Interpolation of Resonance Integrals

Equivalence principles reduce the lattice resonance integral of an absorber to I(σ), a resonance integral of the absorber in a homogeneous mixture with hydrogen, where σ is a microscopic cross section determined by the equivalence approximation. In practice, usually I(σ) is not a densely tabulated function; therefore, the need for an adequate σ interpolation arises. Two such interpolation schemes are found to be inaccurate for high and/or low σ values: the WIMS code interpolation , where a and b are determined from two tabulation entries I(σ₂), I(σ₂), and the 1DX code interpolation 1(σ) = I(∞) × (1 + A{tanh[B ln(σ) + C] − 1}), where A, B, and C are determined from three tabulation entries. The interpolation I(σ) = I(∞)[σ/(σ + η)]^P is found to be accurate for all σ values. The determination of p and η involves solving a transcendental equation. An efficient technique for obtaining a numerical solution to the equation is given. In practice, the solution of the equation on a computer is virtually instantaneous.