Studies on the Radial Distribution Analysis in Diffraction Methods : I. Errors due to the Approximation of Integration by Summation

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概要

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• In the calculation of a radial distribution function γD(γ) = (1/2π^2)∫^∞_0sI(s)sin sr ds we usually approximate the integral by such a sum as γD_Σ(γ) = (Δs/2π^2)Σ^∞_<n-1>nΔs・I(nΔs)・sin(nΔsr). In this paper the mathematical property of γD_Σ(γ) is derived and the error due to the approximation is proved to be expressed as [numerical formula]. Furthermore, the formula for the estimation of the error is derived. It turned out that in order to obtain a high accuracy from the approximation we must make the spacing Δs less than π/R_0, where R_0 is the distance beyond which γD(γ) is regarded practically zero.

• 社団法人日本物理学会の論文
• 1957-05-05

著者

• Ino Tadashi

  The Institute Of Polytechnics Osaka City University

関連論文

• Studies on the Radial Distribution Analysis in Diffraction Methods : I. Errors due to the Approximation of Integration by Summation

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