The adc signal from a BSD counter is proportional to the amount of collected light, or in other words to the deposited energy. When one compares different pixels in a given counter, it can be seen that peak position shifts toward lower values for higher pixel index (see Fig 2). The reason for that might be polar angle energy dependence or attenuation of light along the BSD counters. Since the same dependence is observed in both minimum-bias and standard data, it is concluded that attenuation of light is responsible for the observed gain dependence on pixel index. If the effect were due to the dependence of the particle spectrum on polar angle, the gain vs. pixel curve should be different for hadronic (standard) and electromagnetic (minimum-bias) backgrounds.
In order to explore
this dependence, the distribution of mean adc gain as a function of
pixel number is formed for every BSD counter. All
distributions of pixel gains show the same characteristics (see
Fig. 3): fast exponential
drop for the first three pixels and a rather flat tail at higher pixels.
An exponential drop would be expected from attenuation, while
flattening might be due to reflection from the end of the counter. Thus,
the sum of one falling and one increasing exponential function could be
used to describe the data
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Minimum-bias data | Standard data | ||||||||||||||||||||
Three parameters | Two par. | Two par. | |||||||||||||||||||
Counters | B | C | B | C (fix.) | B | C (fix.) | |||||||||||||||
R00 | 5.93 | .034 | 4.23 | .055 | 4.33 | .057 | |||||||||||||||
R01 | 4.74 | .038 | 3.58 | 3.85 | |||||||||||||||||
R02 | 4.49 | .054 | 4.27 | 4.01 | |||||||||||||||||
R03 | 6.80 | .020 | 3.87 | 3.49 | |||||||||||||||||
R04 | 4.85 | .029 | 3.29 | 3.12 | |||||||||||||||||
R05 | 5.58 | .046 | 4.64 | 4.87 | |||||||||||||||||
R06 | 4.64 | .063 | 5.13 | 4.17 | |||||||||||||||||
R07 | 4.44 | .073 | 5.91 | 4.42 | |||||||||||||||||
R08 | 7.87 | .066 | 9.42 | 5.98 | |||||||||||||||||
R09 | 15.67 | .008 | 6.49 | 4.49 | |||||||||||||||||
R10 | 7.57 | .032 | 5.15 | 3.72 | |||||||||||||||||
R11 | 5.95 | .059 | 6.21 | 5.06 | |||||||||||||||||
L12 | 10.99 | .026 | 6.26 | 5.83 | |||||||||||||||||
L13 | 7.54 | .051 | 6.74 | 5.33 | |||||||||||||||||
L14 | 5.75 | .058 | 5.88 | 3.69 | |||||||||||||||||
L15 | 5.77 | .071 | 7.36 | 5.19 | |||||||||||||||||
L16 | 3.45 | .062 | 3.77 | 2.97 | |||||||||||||||||
L17 | 4.35 | .065 | 5.02 | 3.99 | |||||||||||||||||
L18 | 3.69 | .068 | 4.49 | 3.81 | |||||||||||||||||
L19 | 5.59 | .062 | 6.24 | 5.12 | |||||||||||||||||
L20 | 7.76 | .033 | 5.19 | 4.64 | |||||||||||||||||
L21 | 6.63 | .044 | 5.40 | 4.74 | |||||||||||||||||
L22 | 5.89 | .029 | 3.96 | 3.97 | |||||||||||||||||
L23 | 9.81 | -.001 | 3.95 | 3.49 | |||||||||||||||||
average/rms | 6.49 | 2.61 | .05 | .02 | 5.27 | 1.4 | 4.35 | 0.8 | |||||||||||||
S24 | 4.88 | .048 | 5.88 | 0.035 | 4.16 | .037 | |||||||||||||||
S25 | 16.91 | .015 | 10.50 | 8.03 | |||||||||||||||||
S26 | 19.81 | .003 | 9.25 | 7.42 | |||||||||||||||||
S27 | 11.23 | .021 | 8.18 | 6.45 | |||||||||||||||||
S28 | 20.86 | .001 | 9.38 | 7.67 | |||||||||||||||||
S29 | 6.12 | .039 | 6.31 | 5.09 | |||||||||||||||||
S30 | 4.26 | .041 | 4.59 | 3.60 | |||||||||||||||||
S31 | 5.79 | .049 | 7.33 | 6.65 | |||||||||||||||||
S32 | 14.22 | .018 | 9.67 | 8.69 | |||||||||||||||||
S33 | 43.43 | -.021 | 9.17 | 7.67 | |||||||||||||||||
S34 | 47.81 | -.036 | 7.35 | 6.36 | |||||||||||||||||
S35 | 48.22 | -.029 | 8.31 | 6.54 | |||||||||||||||||
S36 | 23.32 | -.012 | 7.83 | 6.87 | |||||||||||||||||
S37 | 8.64 | .031 | 7.66 | 5.97 | |||||||||||||||||
S38 | 21.97 | -.030 | 5.84 | 6.49 | |||||||||||||||||
S39 | 19.88 | -.025 | 5.79 | 5.74 | |||||||||||||||||
S40 | 31.65 | -.030 | 6.86 | 6.56 | |||||||||||||||||
S41 | 6.14 | .014 | 4.32 | 3.54 | |||||||||||||||||
S42 | 12.74 | -.007 | 5.74 | 4.73 | |||||||||||||||||
S43 | 22.98 | .001 | 9.91 | 6.96 | |||||||||||||||||
S44 | 19.45 | .013 | 11.24 | 6.23 | |||||||||||||||||
S45 | 8.80 | .019 | 6.47 | 4.35 | |||||||||||||||||
S46 | 11.21 | .034 | 10.33 | 7.77 | |||||||||||||||||
S47 | 8.65 | .038 | 8.84 | 6.07 | |||||||||||||||||
average/rms | 18.28 | 12.76 | .008 | .02 | 7.79 | 1.89 | 6.24 | 1.4 |
In conclusion, the analog signal from the BSD detector is analysed. It is observed that all BSD paddles have similar adc distributions. However, because of different characteristics of the counters, the position of the maximum varies from counter to counter. In order to correct for this, relative gain constants are found so that integrated spectra are matched to one chosen reference counter. In addition, it is seen that average gain depends on pixel position. Average gain decreases exponentially as pixel index increases, independent of the trigger type. Comparing standard and minimum-bias data it is concluded that the observed gain dependence comes from the attenuation of light along the BSD paddle. The gain dependence on pixel index is best described by a superposition of one falling exponential and one increasing linear function. Fit to the pixel gain distributions yields coefficients that can be used to correct for attenuation losses. These coefficients have similar values for different BSD counters.
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