Scattering theory, linear operators, singular integral equations,
scientific computing.
Brief Description of Research
A long-standing problem in the field of nuclear reactions is to develop
an N-body theory that is based on the Schrodinger equation in a
mathematically rigorous way and yet is practical for reactions with more
than three bodies.
Research over the past several years, in collaboration with Colston
Chandler of the UNM Department of Physics and Astronomy,
has led to the derivation of a mathematical theory of N-body
nonrelativistic quantum scattering. The main result is a system of integral
equations, now known as the Chandler-Gibson equations, which has a compact
kernel and a unique solution that determines the multichannel transition
amplitudes. Current work is focused on the question of how to implement
the theoretical ideas in a computer code to calculate reaction amplitudes
for particular scattering processes. Facilities being used in this project
are a network of Sun and IBM microcomputers and the Maui High Performance
Supercomputer.
In collaboration with C. Chandler and physicists from CRIP Budapest, a method
is being developed to include the Coulomb interaction into the theory.
This method does not depend on screening the Coulomb potential, as does
most of the work in the field. Future plans are to apply this work to
calculations of reaction amplitudes for p-d scattering.
Return to:
-
Department of Mathematics and Statistics,
-
University of New Mexico.
Send mail to:
-
<archie@math.unm.edu>
Last updated: July 8, 2002