Neutron counting statistics

The water thickness measurement uncertainty due to neutron counting statistics can be calculated from Poisson counting statistics. For a random process, the standard deviation, Ah in the observed counts I is A/ = y7. The number of neutrons in the incident, or open beam, I0, is the product of the neutron fluence rate (cur2 s 1), integration time T (s), integration area A (cm2), and neutron detection efficiency, ip... 

In powder diffraction, x-ray photons or neutrons (in x-ray and neutron diffraction experiments, respectively) are registered by the detector as random events. The measured intensity is directly proportional to the number of counts and therefore, the accuracy of intensity measurements is governed by statistics. Even though below we will refer to x-ray diffraction and photons, all conclusions remain identical when neutron diffraction and neutron count is considered. 

A large variance for Na by INAA could be explained by the application of a low neutron flux and short irradiation and measuring times the uncertainty was related to the statistics of counting low numbers. A large standard deviation was also observed for Fe, also dictated by counting statistics. 

Figure A4-W is a plot of the neutron flux along the vertical centerline of the active lattice, starting at the bottom of the lattice and continuing up to the shim rod electromagnets. The flux at the magnets is seen to be too low to give good counting statistics. To check this measurement, the neutron atte.nuation curve from the X-10 reactor lid tank was normalized and plotted with the curve from the Mock-Up, considering the top of the Mock-Up lattice to be the source plate.

For each absorbed x-ray photon or neutron, the proportional or scintillation counter produces a discrete electric pulse. The flux J of the beam of x-rays or neutrons is measured as the number of counts of such pulses observed per second. If measurements are made repeatedly with a beam of constant flux, the number of counts observed during a fixed time period is not exactly the same, but is rather subject to statistical fluctuations. The arrival time of any one particle (x-ray photon or neutron) is totally uncorrelated with the arrival time of the next particle. The flux J of the particles,... 

A further argument concerns the parameter v for the neutron width distribution, as obtained by the maximum likelihood method from the three experiments. For both of the earlier experiments, v is amazingly close to the theoretical value of one, although the statistical uncertainty is at least 10%. Garg et al. 47) report that they found v = 0.89, if all the levels are counted, and v = 1.13, if the uncertain levels are excluded. One could speculate that inclusion of about half of the uncertain levels would yield the desired value v = 1, which corresponds to an average spacing of about 19.3 eV. Thus, one could favor a value in the range 18.5 to 19.3 eV for use in calculations. 

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