Generalized Hylleraas Calculation of Positron-Hydrogen Scattering

Positron - Hydrogen Scattering at Intermediate Energies

“…First, if a complete set of positronium and hydrogen type channels is included, the basis could become over-complete and this could cause linear dependence problems when attempting to solve the Lippmann-Schwinger equations (Bransden and Noble 1994;Stelbovics and Berge 1996). The second is more pragmatic, as a larger calculation would have been beyond the scope of the available computing resources (a DEC 3000/800S workstation).…”

“…There have been a number of high precision calculations at incident positron energies below the positronium formation threshold and in the Ore gap which are expected to give cross sections that are accurate to within 1% or 2% (Bhatia et al 1971(Bhatia et al , 1974Brown and Humberston 1985;Humberston 1982Humberston , 1984l\Iitroy 1995;Mitroy et al 1994).…”

“…Scattering calculations are almost always more difficult than calculations for bound-state systems and progress in the area of positron-hydrogen scattering has been steady, if not spectacular for the last two decades. A number of different groups have gradually increased the accuracy and range of validity of the calculations (Bhatia et al 1971(Bhatia et al , 1974Brown and Humberston 1985;Humberston 1982Humberston , 1984. Recently, the development of improved theoretical procedures coupled with the availability of faster computers has resulted in a spurt of calculations for the low energy region (Archer et al 1990;Igarashi and Toshima 1994;Mitroy 1993bMitroy , 1995 Mitroy and Ratnavelu 1995;Zhou andLin 1994, 1995).…”

“…The other difficulty is more fundamental and arises from the fact that two different manifolds of states need to be included in the CC expansion. If both sets of states are expanded towards completeness, then the degree of linear dependence will increase and this could lead to numerical instabilities (Bransden and Noble 1994). Numerical instabilities of a minor nature have been observed in a large basis calculation of positron-hydrogen scattering (Mitroy 1995).…”

Positron scattering and annihilation from hydrogenlike ions

“…Unlike some other applications of the Kohn method to simple systems [5,7,8], the present approach does not include basis functions with interelectronic coordinates and instead uses a basis of functions all centered on the nucleus. The use of such a configuration-interaction (CI) -type basis does entail some large-scale calculations, but the issues involved in doing these calculations at low energies have been effectively solved [9].…”