more repotr changes, new bib item

adv_lab.bib

@@ -42,4 +42,9 @@ url = {http://www.test.org/doe/}
   %month        = ,
   %year         = ,
   note         = {Instruction Manual}
+}
+
+@ONLINE{EngToolbox:AirDensity,
+title = {Air - Density and Specific Weight},
+url = {http://www.engineeringtoolbox.com/air-density-specific-weight-d_600.html}
 }

alpha_spectroscopy/report/report.tex

@@ -66,7 +66,7 @@ The primary mode of study here will be to compare energy values determined by fi
 \label{subsec:activity}
     The absolute activity $I_\alpha$ of the Americium-241 alpha emitter, in alpha particles per second, is computed from counts of alpha particles through the detector over a known amount of time. The number of alpha particles detected $\Sigma\_{\alpha}$ is related by the solid angle subtended by the detector on the source, and the time the detector was live $t_L$, to the total number of alpha particles emitted by the sample. The cross-sectional area of the circular detector is $\pi r^2$, with $r$ the radius of the detector, $s$ is the distance from the source to the detector, and assuming there are no reflection effects, then
     \begin{center}
-    $I_\alpha = \left(\frac{\Sigma\_{\alpha}}{t_L}\right)\left(\frac{4 \pi s^2}{\pi r^2}\right)$ \cite{ORTEC:Alpha:Exp4}
+    $I_\alpha = \left(\frac{\Sigma\_{\alpha}}{t_L}\right)\left(\frac{4 \pi s^2}{\pi r^2}\right)$. \cite{ORTEC:Alpha:Exp4}
     \end{center}
 
     There are three significant energy modes of the alpha emission from Americium-241, with varying probability of incidence: $5486 keV (85\% probability)$; $5443 keV (13\%)$; and $5388 keV (1\%)$. \cite{AMERICIUM-241} The sum of each peak must be added to obtain a total count of alpha particles detected. These peaks were impossible to discern from inspection, as the overall magnitude of the activity across that domain out-competed the nuanced distinction. The counts were summed over a bin deemed sufficient to cover all three modes based on the referenced relative energies. This bin is marked in red on figure \ref{fig:activity}.
@@ -103,17 +103,20 @@ When an absorber is present between the alpha radiation source and the detector,
         \caption{Nickel foil thicknesses and the associated loss of kinetic energy by the alpha particles reaching the detector.}
     \end{table}
 
-
-
-
- $\frac{\Delta E}{\Delta X}$
-
-
-
 \subsection{Interference from a Gas}
 \label{subsec:gas}
-    A gas can act as an attenuator similarly to a film. An alpha spectrum is collected under increasing pressure (8 settings total). The penetration depth is computed 
+    A gas can act as an attenuator similarly to a film. An alpha spectrum is collected under increasing pressure (8 settings total). The gas occupies the entire space between the source and the detecter, so the depth is exactly that distance, but at each step the density changes, dependent on the pressure. Here, air is used as the absorbant gas, and the pressure is reported by a simple spin gauge connected to the vacuum chamber. The density of air at room temperature can be estimated as $\rho_A = 1.28 mg/cm^2$, and while this number is presented without uncertainty, it is an estimate only and can be considered accurate to the precision it is quoted here. Then, assuming any changes to equilibrium between gasses inside the chamber and outside occur quasistatically, the density of the gas at a given pressure can be related to its density at atmospheric pressure as
 
+    \begin{center}
+        $\rho_P = \frac{P}{P_A} \rho_A$.
+    \end{center}
+
+    From these densities, and using the distance from the source to the detector, an absorption depth can be computed with the same units as the thin film, using the relationship
+    \begin{center}
+        $\Delta x = \rho_P s$,
+    \end{center}
+    where $s$ is the distance from the source to the detector.
+    
 \section{Radium Alpha Decay Chain}
 \label{sec:radium}