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This commit adds the absorption length to the likelihood calculation. For now
I'm just using a single number independent of wavelength. I should update this
in the future to actually use the absorption lengths as measured by SNO and
then calculate an overall absorption length weighted by the Cerenkov spectrum
and the PMT quantum efficiency.
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This commit adds code to read in the PMT response from the PMTR bank from
SNOMAN. This file was used for the grey disk model in SNOMAN and was created
using a full 3D simulation of the PMT and concentrator. Since the PMT response
in SNOMAN included the quantum efficiency of the PMT, we have to divide that
out to get just the PMT response independent of the quantum efficiency.
I also updated the likelihood calculation to use the pmt response. Currently
the energy is being fit too high which I think will improve when we update the
solid angle calculation to use the radius of the concentrator instead of the
PMT.
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This commit updates the likelihood fit to use the KL path expansion. Currently,
I'm just using one coefficient for the path in both x and y.
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Previously I had been assuming that a particle undergoing many small angle
Coulomb scatters had a track direction whose polar angle was a Gaussian.
However, this was just due to a misunderstanding of the PDG section "Multiple
scattering through small angles" in the "Passage of particles through matter"
article. In fact, what is described by a Gaussian is the polar angle projected
onto a plane. Therefore the distribution of the polar angle is actually:
(1/(sqrt(2*pi)*theta0**2))*theta*exp(-theta**2/(2*theta0))
This commit updates the code in scattering.c to correctly calculate the
probability that a photon is emitted at a particular angle. I also updated
test-likelihood.c to simulate a track correctly.
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The RMS scattering angle calculation comes from Equation 33.15 in the PDG
article on the passage of particles through matter. It's not entirely obvious
if this equation is correct for a long track. It seems like it should be
integrated along the track to add up the contributions at different energies,
but it's not obvious how to do that with the log term.
In any case, the way I was previously calculating it (by using the momentum and
velocity at each point along the track) was definitely wrong.
I will try this out and perhaps try to integrate it later.
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