\contentsline {figure}{\numberline {1}{\ignorespaces The left plot shows a case where the data agree with a linear model, and the right plot shows disagreement with a linear model.}}{25}{figure.1}
\contentsline {figure}{\numberline {2}{\ignorespaces The top left plot has small random error, and small systematic error. The top right plot shows small random error, and large systematic error. The bottom left plot shows large random error, and small systematic error. The bottom right plot shows large random error, and large systematic error.}}{27}{figure.2}
\contentsline {figure}{\numberline {3}{\ignorespaces Gaussian distribution, and its $68$\% area around the mean.}}{29}{figure.3}
\contentsline {figure}{\numberline {4}{\ignorespaces Binomial distribution for rolling a 3 or 4 $k$ times in 10 rolls, compared to the Gaussian approximation $P_{gauss}(\mu =3.33,\sigma =1.49)$.}}{32}{figure.4}
\contentsline {figure}{\numberline {5}{\ignorespaces Poisson probability distribution function.}}{32}{figure.5}
\contentsline {figure}{\numberline {6}{\ignorespaces Overview of Agilent oscilloscope controls. Figure from \cite {agilentmanual}.}}{42}{figure.6}
\contentsline {figure}{\numberline {7}{\ignorespaces Example of a pulser pulse.}}{44}{figure.7}
\contentsline {figure}{\numberline {8}{\ignorespaces Pulser pulse as seen on the oscilloscope, and connection of tee with termination to oscilloscope.}}{45}{figure.8}
\contentsline {figure}{\numberline {9}{\ignorespaces Block diagram for amplifier test procedure.}}{46}{figure.9}
\contentsline {figure}{\numberline {10}{\ignorespaces Pulse timing for logic pulses. The left plot shows that leading-edge (or threshold) timing leads to a time jitter, while the right plot shows that the zero crossing time will lead to better time resolution.}}{48}{figure.10}
\contentsline {figure}{\numberline {11}{\ignorespaces Block diagram for SCA test procedure.}}{48}{figure.11}
\contentsline {figure}{\numberline {12}{\ignorespaces Block diagram for linear gate test procedure.}}{50}{figure.12}
\contentsline {figure}{\numberline {13}{\ignorespaces Diagram showing the main elements inside of a PMT. Image from Wikimedia commons. }}{53}{figure.13}
\contentsline {figure}{\numberline {14}{\ignorespaces Gamma ray interactions in a NaI(Tl) scintillator detector. Figure from Ortec\nobreakspace {}\cite {ortecan34}.}}{54}{figure.14}
\contentsline {figure}{\numberline {15}{\ignorespaces Typical gamma ray spectrum for a mono-energetic gamma ray detected with a NaI(Tl) scintillator. }}{55}{figure.15}
\contentsline {figure}{\numberline {16}{\ignorespaces Block diagram showing the electronics and detector connections for the SCA lab.}}{56}{figure.16}
\contentsline {figure}{\numberline {17}{\ignorespaces Asymmetric Probability Distribution Function for some measured quantity $x$. If the distribution was symmetric the meaning of the mean and width ($\sigma $) would be well defined. For an asymmetric PDF it might be better to report the peak value, and have an asymmetric error bar.}}{62}{figure.17}
\contentsline {figure}{\numberline {18}{\ignorespaces Measured length as a function of temperature for the two measurements. The horizontal dashed areas represent the two length measurement $1\sigma $ uncertainty bands, and the vertical dashed area represents the temperature measurement $1\sigma $ uncertainty band.}}{65}{figure.18}
\contentsline {figure}{\numberline {19}{\ignorespaces Example of linear fit for an energy to channel calibration.}}{66}{figure.19}
\contentsline {figure}{\numberline {20}{\ignorespaces Frequency of count of number of heads for 20 coin tosses repeated 10000 times is shown as the fine-dashed (green) line. The solid line is the binomial distribution. The smooth dot-dashed (blue) line is the Poisson distribution, and the histogram dot-dashed (red) line is sampling from the Poisson distribution. }}{69}{figure.20}
\contentsline {figure}{\numberline {21}{\ignorespaces Chi-squared test probabilities, calculated using the root function TMath::Prob($\chi ^2$,$\nu $) \cite {cernroot}. }}{71}{figure.21}
\contentsline {figure}{\numberline {22}{\ignorespaces Block diagram for counting statistics experiment setup. }}{72}{figure.22}
\contentsline {figure}{\numberline {23}{\ignorespaces Gamma ray total cross section versus energy, showing the contribution to the cross section from various processes for carbon (top), and lead (bottom)\cite {pdg}. }}{74}{figure.23}
\contentsline {figure}{\numberline {24}{\ignorespaces Electronics block diagram for the gamma ray spectroscopy experiment.}}{75}{figure.24}
\contentsline {figure}{\numberline {25}{\ignorespaces Cobalt-60 decay energy level diagram. Figure from wikimedia commons.}}{76}{figure.25}
\contentsline {figure}{\numberline {26}{\ignorespaces Equilibrium charge carrier concentrations in a p-n junction diode. Figure from Wikimedia commons. }}{77}{figure.26}
\contentsline {figure}{\numberline {27}{\ignorespaces Nuclear de-excitation energy levels after electron capture in $^{207}$Bi\cite {gammabooklet}. }}{80}{figure.27}
\contentsline {figure}{\numberline {28}{\ignorespaces Kinetic energy spectrum of beta particles from the radioactive decay of $^{204}$Tl. }}{81}{figure.28}
\contentsline {figure}{\numberline {29}{\ignorespaces Experimental set up. }}{82}{figure.29}
\contentsline {figure}{\numberline {30}{\ignorespaces The solid line in the figure above is a PDF we wish to sample from. The black points are the $(x,y)$ coordinates of uniform random values in the range $0,1$. The x value for the darker black points are accepted as random numbers with the distribution of the PDF.}}{87}{figure.30}
\contentsline {figure}{\numberline {31}{\ignorespaces This picture shows one end of the wrapped scintillator and the PMT coupled to it. }}{110}{figure.31}
\contentsline {figure}{\numberline {32}{\ignorespaces The high voltage supply is shown in this figure. We will only be using channels one and two. }}{111}{figure.32}
\contentsline {figure}{\numberline {33}{\ignorespaces The NIM and VME electronics used for this lab are shown in this picture. }}{112}{figure.33}
\contentsline {figure}{\numberline {34}{\ignorespaces Electronics diagram showing how the PMT signals are sent to the digitizer, and processed to make a trigger based on a coincidence between the two PMTs. }}{114}{figure.34}
\contentsline {figure}{\numberline {35}{\ignorespaces To check the signals from our LED pulser, and the signals from our PMTs, we will use three channels of an oscilloscope, as shown in this picture. }}{115}{figure.35}
\contentsline {figure}{\numberline {36}{\ignorespaces Tree viewer window showing the variables in the table as leaves. }}{116}{figure.36}
\contentsline {figure}{\numberline {37}{\ignorespaces Block diagram of a lock-in amplifier. }}{119}{figure.37}
\contentsline {figure}{\numberline {38}{\ignorespaces Block diagram for the one ohm resistance measurement (left), and photograph of the physical setup (right). }}{120}{figure.38}
\contentsline {figure}{\numberline {39}{\ignorespaces Block diagram for the brass rod resistance measurement (left), and photograph of the physical setup (right). }}{121}{figure.39}
\contentsline {figure}{\numberline {40}{\ignorespaces Block diagram for the shielding measurements (top), conceptual diagram of connections for shielding measurements (left), and photograph of the physical setup (right). }}{123}{figure.40}