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A Simple Analytical Approximation to an Inhomogeneously-Broadened Dispersion Spectrum. Application to Absorption-Dispersion Admixtures

Authors
  • Bales, Barney L.1
  • 1 California State University at Northridge, Department of Physics and Astronomy, Northridge, CA, 91330, USA , Northridge (United States)
Type
Published Article
Journal
Cell Biochemistry and Biophysics
Publisher
Springer-Verlag
Publication Date
Sep 19, 2016
Volume
75
Issue
2
Pages
171–184
Identifiers
DOI: 10.1007/s12013-016-0760-7
Source
Springer Nature
Keywords
License
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Abstract

A simple analytical approximation to an inhomogeneously-broadened dispersion signal is proposed and tested with resonance lines broadened by unresolved hyperfine structure. Spectral parameters may be rapidly and accurately extracted using a nonlinear least-squares fitting algorithm. Combining the new approximation to a dispersion signal with a well-known approximation to the absorption signal allows dispersion-absorption admixtures, a problem of growing importance, to be analyzed quickly and accurately. For pure dispersion signals, the maximum difference between the fit and the signal for unresolved lines is 1.1 % of the maximum intensity. For pure absorption, the difference is 0.33 % of the peak-to-peak intensity, and for admixtures up to 40 % dispersion (maximum intensity/peak-to-peak intensity), the difference is 0.7 %. The accuracy of the recovered spectral parameters depends on the degree of inhomogeneously-broadened and the percentage admixture, but they are generally about 1 % at most. A significant finding of the work is that the parameters pertinent to the dispersion or the absorption are insignificantly different when fitting isolated lines vs. fitting admixtures. Admixtures with added noise or an unsuspected extraneous line are investigated.

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