Fitted temperature-corrected Compton cross sections for Monte Carlo applications and a sampling distribution
Simple temperature-corrected cross sections, which replace the static Klein-Nishina set in a one-to-one manner, are developed for Monte Carlo applications. The reduced set is obtained from a nonlinear least-squares fit to the exact photon-Maxwellian electron cross sections by using a Klein-Nishina-like formula as the fitting equation. Two parameters are sufficient, and accurate to two decimal places, to explicitly fit the exact cross sections over a range of 0 to 100 keV in electron temperature and 0 to 1 MeV in incident photon energy. Since the fit equations are Klein-Nishina-like, existing Monte Carlo code algorithms using the Klein-Nishina formula can be trivially modified to accommodate corrections for a moving Maxwellian electron background. The simple two parameter scheme and other fits are presented and discussed and comparisons with exact predictions are exhibited. The fits are made to the total photon-Maxwellian electron cross section and the fitting parameters can be consistently used in both the energy conservation equation for photon-electron scattering and the differential cross section, as they are presently sampled in Monte Carlo photonics applications. The fit equations are motivated in a very natural manner by the asymptotic expansion of the exact photon-Maxwellian effective cross-section kernel. A probability distribution is also obtained for the corrected set of equations.
- Research Organization:
- Los Alamos National Laboratory, Los Alamos, NM
- OSTI ID:
- 6298052
- Journal Information:
- Nucl. Sci. Eng.; (United States), Vol. 88:1
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
COMPTON EFFECT
KLEIN-NISHINA FORMULA
ALGORITHMS
ASYMPTOTIC SOLUTIONS
COMPARATIVE EVALUATIONS
CROSS SECTIONS
ELECTRON TEMPERATURE
ELECTRONS
ENERGY CONSERVATION
EQUATIONS
FORECASTING
KEV RANGE
LEAST SQUARE FIT
MEV RANGE 01-10
MONTE CARLO METHOD
NONLINEAR PROBLEMS
PHOTONS
PROBABILITY
SAMPLING
SCATTERING
TEMPERATURE DEPENDENCE
BASIC INTERACTIONS
ELASTIC SCATTERING
ELECTROMAGNETIC INTERACTIONS
ELEMENTARY PARTICLES
ENERGY RANGE
FERMIONS
INTERACTIONS
LEPTONS
MASSLESS PARTICLES
MATHEMATICAL LOGIC
MAXIMUM-LIKELIHOOD FIT
MEV RANGE
NUMERICAL SOLUTION
654001* - Radiation & Shielding Physics- Radiation Physics
Shielding Calculations & Experiments