1994 # Momentum-transfer dispersion relations for electron-atom cross sections

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“…For the data contaminated with noise ͑␣ = 0.001͒ the border shrinks, the number of correctly reproduced diffraction poles reduces to two and more poles and zeroes form Froissart doublets (pole-zero pairs mimicking high-frequency noise of the modeled function [16]) in the vicinity of the real axis. For ␣ = 0.05, i.e., the error of about 5% expected to be present in realistic reactive scattering calculations, the border disintegrates into a loose collection of spurious poles and zeroes with only the resonance and the first diffraction poles reproduced with some accuracy.…”

confidence: 97%

“…For the data contaminated with noise ͑␣ = 0.001͒ the border shrinks, the number of correctly reproduced diffraction poles reduces to two and more poles and zeroes form Froissart doublets (pole-zero pairs mimicking high-frequency noise of the modeled function [16]) in the vicinity of the real axis. For ␣ = 0.05, i.e., the error of about 5% expected to be present in realistic reactive scattering calculations, the border disintegrates into a loose collection of spurious poles and zeroes with only the resonance and the first diffraction poles reproduced with some accuracy.…”

confidence: 97%

“…using 2K + 1 values of S͑J +1/2͒, J =0,1,2, ... ,2K to determine pole positions j , zero positions j and the constant C [12,16]. Note that in Eq.…”

confidence: 98%