Published 1973 | Version v1
Miscellaneous Open

Effects of energy dependent anisotropy of neutron elastic scattering

Creators

  • 1. Institute of nuclear sciences Boris Kidric, Vinca, Beograd (Yugoslavia)

Description

General form of the differential equation was developed for the slowing-down Green function. Energy dependent anisotropy of the elastic scattering was treated. Differential scattering cross section was presented by Legendre polynomial expansion (scattering angular dependence) with energy dependent series expansion coefficients. Scattering function derived from this expansion is given in matrix form as a product of two matrices dependent on incident and scattered neutron energy respectively. This form of scattering function, i.e. matrix degeneration of the kernel of integral slowing-down function enables calculating the Green slowing down function. Differential equation of the Green slowing-down function is solved analytically in case of constant coefficients in the expansion of differential cross section by Legendre polynomials and some special cases of energy dependent anisotropy. In case of arbitrary energy dependence equation is solved numerically by using standard computer codes

Availability note (English)

Available from INIS in electronic form; Also available from the Institute of nuclear sciences Vinca

Abstract (Serbian)

Za slucaj energetski zavisne anizotropije elasticnog rasejanja izveden je opsti oblik diferencijalne jednacine za Greenovu funkciju usporavanja. Pritom je, prvo, diferencijalni presek za rasejanje predstavljen razvojem po Legendreovim polinomima (zavisnost od ugla rasejanja) sa energetski zavisnim koeficijentima razvoja. Drugo, funkcija rasejanja koja se izvodi iz tog razvoja predstavljena je matricno, kao proizvod dve matrice koje zavise od energije upadnog i rasejanog neutrona respektivno. Taj oblik funkcije rasejanja odnosno, matricna degeneracija jezgra integralne jednacine usporavanja omogucuje izvodjenje opsteg oblika diferencijalne jednacine za odredjivanje Greenove funkcije usporavanja. Diferencijalna jednacina Greenove funkcije usporavanja za konstantne koeficijente razvoja diferencijalnog preseka po Legendreovim polinomima i za neke specijalne slucajeve energetski zavisne anizotropije, se resava analitickim metodama; za proizvoljnu zavisnost od energije numericko resavanje je jednostavno koriscenjem standardnih masinskih programa (author)

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Additional details

Additional titles

Original title (Serbian)
Efekti energetski zavisne anizotropije, elasticnog rasejanja neutrona

Publishing Information

Imprint Pagination
13 p.
Report number
INIS-RS--0042

INIS

Country of Publication
Serbia
Country of Input or Organization
Serbia
INIS RN
38013767
Subject category
S73: NUCLEAR PHYSICS AND RADIATION PHYSICS;
Descriptors DEI
ANALYTICAL SOLUTION; ANGULAR DISTRIBUTION; ANISOTROPY; DIFFERENTIAL CROSS SECTIONS; DIFFERENTIAL EQUATIONS; ENERGY DEPENDENCE; GREEN FUNCTION; LEGENDRE POLYNOMIALS; NEUTRON SLOWING-DOWN THEORY; NUMERICAL SOLUTION; SLOWING-DOWN KERNELS
Descriptors DEC
CROSS SECTIONS; DISTRIBUTION; EQUATIONS; FUNCTIONS; MATHEMATICAL SOLUTIONS; POLYNOMIALS

Optional Information

Notes
3 refs
Secondary number(s)
IBK--1192