ANS is committed to advancing, fostering, and promoting the development and application of nuclear sciences and technologies to benefit society.
Explore the many uses for nuclear science and its impact on energy, the environment, healthcare, food, and more.
Division Spotlight
Thermal Hydraulics
The division provides a forum for focused technical dialogue on thermal hydraulic technology in the nuclear industry. Specifically, this will include heat transfer and fluid mechanics involved in the utilization of nuclear energy. It is intended to attract the highest quality of theoretical and experimental work to ANS, including research on basic phenomena and application to nuclear system design.
Meeting Spotlight
International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C 2025)
April 27–30, 2025
Denver, CO|The Westin Denver Downtown
Standards Program
The Standards Committee is responsible for the development and maintenance of voluntary consensus standards that address the design, analysis, and operation of components, systems, and facilities related to the application of nuclear science and technology. Find out What’s New, check out the Standards Store, or Get Involved today!
Latest Magazine Issues
Apr 2025
Jan 2025
Latest Journal Issues
Nuclear Science and Engineering
June 2025
Nuclear Technology
Fusion Science and Technology
May 2025
Latest News
Ariz. governor vetoes “fast track” bill for nuclear
Gov. Katie Hobbs put the brakes on legislation that would have eliminated some of Arizona’s regulations and oversight of small modular reactors, technology that is largely under consideration by data centers and heavy industrial power users.
J. Ligou
Nuclear Science and Engineering | Volume 50 | Number 2 | February 1973 | Pages 135-146
Technical Paper | doi.org/10.13182/NSE73-A23237
Articles are hosted by Taylor and Francis Online.
Polynomial approximations in space are used for solving the integral transport equations for multilayers systems, in one dimensional spherical or cylindrical geometry with scattering anisotropy. These polynomial approximations are applied to the neutron sources (collided neutrons) in each layer, in such a way that the mean quadratic error is a minimum. The form of this approximation allows a less complicated treatment of the anisotropic components of the collided neutron sources than the usual approach (collision probabilities for uniform sources). In order to reduce the number of necessary integral equations when the scattering anisotropy is present, some differential equations relating the spherical harmonics components of the angular flux are used. This is very useful from a numerical point of view, especially when polynomial approximations in space are introduced. A very important link between the scattering anisotropy and the degree of polynomial approximations is also derived. Based on this method the SHADOK code was written. Several numerical examples dealing with multigroup calculations of fast critical assemblies for spherical geometry (FRO-GODIVA-TOPSY-ZPR.43/8) are given. The results show that (a) the large optical dimensions are not a problem for this improved integral method, (b) the scattering.anisotropy (at least PI) does not increase the time of computation, and (c) the heterogeneous systems (reflected cores) can be calculated easily. The calculations with the proposed method are considerably faster than those of the SN method.
