View source for LB Thesis Theory Section

=PAA Theory=


==General PAA Method==
Photon activation analysis (PAA) is a method used to determine the isotopic composition of a sample based on the characteristic photon energies emitted by gamma decays of radioactive isotopes that have been activated by bremsstrahlung photons.. The sample is activated using a Linear Accelerator (LINAC) to accelerate electrons towards an aluminum/tungsten radiator and produce Bremsstrahlung radiation from those electrons that slow down within the radiator.  Some of those Bremsstrahlung photons are of sufficient energy to free a nucleon(s) from the target nuclei in the sample of interest. After the nucleons have been removed from the nucleus, the nucleus becomes unstable and starts to undergo nuclear decay. The nuclear decay can emit photons  that have energies characteristic to each isotope enabling the construction of a compositional fingerprint once the detected photon emission rates are also shown to have the half life of the assumed isotope. Typically High Purity Germanium Detectors are used to count the photons and measure the photon energy for the sample of interest. A typical photon energy distribution from an activated sample as measured by the HpGe detector is shown below

[[File:170063 EnergySpectrumSample.png|200px]]

Note that there will be many different isotopic decay lines present in the spectrum, but there are several methods to ensure that information about the isotope of interest can be found. The first step to proving that a specific isotope is present in the sample is to first look at the energy lines. Since each isotope has characteristic gamma decay lines, if the isotope is present, then those lines should be apparent in the spectrum (assuming the branching ratio is high enough that the lines don't get washed out in the background). Consider some isotope of interest that has 3 large characteristic decay lines. If all of those 3 lines are present in the spectrum, then that would be a good indicator that the isotope of interest is in the sample. Unfortunately more information is needed due to the fact that there are so many isotopes that 3 separate isotopes (or some other combination) could produce lines close the energy lines of the isotope of interest, which would produce a false positive. To strengthen the argument, multiple measurements can be made using the same sample to see how the rate of photons into the HpGe detector change with time. By finding how the number of counts seen by the HpGe detector change with time can be used to find the half life of the decay via the standard radioactive decay equation

<math> A_{Measured} = A_0 e^{-\lambda t} </math>

An example of a decaying energy line can be seen below

[[File:Se81 Metastable 103keV overlay.png|200px]]

It can be seen above that the same energy line will become less apparent as time goes on due to the decay. By measuring the activity at several points in time, a plot of the measured activity as a function of time can be created. By fitting this function (whether linearly of exponentially), the fit parameters of the initial activity and the decay constant can be found. If the energy lines are present and the half life agrees with the isotope of interest, then the argument strengthens. There is one more step that can be taken to ensure the isotope of interest is present in the sample. Looking at the branching ratios for the different energy lines can provide a stronger argument. Consider some isotope of interest A that has two decay lines with branching ratios of 80% and 40%. By looking at the rate seen by the detector for these lines, the ratio between the activities measured should be around 2, meaning that the first decay happens roughly twice as often as the second decay. Using all three of these pieces the experimenter can provide a strong argument for the isotope of interest being present in the sample. 

This method of compositional analysis has many applications such as verifying a counterfeit product, and finding concentrations of contaminants in a sample.

==Neutron Knockout of Selenium==
Talk bout the 3 neutron knockouts of interest (81,75,79) and provide the half lives for each isotope. Also here include the cross section plots.

==Predicted Activities==
[[LB PAA Nickel Investigation]]

==Minimum Detectable Activity Calculations==
Reference: [[LB MDA/Se Mass Calculations]]

==Calibration Methods==
When using the HpGe detector, the energy isn't directly given due to the fact that the energy deposited by the photon into the crystal is converted into an ADC channel number. The energy calibration is quite simple. By using calibrated sources with known activities and energy lines, one can place the calibrated source in front of the HpGe detector and find which channel number corresponds to the energy line of interest. This would be a single data point in your calibration. To ensure that the calibration is of a high quality, take several sources with several different energy lines that span the channel range of the detector and compare the channel number to the energy. Once this information has been found, simply make a file with the energy the line was supposed to be, the channel number, and the standard deviation from a Gaussian fit and plot the points. Once the points are plotted a linear fit can be done to find exactly how the energy lines deviate from the raw channel number.

==Geometric Efficiency Calculations==