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Mark S. Brown edited Method 2.tex
about 10 years ago
Commit id: 2b8a0fdb90bb00abbdfcf1c0ecb6d41be88cd63f
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The positron emission from the Na22 source will generate two 0.511MeV gamma ray photons in opposition correlated in time. By selecting for events which interact solely by the photoelectric effect we ensure that the incident gamma ray photon has interacted with matter only once. Therefore if two gamma ray photons are detected in opposition within a small time window, it is highly likely they are from the same electron-positron annhilation. It is this 'electronic collimination' timing property which ensures we only record events from within the confinement region. These events are found by selecting the subset of interactions which fall within $2\sigma$ of the photopeak centroid of their respective energy spectra. This narrow range is chosen to drastically reduce the contribution of overlapping Compton interactions. When two gamma ray photons are detected within their respective photopeak energy ranges, within a nanosecond of each other, the relative time delay between the two is recorded. For many such true events the relative difference in arrival time is histogrammed to produce a Gaussian distribution. This will be referred to as the (relative) delay peak. For two identical photodetectors the FWHM of the delay peak is defined as the coincidence time resolution (CTR), such that
\begin{align}
\text{CTR} &=
2\sqrt{2\ln{2}}\sigma_\textrm{measured}\\ 2\sqrt{2\ln{2}}\sigma_\text{measured}\\
\text{CTR} &= 4\sqrt{\ln{2}}\sigma
\label{eqn:ctrtoscale}
\end{align}