My project for the past six weeks has been to test our code by simulating a weak electric field and seeing how the model positronium responds. The main thing I've been looking at is the average separation <z> of the electron and positron in the direction of the electric field. This value is given by the equation:
<z> = a E / e
where E is the stength of the electric field, e is the magnitude of the charge (1 in a.u.), and a is the polarizability. For positronium, a is 36 au3.
I have been taking data at four different field stengths: 0.0025, 0.005, 0.0075, and 0.01 au (a field of 0.02 au is about one volt per angstrom). At fields much stronger than 0.01 au the Stark effect becomes non-linear. At fields weaker than 0.0025 au the signal to noise ratio is very poor and the effects are hard to see.
At each field strength I sampled five values of P (500, 600, 700, 800, and 1000 beads) while lowering the yukawa radius a so that aP-2/3 was constant. After sampling each point three times I extrapolated to a = 0 to determine the theoretical value for <z> at that field strength.
Extrapolations by field strength:
E=0.0025 E=0.0050 E=0.0075 E=0.0100
Final Result: <z> vs. E plot and extrapolation.
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