Benchmarking the invariant embedding method against analytical solutions in model transport problems
Journal article, 2006

The purpose of this paper is to demonstrate the use of the invariant embedding method in a few model transport problems, for which it is also possible to obtain an analytical solution. The use of the method is demonstrated in three different areas. The first is the calculation of the energy spectrum of sputtered particles from a scattering medium without absorption, where the multiplication (particle cascade) is generated by recoil production. Both constant and energy dependent cross sections with a power law dependence were treated. The second application concerns the calculation of the path length distribution of reflected particles from a medium without multiplication. This is a relatively novel application, since the embedding equations do not resolve the depth variable. The third application concerns the demonstration that solutions in an infinite medium and in a half-space are interrelated through embedding-like integral equations, by the solution of which the flux reflected from a half-space can be reconstructed from solutions in an infinite medium or vice versa. In all cases the invariant embedding method proved to be robust, fast and monotonically converging to the exact solutions.

path length distribution

analytical solutions


transport theory.

reflected flux

Invariant embedding


Malin Wahlberg

Chalmers, Applied Physics, Nuclear Engineering

Imre Pazsit

Chalmers, Applied Physics, Nuclear Engineering

Nuclear Technology and Radiation Protection

1451-3994 (ISSN)

Vol. 21 2 3 - 13

Subject Categories

Atom and Molecular Physics and Optics

Other Physics Topics

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