This work is concerned with the process
of ionization of atomic hydrogen and lithium by positron
impact. The experimental group at the University of Bielefeld
(Germany) measured integrated cross sections that were much
larger than most early theoretical calculations. Independently
measured results taken at University College London were
considerably lower than those of the University of Bielefeld.
Later work at Brookhaven National Laboratory by the University
of Bielefeld group, using a more intense positron source, has
resulted in cross sections comparable in magnitude to their
earlier data. No integrated cross sections for positron impact
ionization of lithium have been experimentally measured yet.
Presently, the integrated ionization
cross section is considered within the framework of the
distorted wave theory. Distorted wave theory performs well
over a wide range of individual particle momenta, and is an
intuitive approach. In the present implementation of this
method the distortion potential in the final channel
represents a sum of Coulomb interactions between the nucleus
and both the scattered positron and the ejected electron. The
strength of these interactions is given by effective charges
that vary with the energies of the two free particles. Two
different sets of effective charges are used. The two models
effectively exclude positronium formation as do the
experimental measurements. The initial channel distortion
potential is defined by a sum of the static and the
polarization potentials of the target atom. The theory may be
readily extended to other atoms in the alkali family.
Special techniques for dealing with the
long-range Coulomb forces are applied. These include an
asymptotic correction to the projectile radial integral (to
complete the integration from a finite maximum value through
to infinity), and the Born subtraction technique (where we
calculate the difference between the distorted wave cross
section and a well established first approximation). With
these techniques we can reduce computational effort while
obtaining accurate cross sections.
The two effective charge models result
in good agreement with the early experimental data of the
University of Bielefeld group and with their later data taken
at Brookhaven National Laboratory. Both models produce cross
sections of similar size, suggesting some insensitivity to the
choice of effective charges. On the other hand the results do
not agree well with the data of the University College London
group, which are closer to the values predicted by more
rudimentary theoretical calculations. This indicates a need
for more accurate theoretical calculations of this problem as
well as further experimental measurements.
The integrated cross section is our
primary interest. Upon further examination of the models in
differential cross section calculations we found good
agreement with the results of others. Extension of the
expressions obtained here for hydrogen allow calculations for
the lithium target. The results predict a larger positron
impact ionization cross section than the previous estimates.
