Last update Nov 4th, 1997
Once the raw data from the TDCs of the E-counters have been histogrammed, one can attempt to fit the resulting spectra. As shown on the preceding page, the peak from correlated events sits atop a background. This background can safely be assumed to be flat, and is modeled by a polynomial of order 0.
The peak itself should closely resemble a binomial distribution. As seen on the raw spectra this assumption seems to be, in general, correct, with most deviations being attributed to the low resolution (.5nsec/channel) of the 1877s, resulting in a very sharp line.
As a result, the function describing the spectra is determined to be of the form:
y= P0 + P1*e(-0.5*((x-P2)/P3)**2)
Where:
The form of the function having been established, one can proceed to the fitting procedure. This is done using a kumac file, scan_e.kumac , in the PAW environment. One will note the use of the fitting package 'minuit' which is part of PAW and more accurately HBOOK.
The fitting procedure is essentially based on the old MIGRAD program. The major difficulty lies in the passing of initial parameters since the peaks are so narrow. The kumac file does attempt to provide a different set of initial parameters in the event of a failure on the part of the program to find a good fit. This method was found to be appropriate for all but a very few cases at 1700V.
If the program identifies a set of parameters which fit the data, it proceeds to integrate the true number of counts up to 2.5 sigmas about the centroids. This constitutes the integral under the peak.
The results are then tabulated in the file named 'centroids.dat', where the variables are in order P0, P1, P2, P3, the integrated counts under the peak, the noise level under the peak, and finally the total number of counts in the pair counter for the run in particular. The number of counts in the pair counter is provided as a means to normalize the results between different runs.
This operation then charaterizes the response of E-counters for specific supplied high voltages. In the present example, only 6 high voltages were available: 1700V, 1800V, 1900V, 2000V, 2100V, and 2200V.
Two quantities are of importance in our determination of the operational H.V. The first is the response. It is defined as the integrated number of counts under the peak, up to 2.5 sigmas from the centroid, from which the background noise has been subtracted. The noise is defined as the quantity P0 multiplied by the number of channels over which the integration is performed. The response is then normalized by the number of counts in the pair counter. Since this is a very small quantity, this number is then multiplied by a factor of 106.
The second quantity is the signal to noise ratio. It is defined as the ratio of the response to the background noise. Values much greater than '1' are preferred .
From our results, it is then possible to determine both the response and the signal to noise ratio for each counter and tabulate it as a function of applied H.V. The results, for all 384 counters, are shown graphically in e-plateaux.ps