Date of Award

2006

Document Type

Restricted Thesis

Terms of Use

© 2006 Zachary Wolfson. All rights reserved. Access to this work is restricted to users within the Swarthmore College network and may only be used for non-commercial, educational, and research purposes. Sharing with users outside of the Swarthmore College network is expressly prohibited. For all other uses, including reproduction and distribution, please contact the copyright holder.

Degree Name

Bachelor of Arts

Department

Physics & Astronomy Department

First Advisor

Amy Lisa Graves

Abstract

Positronium (Ps), the bound state of an electron and a positron, may be used as a probe of the porous space in bulk materials due to its long vacuum lifetime and the fact that this lifetime depends strongly on its environment. In particular, an accurate model relating the lifetime of the positronium to the size of the pore is necessary. The primary outcome of this research is a computer program that models Ps exactly as two quantum particles, using Path Integral Monte Carlo (PIMC) to simulate the electron and positron each as a classical polymer. As a further correction, we include the dielectric response of the surrounding material to the presence of the two charges.

We find that the material's polarization causes the Ps to be more attracted to the wall, decreasing the pickoff lifetime; this decrease is even more dramatic in the case of a bare positron within the cavity. Although this effect is more substantial for larger cavities, it does approach a limit as the radius of the cavity approaches infinity, since then the situation is that of Ps near a flat dielectric wall. Also a limit is reached in the behavior of the lifetime as the dielectric constant ko increases, since the energy scales approximately like (1 - ko)/(1 + ko). Using a two-particle simulation with no dielectric energy (or equivalently, setting ko = 1) in general produces lifetimes significantly higher than the standard Tao-Eldrup model, but having ko > 1 reduces the lifetime once more, agreeing with Tao-Eldrup in certain cases. We found that typical values of ko have the same order of magnitude effect as do different pore geometries, and that our results explain certain discrepancies in data that other models could not.

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