Point model equations for neutron correlation counting: Extension of Böhnel's equations to any order
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
In this study, various methods of autocorrelation neutron analysis may be used to extract information about a measurement item containing spontaneously fissioning material. The two predominant approaches being the time correlation analysis (that make use of a coincidence gate) methods of multiplicity shift register logic and Feynman sampling. The common feature is that the correlated nature of the pulse train can be described by a vector of reduced factorial multiplet rates. We call these singlets, doublets, triplets etc. Within the point reactor model the multiplet rates may be related to the properties of the item, the parameters of the detector, and basic nuclear data constants by a series of coupled algebraic equations – the so called point model equations. Solving, or inverting, the point model equations using experimental calibration model parameters is how assays of unknown items is performed. Currently only the first three multiplets are routinely used. In this work we develop the point model equations to higher order multiplets using the probability generating functions approach combined with the general derivative chain rule, the so called Faà di Bruno Formula. Explicit expression up to 5th order are provided, as well the general iterative formula to calculate any order. Finally, this work represents the first necessary step towards determining if higher order multiplets can add value to nondestructive measurement practice for nuclear materials control and accountancy.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- Grant/Contract Number:
- AC52-06NA25396; AC05-00OR22725
- OSTI ID:
- 1236715
- Alternate ID(s):
- OSTI ID: 1247229; OSTI ID: 1341538
- Report Number(s):
- LA-UR-15-23503; PII: S0168900215007548
- Journal Information:
- Nuclear Instruments and Methods in Physics Research. Section A, Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 795, Issue C; ISSN 0168-9002
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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