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Assuming that V(x) approximate to (1 - mu) G(1)(x) mu L-1(x) is a very good approximation of the Voigt function, in this work we analytically find mu from mathematical properties of V(x). G(1)(x) and L-1(x) represent a Gaussian and a Lorentzian function, respectively, with the same height and HWHM as V(x), the Voigt function, x being the distance from the function center. In this paper we extend the analysis that we have done in a previous paper, where mu is only a function of a; a being the ratio of the Lorentz width to the Gaussian width. Using one of the differential equation that V(x) satisfies, in the present paper we obtain mu as a function, not only of a, but also of x. Kielkopf first proposed mu(a, x) based on numerical arguments. We find that the Voigt binction calculated with the expression mu(a, x) we have obtained in this paper, deviates from the exact value less than mu(a) does, specially for high vertical bar x vertical bar values.

acta physica polonica. a

The Voigt Profile as a Sum of a Gaussian and a Lorentzian Functions, when the Weight Coefficient Depends on the Widths Ratio and the Independent Variable