Path Integral Monte Carlo Simulation of Positronium within a Dielectric Spherical Cavity
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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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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)/(l + 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.