CrossTalk

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Geometry

An array of 6 detectors are placed radially at a distance of 1 meter from an uncorrelated 252-CF source. The image below shows a top down view of the simulation geometry. The detector setups have a vertical extent of 30".

Detector physics

The detector physics used in the simulation is MCNP-POLIMI's default treatment of plastic organic scintillators. POLIMI uses electron equivalent light output (MeVee) for simulating detector responses. I assumed the detectors have a neutron energy deposition threshold of 0.2 MeV, giving an equivalent light output threshold of 0.03 MeVee.

Neutron energy deposition from collisions with both hydrogen and carbon are converted to electron equivalent light output (MeVee). All neutron collisions that occur within the pulse collection time window of 10 ns of one another are summed together. If the cumulative light output of a pulse exceeds the 0.03 MeVee threshold, then a detection is registered. The value 0.03 MeVee was chosen because it corresponds to a mean neutron energy deposit of 0.2 MeV.

Statistics

n-n correlation was not simulated, as source particles were emitted isotropically, one by one. Nonetheless, given a fission rate and neutron multiplicity, a theoretical n-n coincidence rate can be estimated to provide a quantity that can be compared against the simulated crosstalk rate. This rate can be described as the rate of n-n events if the fission neutrons were emitted together uncorrelated and isotropic. This rate is estimated from the simulation as follows:

[math]R_{nn}=f*\nu(\nu-1)*N(N-1)*P_{d}^{2}[/math]

[math]f[/math] is the fission rate,

[math]\nu[/math] mean neutron multiplicity,

[math]N[/math] in the number of detectors, and

[math]P_{d}[/math] is the probability that a single neutron registers a hit in a single given detector. This value can be calculated directly from the simulation: [math]P_{d}=\frac{\text{total number of single hits}}{N*(\text{total number of src neutrons})}[/math]

The crosstalk rate, [math]R_{X}[/math], simply scales proportionally with neutron multiplicity, fission rate, and the number of detectors. The estimated crosstalk rate is given by:

[math]\displaystyle R_{X}=f*\nu*N*P_{X}[/math]

where [math]P_{X}[/math] is the probability of crosstalk per source neutron, which is calculated directly from the simulation result:

[math]P_{X}=\frac{\text{total number of cross talk events}}{\text{total number of src neutrons}}[/math]

In order to quantify the amount of crosstalk contamination, I define a 'signal-to-noise ratio' equal to the ratio between the estimated signal and crosstalk rates.

[math]SNR=\frac{R_{nn}}{R_X}=\frac{(\nu-1)*(N-1)*P_{d}^{2}}{P_{X}}[/math]

I'm uncertain about the exact value for neutron multiplicity, so I will assume it's equal to 2, since this value is reasonable and serves as a worst case scenario.

Result

Out of [math]10^8[/math] source particles there were [math]3.236572\times10^6[/math] singles and [math]5.074 \times10^3[/math] crosstalk events. This gives a signal-to-noise-ratio (defined above) of 8.6.

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