Use of Padé Approximations in the Analytical Evaluation of theJ(θ,β) Function and Its Temperature Derivative

Resonance Self-Shielding Corrections for Activation Cross Section Measurements

“…Comparatively recently, a new analytical approximation for the Doppler broadening function ψ(θ, x) have been proposed by Keshavamurthy and Harish, 5) as the imaginary part of the plasma dispersion function Z (t): 11) …”

“…show the results of calculations of the Doppler broadening function ψ(θ, x) using expressions(5),(12) and(13) with parameter θ =0.1, 0.25, 0.5 and 1. These were carried out by means of the three versions 5) of Pade approximations: two 2-pole and one 4-pole versions, shown as Pade 2 (case 1), Pade 2 (case 2) and Pade 4, respectively.…”

The Derivation of the Doppler Broadening Function using Frobenius Method

“…For the purpose of validation of the approximation proposed in this paper for the Doppler broadening function and for comparison to previously published results, as described in papers from Shcherbakov 1) and Keshavamurthy,6) graphs based on the numeric calculation, the 4-poles Padé's By analyzing the obtained data, one can conclude that the percentage errors obtained using Padé's approximation are, except in the interval around x¼0, systematically bigger than the errors obtained using the analytical expression proposed in this paper.…”

An Approximation for the Doppler Broadening Function and Interference Term Using Fourier Series

“…Replacing Equations (8) and (9) in Eq obtains the following expression for the average scatte uation (1) one ring cross section: 9, and the 4-pole Padé method, Equations 4) and (15) onsidering the benchmark results from Gauss-Legendre quadrature method that is well described in the literature [10]. sion that the proposed method proved to be ery precise and stable, having a 0.1% maximum relative er…”