2NCorr Photon flux estimate - Revision history

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@@ Line 16: / Line 16: @@
 :<math>N_{\gamma}</math> is the number of photons incident on the target with energy greater than 2.3 MeV, the threshold for photo-disintegration of D2O.
 :<math>E</math> is photon energy as a function
-:<math>\epsilon</math> is the detector efficiency for D2O photo-neutrons.
+:<math>\epsilon</math> is the detector efficiency for D2O photo-neutrons, integrated over the neutron energy spectrum.
 :<math>P(n_0|E) </math> is the probability of a photo-disintegration event given that the photon has energy E.
 :<math>P(E|E>2.3) </math> is the probability of a photon having energy E, given that the photon is above threshold.
-:<math>n_{rate}</math> is the mean number of neutrons observed per pulse.
+:<math>n_{rate}</math> is the mean number of neutrons observed per pulse (1.74E-2).
 :<math>\Omega</math> is the solid angle for the entire detector array (0.056/4pi).

@@ Line 27: / Line 27: @@
 The integral above was calculated numerically with software.
-The unknown detector efficiency can be set to 1, which brings <math>N_{\gamma}</math> to its theoretical minimum, or roughly 1,000 photons per pulse. The detector efficiency is not known exactly, but it lies within the range of 5-25%, so there are between 4,000 and 20,000 photons above 2.3 MeV incident on the target. Each photon can be considered a independent "binomial trial", and with such a large number of such trials, Poissonian distribution is a good approximation for the probability distribution of the number of photo-nuclear reactions in a given pulse.
+The unknown detector efficiency can be set to 1, which brings <math>N_{\gamma}</math> to its theoretical minimum, or roughly 1,000 photons per pulse. The detector efficiency is not known exactly, but it lies within the range of 5-25%, so there are between 4,000 and 20,000 photons above 2.3 MeV incident on the target. Each photon can be considered an independent "binomial trial", and with such a large number of such trials, Poissonian distribution is a good approximation for the probability distribution of the number of photo-nuclear reactions in a given pulse.
 [[File:2NCorrPhotonFluxRate.png|thumb| 500px| left|Photon flux on the target over a range of photon energies, estimated from observed neutron rates, while assuming the detector array's intrinsic efficiency is 100%. Correcting for an efficiency less than 100% is done by dividing the distribution by the efficiency.]]

@@ Line 25: / Line 25: @@
 ;<math> n_{rate} = N_{\gamma}\Omega\epsilon \int_{2.3}^{10.5}\! (1.89 e^{-0.54E})*(0.21\sigma(E))\,dE</math>
-The integral above was calculated using numerically with software.
+The integral above was calculated numerically with software.
 The unknown detector efficiency can be set to 1, which brings <math>N_{\gamma}</math> to its theoretical minimum, or roughly 1,000 photons per pulse. The detector efficiency is not known exactly, but it lies within the range of 5-25%, so there are between 4,000 and 20,000 photons above 2.3 MeV incident on the target. Each photon can be considered a independent "binomial trial", and with such a large number of such trials, Poissonian distribution is a good approximation for the probability distribution of the number of photo-nuclear reactions in a given pulse.
 [[File:2NCorrPhotonFluxRate.png|thumb| 500px| left|Photon flux on the target over a range of photon energies, estimated from observed neutron rates, while assuming the detector array's intrinsic efficiency is 100%. Correcting for an efficiency less than 100% is done by dividing the distribution by the efficiency.]]

@@ Line 24: / Line 24: @@
 Now writing <math>P(n_0|E)</math> in terms of the cross-section and substituting a normalized photon energy distribution taken from MCNP in place of <math>P(E|E>2.3)</math>, the above becomes:
 ;<math> n_{rate} = N_{\gamma}\Omega\epsilon \int_{2.3}^{10.5}\! (1.89 e^{-0.54E})*(0.21\sigma(E))\,dE</math>
 The unknown detector efficiency can be set to 1, which brings <math>N_{\gamma}</math> to its theoretical minimum, or roughly 1,000 photons per pulse. The detector efficiency is not known exactly, but it lies within the range of 5-25%, so there are between 4,000 and 20,000 photons above 2.3 MeV incident on the target. Each photon can be considered a independent "binomial trial", and with such a large number of such trials, Poissonian distribution is a good approximation for the probability distribution of the number of photo-nuclear reactions in a given pulse.
 [[File:2NCorrPhotonFluxRate.png|thumb| 500px| left|Photon flux on the target over a range of photon energies, estimated from observed neutron rates, while assuming the detector array's intrinsic efficiency is 100%. Correcting for an efficiency less than 100% is done by dividing the distribution by the efficiency.]]

@@ Line 25: / Line 25: @@
 ;<math> n_{rate} = N_{\gamma}\Omega\epsilon \int_{2.3}^{10.5}\! (1.89 e^{-0.54E})*(0.21\sigma(E))\,dE</math>
-The unknown detector efficiency can be set to 1, which brings <math>N_{\gamma}</math> to its theoretical minimum, or roughly 1,000 photons per pulse. The detector efficiency is not known exactly, but it lies within the range of 5-25%, so there are between 4,000 and 20,000 photons above 2.3 MeV incident on the target. Each photon can be considered a independent "binomial trial", and with such a large number of such trials, Poissonian distribution is a good approximation for the probability distribution of the number of photo-nuclear reactions per pulse.
+The unknown detector efficiency can be set to 1, which brings <math>N_{\gamma}</math> to its theoretical minimum, or roughly 1,000 photons per pulse. The detector efficiency is not known exactly, but it lies within the range of 5-25%, so there are between 4,000 and 20,000 photons above 2.3 MeV incident on the target. Each photon can be considered a independent "binomial trial", and with such a large number of such trials, Poissonian distribution is a good approximation for the probability distribution of the number of photo-nuclear reactions in a given pulse.
 [[File:2NCorrPhotonFluxRate.png|thumb| 500px| left|Photon flux on the target over a range of photon energies, estimated from observed neutron rates, while assuming the detector array's intrinsic efficiency is 100%. Correcting for an efficiency less than 100% is done by dividing the distribution by the efficiency.]]