Set of orthogonal polynomials for absorption and scattering problems

Technical Report · Thu Jan 01 04:00:00 EST 1981

OSTI ID:5226818

Zahrt, J D

In the solution of various x-ray absorption and scattering problems one usually encounters multiple integrals with exponential functions in the integrands. The Monte Carlo method can yield solutions, but we have chosen the analytic method of Gaussian quadrature. This method requires the roots of a set of polynomials which are orthogonal over the range of integration. We have developed a set of such polynomials with weight function e/sup -//sup Ax/ (0 less than or equal to x less than or equal to 1). In this report we develop the polynomials, find their roots, compute the necessary weight factors for Gaussian quadrature, and give several examples of application. While better results are obtained with these polynomials than with Legendre polynomials (weight function of 1), they probably will not replace them, because they lack the symmetry of the Legendre polynomials, and they require extra computational machinery.

• Research Organization: Lawrence Livermore National Lab., CA (USA)
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 5226818
• Report Number(s): UCRL-53274; ON: DE82016317
• Country of Publication: United States
• Language: English

Related Subjects

654001* -- Radiation & Shielding Physics-- Radiation Physics
Shielding Calculations & Experiments
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ABSORPTION
ANALYTICAL SOLUTION
ELECTROMAGNETIC RADIATION
FUNCTIONS
IONIZING RADIATIONS
NEUTRAL-PARTICLE TRANSPORT
PHOTON TRANSPORT
POLYNOMIALS
RADIATION TRANSPORT
RADIATIONS
SCATTERING
WEIGHTING FUNCTIONS
X RADIATION