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# Accession Number:

## AD0617882

# Title:

## ENERGY-DEPENDENT NEUTRON TRANSPORT THEORY IN PLANE GEOMETRY. III. HALF-RANGE COMPLETENESS AND HALF-SPACE PROBLEMS,

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CALIF

# Report Date:

## 1965-06-01

# Pagination or Media Count:

##
35.0

# Abstract:

## A set of elementary solutions to the energy-dependent Boltzmann equation, which was derived in an earlier paper, is shown to possess a half-range completeness property allowing the exact solution to energy-dependent half-space problems and the reduction of finiteslab problems to rapidly convergent Fredholm equations. Results follow in analogy with Cases work on the one-velocity transport equation except that a system of singular integral equations is encountered, giving rise to the Hilbert problems for matrices. It is shown that the methods of Muskhelishvili and Vekua are applicable to this matrix problem and lead to the consideration of a class of Fredholm equations to obtain the solution. The explicit form the Fredholm equation for the present problem is derived by extending the analysis of the scalar Hilbert problem to the matrix case. Applications of the completeness proof are made to the albedo and Milne problems for a half-space. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#