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.
Explore membership for yourself or for your organization.
Conference Spotlight
Nuclear Energy Conference & Expo (NECX)
September 8–11, 2025
Atlanta, GA|Atlanta Marriott Marquis
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
Jul 2025
Jan 2025
Latest Journal Issues
Nuclear Science and Engineering
August 2025
Nuclear Technology
Fusion Science and Technology
July 2025
Latest News
Spent fuel transfer project completed at INL
Work crews at Idaho National Laboratory have transferred 40 spent nuclear fuel canisters into long-term storage vaults, the Department of Energy’s Office of Environmental Management has reported.
Mark Goldsmith
Nuclear Science and Engineering | Volume 17 | Number 1 | September 1963 | Pages 111-124
Technical Paper | doi.org/10.13182/NSE17-111-124
Articles are hosted by Taylor and Francis Online.
A number of problems in reactor analysis require the determination of the second largest reactor eigenvalue. If one limits himself to a one-velocity description of neutron diffusion, this eigenvalue and the corresponding eigenfunction may be determined by familiar methods. When (as is almost universally the case) one must consider more than one energy group of neutrons, the neutron diffusion equations are no longer self-adjoint and the customary analysis yields information only about the eigenfunction of largest eigenvalue. In the present work the symmetry properties of reactor eigenfunctions have been applied to the calculation of the first few reactor eigenvalues. Each reactor has geometrical symmetry elements that enable one to define what is known as the symmetry group of the reactor, and the transformations of the reactor under the elements of this group enable one to determine the degeneracy and symmetry properties of the reactor eigenfunctions. After a detailed review of the necessary group theoretical fundamentals, the eigenfunctions of a reactor with a trigonal control element are investigated and the adaptation of an existing diffusion theory code to the computation of higher reactor eigenvalues discussed.