Abstract
A simple approximation scheme to describe the half width of the Voigt profile as a function of the relative contributions of Gaussian and Lorentzian broadening is presented. The proposed approximation scheme is highly accurate and provides an accuracy better than 10−17 for arbitrary αL/αG ratios. In particular, the accuracy reaches an astonishing 10−34 (quadruple precision) in the domain 0 ≤ αL/αG ≤ 0.2371 ∪ αL/αG ≥ 33.8786.
Highlights
We present a simple approximation scheme to describe the half width of the Voigt profile as a function of the relative contributions of Gaussian and Lorentzian broadening
A simple approximation scheme to describe the half width of the Voigt profile as a function of the relative contributions of Gaussian and Lorentzian broadening is presented in this work
The numerical calculations suggest that the proposed approximation scheme can achieve super-accuracy calculation for Voigt profiles for arbitrary αL /αG ratios
Summary
There is no analytically exact expression to describe the HWHM of the Voigt profile as a function of the HWHMs of the Lorentzian and Gaussian profiles, αL and αG , respectively, and many approximations have been presented in the past to find simple relationships, i.e., composed of basic elementary functions only, between αV , αL and αG [13,14,15,16,17]. A highly accurate approximate scheme specially used to evaluate the half width at half maximum of the Voigt profile is urgently needed. We present a simple approximation scheme to describe the half width of the Voigt profile as a function of the relative contributions of Gaussian and Lorentzian broadening.
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