RESONANCE ESCAPE PROBABILITY IN SLAB LATTICES

Technical Report · Thu Mar 01 04:00:00 EST 1956

OSTI ID:4311753

Gorngold, N

The slowing down of neutrons in a lattice consisting of alternate slabs of noncapturing moderator and nonmoderating fuel whose cross sections vary arbitrarily with energy is examined. The Boltzmann equation is transformed to an integral equation into which appropriate boundary conditions are incorporated. Expansion of the flux functions in terms of orthogonal polynomials in space and angle coordinates yields an infinite set of coupled integral equations in energy. In the simplest approximation and for a hydrogen moderator, these equations are easily integrated to give an expression for the resonance escape probability identical with the one recently derived---from quite different considerations--- by J. Chernick. It is shown that higher order terms in the equations should contribute little to neutron absorption in those capture resonances that contribute most to the integrated capture probability. Thus, while the simplest approximation is not a good one for determining flux distributions, it will be quite good for determining resonance escape probabilities. Numerical results will be given. It should be added that the method of analysis given herein is quite general and in no way limited to the specific model (nonmoderating fuel,...) which was chosen to facilitate detailed calculation. (auth)

• Research Organization: Brookhaven National Lab., Upton, N.Y.
• NSA Number: NSA-12-005618
• OSTI ID: 4311753
• Report Number(s): BNL-445
• Country of Publication: United States
• Language: English

Related Subjects

ABSORPTION
BOLTZMANN EQUATION
CONFIGURATION
DIFFERENTIAL EQUATIONS
INTEGRAL EQUATIONS
INTEGRALS
MATHEMATICS
NEUTRON FLUX
NEUTRONS
PHYSICS
PLATES
QUANTITATIVE ANALYSIS
REACTORS
RESONANCE ESCAPE PROBABILITY
SLOWDOWN
SURFACES
ZONES