Toward a Rigorous Justification of the Three-Body Impact Parameter Approximation

The impact parameter (IP) approximation is a semiclassical model in quantum scattering theory wherein N large masses interact with one small mass. We study this model in one spatial dimension using the tools of time-dependent scattering theory, considering a system of two large-mass particles and one small-mass particle. We demonstrate that the model's predictive power becomes arbitrarily good as the masses of the two heavy particles are made larger by studying the S-matrix for a particular scattering channel. We also show that the IP wave functions can be made arbitrarily close to the full three-body solution, uniformly in time, provided one of the large masses is fixed in place, and that such a result probably will not hold if we allow all the masses to move.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2014

Author dc:creator

• Bowman, Adam

Chair dc:contributor.committeechair

• Hagedorn, George A.

Committee members dc:contributor.committeemember

• Klaus, Martin
• Ball, Joseph A.
• Elgart, Alexander

• Scattering Theory
• Stationary Phase
• Quantum Mechanics
• Impact Parameter Approximation
• Charge Transfer Model
• Dyson Series

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:2347

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/56623