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
Education, Training & Workforce Development
The Education, Training & Workforce Development Division provides communication among the academic, industrial, and governmental communities through the exchange of views and information on matters related to education, training and workforce development in nuclear and radiological science, engineering, and technology. Industry leaders, education and training professionals, and interested students work together through Society-sponsored meetings and publications, to enrich their professional development, to educate the general public, and to advance nuclear and radiological science and engineering.
Meeting Spotlight
2025 ANS Annual Conference
June 15–18, 2025
Chicago, IL|Chicago Marriott 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
Jun 2025
Jan 2025
Latest Journal Issues
Nuclear Science and Engineering
July 2025
Nuclear Technology
Fusion Science and Technology
Latest News
Smarter waste strategies: Helping deliver on the promise of advanced nuclear
At COP28, held in Dubai in 2023, a clear consensus emerged: Nuclear energy must be a cornerstone of the global clean energy transition. With electricity demand projected to soar as we decarbonize not just power but also industry, transport, and heat, the case for new nuclear is compelling. More than 20 countries committed to tripling global nuclear capacity by 2050. In the United States alone, the Department of Energy forecasts that the country’s current nuclear capacity could more than triple, adding 200 GW of new nuclear to the existing 95 GW by mid-century.
Manoj K. Prasad, Neal J. Snyderman
Nuclear Science and Engineering | Volume 172 | Number 3 | November 2012 | Pages 300-326
Technical Paper | doi.org/10.13182/NSE11-86
Articles are hosted by Taylor and Francis Online.
The neutron counting probability distribution for a multiplying medium was shown by Hage and Cifarelli to be a generalized Poisson distribution that depends on the fission chain number distribution. An analytic formula is obtained for this number distribution, the probability to produce a number of neutrons in a fission chain. The formula depends on the probability that a fission spectrum neutron induces a subsequent fission and depends on the probability distribution for a specific number of neutrons to be produced in an individual induced fission. The formula is an exact solution to a functional equation due to Böhnel for the probability generating function. The Böhnel equation is derived as the t [right arrow] limit of a rate equation for a neutron population generating function, related to a rate equation studied by Feynman. The Böhnel equation is also shown to be a fixed point of an iteration problem, related to one studied by Hawkins and Ulam, where the iteration generates the chain a generation at a time. The discrete iteration problem is shown to be connected to the continuous time evolution of the chain. An explicit solution for the time evolution of the chain is given in the simplified approximation where at most two neutrons are created by an induced fission. The t [right arrow] limit of this equation gives a simple analytic expression for the solution to the Böhnel equation in this approximation. A generalized Poisson counting distribution constructed from the theoretical fission chain probability number distribution is compared to experimental data for a multiplying Pu sample.
