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Use of Variational Techniques for the Estimation of Neutron Detection Efficiency

Sheng-Chi Lin, J. C. Robinson, D. L. Selby

Nuclear Science and Engineering

Volume 67 / Number 1 / July 1978 / Pages 61-73


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The Lewins variational functional was employed to formulate approximations to the neutron detection efficiency, which is a parameter required in the measurement of reactivity by the modified source multiplication technique. In particular, a conventional variational method, a variational extrapolation method, a variational interpolation method, and a multi-reference-state variational method were developed for estimating neutron detection efficiency. Results obtained using the various approximate techniques in one and two dimensions were compared with results from exact formulations. The results obtained using the multi-reference-state variational method in all cases and the variational interpolation method in most cases compared very favorably (discrepancies <5%) with results from the exact calculations. The approximate techniques can be cast in a form where very simple calculational capabilities are all that are required to obtain detection efficiency for any given (but arbitrary) subcritical state. Therefore, we conclude that the methodology developed herein would be applicable to on-line applications using minimal computer capabilities.

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