereby the self — consistent features of the Hartree approach can be incorporated into a form.for the wave function which will contain correlations and satisfy the asymptotic boundary conditions. We have accomplished this by adding a sum of products of one particle functions to a product of the unperturbed bound state wave function and a function which will have the proper asymp totic form for a scattered particle. By requiring the terms in the sum to vanish at large distances, we have been able to obtain a set of coupled differential equations for the one particle functions. We can show that these differential equations lead to an effective one-particle Hamiltonian for the scattered particle in which the potential is made up of a sum of induced multipole potentials. We can also show that with a suitable set of approximations, the equations reduce to the adiabatic approximation.