#### Date of Award

9-2006

#### Document Type

Thesis

#### Degree Name

Master of Science

#### Department

Department of Engineering Physics

#### First Advisor

David E. Weeks, PhD

#### Abstract

An algorithm is presented which uses the channel packet method (CPM) to simulate low-energy, wave-packet propagation and compute S-matrix elements. A four-by-four matrix containing the momentum, expansion coefficients of the reactants and products is introduced to account for initial and final states having both positive and negative momentum. The approach does not consider scattering from one side or the other, rather it considers both incoming and outgoing wave packets from the left and right simultaneously. Therefore, during one simulation all four S-matrix elements, and elements, S_{+k,-K}, S_{-k, +k}, S_{+k, +k} and S_{-k,-k} are computed. Numerical simulations of the algorithm are carried out on a conventional desktop computer and compared to the analytic solution of the transmission and reflection functions for a square well. The simulated results agree very well with the known solution up until very low energies, after which the results begin to oscillate about the theoretical values. The results indicate that if the correct Moller states are used the algorithm will produce the correct S-matrix elements across the entire energy range.

#### AFIT Designator

AFIT-GAP-ENP-06-22

#### DTIC Accession Number

ADA457059

#### Recommended Citation

Zeringue, Clint M., "A New Application of the Channel Packet Method for Low Energy 1-D Elastic Scattering" (2006). *Theses and Dissertations*. 3366.

https://scholar.afit.edu/etd/3366