Garrettson, G. and Leonard, A. (1970) Green's functions for multidimensional neutron transport in a slab. Journal of Mathematical Physics, 11 (2). pp. 725740. ISSN 00222488. http://resolver.caltech.edu/CaltechAUTHORS:GARjmp70

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Abstract
The integral form of the onespeed, steadystate Boltzmann transport equation is solved for a point source in a homogeneous, isotropically scattering slab. In addition, solutions are obtained for line sources and plane sources in the slab, both normal and parallel to the slab faces. Using Fuorier and Laplace transforms, the problem is reduced to that of solving a 1dimensional integral equation with a difference kernel. This equation is transformed into a singular integral equation which is solved using standard methods. The Green's functions are subsequently obtained as generalized eigenfunction expansions over the spectrum of the 1dimensional integral operator. This form yields a simple solution far from the source, and alternate expressions are obtained to facilitate evaluation near the source. In a thick slab the exact solutions are shown to reduce to simple closed expressions plus correction terms that decrease exponentially as the slab thickness increases. Most of the work previously done in multidimensional transport in slabs is shown to be easily reproduced using this theory in the thickslab approximation. Also, virtually all other problems of this type can be solved using the theory presented here. In particular, the density from a pencil beam of particles normally incident to the slab is obtained.
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Additional Information:  ©1970 The American Institute of Physics. Received 23 April 1969.  
Group:  GALCIT  
Record Number:  CaltechAUTHORS:GARjmp70  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:GARjmp70  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  12499  
Collection:  CaltechAUTHORS  
Deposited By:  Tony Diaz  
Deposited On:  18 Dec 2008 03:56  
Last Modified:  20 Sep 2016 20:54 
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