Positronium: A Theoretical Lifetime Calculation and a Path Integral Monte Carlo Simulation in an Electric Field

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2003
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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
The theoretical lifetime of para-Positronium is calculated using Feynman rules. Relativistic quantum mechanics is discussed. This is accompanied by an introductory level treatment of classical and relativistic propagator theories with the intention of narrowing the gap between relativistic quantum mechanics and quantum electrodynamics, from which the Feynman rules are derived. The Feynman rules are applied to the two possible first order annihilation Feynman diagrams of p-Ps. We obtain a lifetime of 1.25 x 10-10 s for a free Ps. The dependence of the lifetime of positronium on electric field is calculated indirectly by finding the electron-positron overlap integral for Ps placed in electric field. We show that the overlap integral decreases in proportion to E2 for electric field values below 0.01 a.u. Our simulation is done using the Path Integral Monte Carlo (PIMC) technique which has been used with success in previous computational studies of Ps.
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