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The range and energy loss tables have different maximum values for electrons,
muons, and protons so we have to dynamically set the maximum energy of the fit
in order to avoid a GSL interpolation error.
This commit adds {electron,muon,proton}_get_max_energy() functions to return
the maximum energy in the tables and that is then used to set the maximum value
in the fit.
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To enable the fitter to run outside of the src directory, I created a new
function open_file() which works exactly like fopen() except that it searches
for the file in both the current working directory and the path specified by an
environment variable.
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To characterize the angular distribution of photons from an electromagnetic
shower I came up with the following functional form:
f(cos_theta) ~ exp(-abs(cos_theta-mu)^alpha/beta)
and fit this to data simulated using RAT-PAC at several different energies. I
then fit the alpha and beta coefficients as a function of energy to the
functional form:
alpha = c0 + c1/log(c2*T0 + c3)
beta = c0 + c1/log(c2*T0 + c3).
where T0 is the initial energy of the electron in MeV and c0, c1, c2, and c3
are parameters which I fit.
The longitudinal distribution of the photons generated from an electromagnetic
shower is described by a gamma distribution:
f(x) = x**(a-1)*exp(-x/b)/(Gamma(a)*b**a).
This parameterization comes from the PDG "Passage of particles through matter"
section 32.5. I also fit the data from my RAT-PAC simulation, but currently I
am not using it, and instead using a simpler form to calculate the coefficients
from the PDG (although I estimated the b parameter from the RAT-PAC data).
I also sped up the calculation of the solid angle by making a lookup table
since it was taking a significant fraction of the time to compute the
likelihood function.
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