THE SPECTRUM OF NEUTRONS SLOWING DOWN NEAR AN INTERFACE

Journal Article · Sun Sep 01 04:00:00 EDT 1963 · Nucl. Energy

OSTI ID:4661175

Lewins, J

A variational principle is written for the continuous slowing-down of neutrons in a scattering and lightly absorbing system where the properties are not uniform. Using the semi-direct method, the partial differential equation is reduced to an ordinary differential equation. To do this, trial functions are assumed, composed of arbitrary mixtures of the neutron spectra appropriate to infinite amounts of each property region. A particular example is treated, consisting of two adjacent semi-infinite regions. The solution to the reduced equation is given explicitly so that the problem degenerates to evaluating weighted or effective coefficients of the region properties, and this can be done by quadratures if necessary. To illustrate typical results, certain further approximations are being made enabling a specific solution to be found in terms of the resonance escape probability and the Fermiage for each region. The method is found to save computation compared to the direct solution of the original partial differential equation, and can be applied to a range of problems where a change of properties produces a spatial variation of the spectrum during slowing- down. (auth)

• Research Organization: Originating Research Org. not identified
• NSA Number: NSA-17-036633
• OSTI ID: 4661175
• Journal Information: Nucl. Energy, Journal Name: Nucl. Energy
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ABSORPTION
CONFIGURATION
DIFFERENTIAL EQUATIONS
FERMI AGE
MATHEMATICS
NEUTRONS
NUMERICALS
PHYSICS
RESONANCE ESCAPE PROBABILITY
SCATTERING
SLOWDOWN
SPECTRA
VARIATIONAL METHOD
VARIATIONS