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William P. Gammel added subsection_Gamma_Ray_Spectroscopy_When__.tex
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\subsection{Gamma-Ray Spectroscopy}
When a gamma ray interacts with the NaI:Ti crystal the ray can give all of its energy to an electron via the photoelectric effect. The photoelectric effect will then cause a voltage peak in the spectrum seen by the photomultiplier, known as the photopeak. Data from the photomultiplier was used to first determine an unknown sample, and then to determine the age difference between two samples of Cs-137. As explained in the Section 1.2 the voltage pulse that is produced by the photomultiplier is measured by Analog to Digital Conversion (multi-channel analyzer). For a 10 bit ADC, the result is an integer value between 0 and 1023. Zero is assigned to a pulse less than $\frac{1}{100}$ of a volt, and 1023 is assigned to a pulse that is larger than about 8 volts. Thus pulses between 0V and 8V are proportionally given an integer value between 0 and 1023. This measure is known as the channel number, which the computer records. The resulting spectrum that is displayed is the number of gamma rays observed at each integer value plotted as a function of the channel number. Unfortunately, there is little information that can be extracted from information about the channel number, and thus we must calibrate our program so that there is some correlation between channel number and energy. In order to begin the calibration processes, optimal values for Voltage, Course Gain, and Fine Gain, which can be found in Table \ref{table:Gamma_Settings}, were found. To find these values an auto-calibration function provided by the program was first used on our samples. This allowed us to determine a basis for these settings, which we then modified slightly. The settings were varied so that our data closely matched published spectral data for both Cs-137 and Co-60.
\par After the settings were optimized, samples of Cs-137 and Co-60 were stacked on top of of one another, and were placed approximately $2 cm$ away from the scintillator. Correlation between the channel number and the energy was produced by assigning known energy values to channel numbers. The simplest way to do this is by finding the known values of the photopeak energies for both Cs-137 and Co-60 and manually assigning them to the channel numbers associated with the photopeaks seen in the collected spectral data. The photopeak value for Cs-137 and Co-60 are, 661.6 keV, 1.17 MeV, and 1.33 MeV respectively. While it is possible to calibrate the program with just Cs-137, we decided upon using both Cs-137 and Co-60 since C-137 has only one photopeak, and we wanted to increase the accuracy of the correlation by calibrating the program off of three different values instead of one.
As discussed above in the Introduction, our apparatus was set up to measure cosmic rays going through the scintillator. But, the computer would only record a true muon if it decayed within the scintillator. We gave this a time limit of $12 \mu$ seconds, as seen in Table \ref{table:muonsettings}. The time given just means that we chose an amount of time that the muons had to decay within. For example, a muon can decay twice in $12 \mu$ seconds if each decay is $6 \mu$ seconds. The bin setting was chosen to give the most detail in the spectrum. 60 bins meant that there were 60 different bins the muon decays could fall into. Smaller bins would have resulted in a less detailed spectrum.
