Path Integral Monte Carlo Simulation of Positronium in Cylindrical Pore Spaces

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2006
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Swarthmore College. Dept. of Physics & Astronomy
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Thesis (B.A.)
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Full copyright to this work is retained by the student author. It may only be used for non-commercial, research, and educational purposes. All other uses are restricted.
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Abstract
Positronium (Ps), the bound state formed by a positron and an electron, serves as a valuable probe of void spaces, particularly in materials with irregular porosity such as glasses, low-k dielectrics, and polymers. One experimental method, Positron Annihilation Lifetime Spectroscopy (PALS), relies on the ability to correlate pore size with Ps lifetime for triplet orthopositronium (0-Ps). A purely theoretical model, developed by Tao and verified by Eldrup (thus called the Tao-Eldrup or TE model) has been shown to fit lifetime vs. pore size curves well for pore radii less than rv Inm. In this thesis, we develop a new correspondence between TE models in different geometries; our findings explain in part why the spherical TE model has been robust for other pore shapes. Nonetheless, the TE model and many of its extensions are rather unrealistic, for they do not take into account the two-particle nature of Ps. In this thesis, we undertake a type of computer simulation of fully two-particle Ps called Path Integral Monte Carlo (PIMC). Our simulation results allow us to compare lifetimes of Ps in cylindrical void spaces with PALS experiments and TE models. We find a systematic deviation of our results from both experiment and model, suggesting that we (and the positron community) need to move towards more realistic models of both electronic density and Ps-cavity potential near the pore walls. We also undertake simulation of Ps in cylindrical pores filled with Ar atoms; we find that our annihilation rate vs. Ar density curve has a shape qualitatively similar to that of Ps in bulk Ar. We also observe the tendency of Ps to self-trap in an Ar bubble as the density of Ar in the pore increases. In addition to more realistic modeling of pore walls, future work should also emphasize streamlining the code in order to allow for better comparison of simulation and experiment.
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