#### Date of Award

3-14-2014

#### Document Type

Thesis

#### Degree Name

Master of Science

#### Department

Department of Engineering Physics

#### First Advisor

David E. Weeks, PhD.

#### Abstract

Wave packet propagation methods are used to compute scattering Wigner Distribution Functions (WDF) for the square well potential, square barrier potential, and the H+H2 and OH+CO, and several M+Ng collisions. The scattering WDF are used to interpret how probabilities flow among various potential energy surfaces as a function of time during a collision. Positive values of the scattering WDF correspond to the addition of probability to scatter into the state that corresponds to the asymptotic limit of the potential energy surface of interest. Negative values correspond to the loss of probability to scatter into the state that corresponds to the asymptotic limit of the surface of interest, and zero values correspond to probability associated with the wave packet that is still in the interaction region. The loss of probability on one surface corresponds to the addition of probability on another surface at different times. Bands of oscillating peaks and valleys that form in the structure of the scattering WDF correspond to presence of secondary transmission or reflection with significant probability. The square well frequencies at which probability arrive in a scattering channel corresponds to the depth and width of the well. Scattering WDF were computed for the following combinations: K+He, K+Ne, K+Ar, Rb+He, Rb+Ne, Rb+Ar, Cs+Ne, and Cs+Ar. The scattering WDF revealed that as the mass of the noble gas increased, a significant proportion of probability was transferred from the 2P3/2 pump state to the 2P1/2 lasing state for a larger number of total angular momentum values. Similarily, as the mass of the alkali metal decreased, there was a reduced transfer of probability to make a transition from the 2P3/2 state to the 2P1/2 state. The reduced probability to make a transition from the 2P3/2 to the 2P1/2 manifolds for the M+He collisions is compensated by the large average velocity of He.

#### AFIT Designator

AFIT-ENP-14-M-39

#### DTIC Accession Number

ADA603673

#### Recommended Citation

Wyman, Keith A., "Wigner Distribution Functions as a Tool for Studying Gas Phase Alkali Metal Plus Noble Gas Collisions" (2014). *Theses and Dissertations*. 667.

https://scholar.afit.edu/etd/667