I have finally come around to making a calculation of the scintillator
oil ex post facto of the April gain reset and with current calibrations
that our Hoosier colleagues are supplying. The file
VAXGS::DISK$MACRO2:[HANSONK.DATA]SCINT_ATTEN.PS
is a 6 page histo-graphic summary of what is spelled out in raw numbers
in the 6 (number=SM) files AT[1-6].DAT of the same directory. Each page,
or each line of the file contains the six parameters used in the fit. The
line numbers of the text files, and the horizontal axes of the plots,
correspond to the calmod indices of the box. The fit function,
exp(-z0/lambda_1) + alpha_0*exp(-z0/lambda_2)
gain_factor * ---------------------------------------------
exp(-z1/lambda_1) + alpha_1*exp(-z1/lambda_3)
is compared with the RATIO of photoelectrons, pe0 / pe1. This removes
muon energy deposition fluctuations at the cost of making the function
more non-linear. However, unless you take millions of muons or gang
several boxes together and do a group fit, it is the only way to go.
I explain the parameters in more detail here:
lambda_1 : The "long" attenuation length. The intrinsic length
of the oil probably dominates this with some geometric
effects playing in as well.
lambda_2 : The "short" attenuation length of the 0 end. I can see
this parameter being influenced by the geometry of the
tank, depth of oil, mounting of the reflectors. For
this reason I no longer assume that it is nearly uniform
for all tanks, as was done previously.
lambda_3 : The "short" attenuation of the 1 end. Why not? The
two ends of a tank in light of the above paragraph are
as different as two ends in different tanks.
alpha_0, alpha_1 : See the above equation.
gain_factor : Previously, I needed this multiplier to get good
fits when the calibration constants were old. For
most tanks now this number comes out very close to
unity which is a good measure of faith that the ADC
calibrations are pretty good.
The 6 parameters were not fit at once. Instead with MINUIT it is
possible to freeze some parameters. I first took the region
-200 < z < 200 and only let lambda_1 and the gain_factor vary. Then
these were frozen and each end was fit, freeing only the relevant
parameters. The fit was done via the usual chi-square minimization
where the measurement errors were taken from pe fluctuations and
streamer-tube track errors added in quadrature.
This time I have not visually scanned the fits so I can't say why
the plots of the four parameters besides the overall gain factor and
the "long" length do not inspire much confidence for a large number
of tanks. Unfortunately I did not take the trouble this time to
extract the MINUIT error estimates. I can do some more work on this
if I get feedback in that direction.
Questions, comments, hostile attacks welcome,
Kael