Two detectors face each other across a source

PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Electronics, Instrumentation & Communication · Radiation interactions, detection and dosimetry

The Nucleus Resolved, Ch From a pulse to a number: detectors, resolution and what a spectrum establishes

Problem

Two detectors face each other across a source, each recording singles rates N1=5.0×103 s−1N_1 = 5.0\times10^3\,\mathrm{s^{-1}} and N2=8.0×103 s−1N_2 = 8.0\times10^3\,\mathrm{s^{-1}}, with a coincidence resolving time τres=20 ns\tau_{\rm res} = 20\,\mathrm{ns} (two pulses count as coincident when they arrive within τres\tau_{\rm res} of each other, in either order). ((a)) Calculate the rate of chance coincidences between the two detectors. ((b)) A true coincidence event from two back-to-back annihilation photons is recorded with a timing difference Δt=300 ps\Delta t = 300\,\mathrm{ps} between the two detectors. Calculate the distance of the annihilation point from the midpoint of the line joining the detectors, and state which detector it is closer to (the one that fired first or the one that fired second).

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