Wilson, W.B., Perry, R.T., Shores, E.F., Charlton, W.S., Parish, T.A., Estes, G.P., Brown, T.H., Arthur, E.D., Bozoian, M., England, T.R., et al. (2002) SOURCES4C: A Code for Calculating (α,n), Spontaneous Fission, and Delayed Neutron Sources and Spectra. Proceedings of the American Nuclear Society/Radiation Protection and Shielding Division 12th Biennial Topical Meeting, Santa Fe, NM, 14-18 April 2002.

has been cited by the following article:

• TITLE: Fourth-Order Adjoint Sensitivity Analysis of an OECD/NEA Reactor Physics Benchmark: II. Mathematical Expressions and CPU-Time Comparisons for Computing 4th-Order Sensitivities

  AUTHORS: Dan Gabriel Cacuci, Ruixian Fang

  KEYWORDS: Polyethylene-Reflected Plutonium Sphere, 4th-Order Adjoint Sensitivity Analysis, Microscopic Total Cross Sections

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.11 No.2, May 26, 2021

  ABSTRACT: This work extends to fourth-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. Previous works showed that the third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections are far larger than the corresponding 1st-order and 2nd-order ones, thereby having the largest impact on the uncertainties induced in the PERP benchmark’s response. This finding has motivated the development of the original 4th-order formulas presented in this work, which are valid not only for the PERP benchmark but can also be used for computing the 4th-order sensitivities of response of any nuclear system involving fissionable material and internal or external neutron sources. Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of the largest fourth-order sensitivities of the PERP benchmark’s response to the total microscopic cross sections, and use them for a pioneering fourth-order uncertainty analysis of the PERP benchmark’s response.