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
NRC approves V.C. Summer’s second license renewal
Dominion Energy’s V.C. Summer nuclear power plant, in Jenkinsville, S.C., has been authorized to operate for 80 years, until August 2062, following the renewal of its operating license by the Nuclear Regulatory Commission for a second time.
S. B. Degweker, Imre Pázsit
Nuclear Science and Engineering | Volume 168 | Number 3 | July 2011 | Pages 248-264
Technical Paper | doi.org/10.13182/NSE10-08
Articles are hosted by Taylor and Francis Online.
Invariant imbedding theory is an alternative formulation of particle transport theory. Until very recently, this theory was used only for deterministic calculations, i.e., for calculations of the first moment of the particle distribution. In a previous paper we set up a probability balance equation in the invariant imbedding approach. An equation was also obtained for the probability generating functional (pgfl) of reflected particles from which equations for the first- and second-order densities were derived. The approach was illustrated by a simple forward-backward scattering model with and without incorporating energy dependence to describe sputtering due to an external source of energetic particles on a medium. In this paper we extend these results to the case of a distributed internal source of particles. Among the possible applications, we discuss the problem of internal sputtering. We derive equations for the pgfl and the first- and second-order densities and show their connection with the external source problem. We treat the finite slab problem in addition to the semi-infinite slab geometry considered in our previous paper.