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
Aug 2025
Jan 2025
Latest Journal Issues
Nuclear Science and Engineering
September 2025
Nuclear Technology
Fusion Science and Technology
August 2025
Latest News
Powering the future: How the DOE is fueling nuclear fuel cycle research and development
As global interest in nuclear energy surges, the United States must remain at the forefront of research and development to ensure national energy security, advance nuclear technologies, and promote international cooperation on safety and nonproliferation. A crucial step in achieving this is analyzing how funding and resources are allocated to better understand how to direct future research and development. The Department of Energy has spearheaded this effort by funding hundreds of research projects across the country through the Nuclear Energy University Program (NEUP). This initiative has empowered dozens of universities to collaborate toward a nuclear-friendly future.
D. L. Henderson, C. W. Maynard
Nuclear Science and Engineering | Volume 102 | Number 2 | June 1989 | Pages 172-182
Technical Paper | doi.org/10.13182/NSE89-A23641
Articles are hosted by Taylor and Francis Online.
Time-dependent integral transport equation single-collision kernels for one-dimensional geometries corresponding to the steady-state single-collision kernels found in the available literature have been calculated by making use of the Laplace transform technique, simple geometric transformation relationships, and point kernel integrations. Using the convolution theorem, the time-dependent scalar flux is obtained by convoluting the single-collision kernel with the time-dependent source. Using the multiple collision formulation of the integral transport solution, isotropic sources that are delta distributions in time are considered in several examples. Analytical solutions for the uncollided and first-collided scalar fluxes are obtained for a boundary source having an isotropic angular distribution directed into a semi-infinite medium and into a slab of thickness b and for a point source at the origin of an infinite medium and finite sphere of radius a. A closed form solution is obtained for the simple problem of uniformly distributed sources within an infinite medium.