### Abstract

Solutions of the one-group neutron transport equation are provided for point-beam and finite isotropic line sources in a homogeneous 3-D infinite medium with isotropic scattering. The solution is obtained via Fourier transforms and analytical/numerical inversions. The transport equation is cast into a 2-D equivalent form, which can ultimately be put in terms of a 1-D problem, thereby providing analytical leverage. The inversions use standard numerical techniques such as Gauss-Legendre quadrature and summation of infinite series. Even though the solution obtained here uses equivalent forms in fewer dimensions, it does represent a true 3-D analytical benchmark which is useful for both code verification and educational enrichment.

Original language | English (US) |
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Pages (from-to) | 89-111 |

Number of pages | 23 |

Journal | Transport Theory and Statistical Physics |

Volume | 24 |

Issue number | 1-3 |

DOIs | |

State | Published - Jan 1 1995 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Transportation
- Physics and Astronomy(all)
- Applied Mathematics

### Cite this

*Transport Theory and Statistical Physics*,

*24*(1-3), 89-111. https://doi.org/10.1080/00411459508205121