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Green's Functions for the One‐Speed Transport Equation in Spherical Geometry

### Abstract

Several problems in one‐speed neutron transport theory for spherically symmetrical systems are discussed. The singular eigenfunction expansion technique is used to construct a solution for a specific finite‐slab Green's function. This slab solution is then used to construct the finite‐medium spherical Green's function by extending the point‐to‐plane transformation concept. For the general case, the expansion coefficients are shown to obey a Fredholm equation, and first‐order solutions are obtained; however, in the infinite‐medium limit the solution is represented in closed form. In addition, the solution for the angular density in an infinite‐medium due to an isotropic point source is developed directly from the set of normal modes of the transportequation. A proof that the result so obtained obeys the proper source condition at the origin is given.

© 1968 The American Institute of Physics

Received 04 May 1967
Published online 28 October 2003