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 |

H.O. Di Rocco
^{a,b} and A. Cruzado^{c,d}^{a}Instituto de Física Arroyo Seco (IFAS), Universidad Nacional del Centro de la Pcia. de Buenos Aires, Pinto 399, 7000 Tandil, Buenos Aires, Argentina
^{b}Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Rivadavia 1917, C1033AAJ Buenos Aires, Argentina
^{c}Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Paseo del Bosque s/n, 1900 La Plata, Buenos Aires, Argentina
^{d}Instituto de Astrofísica de La Plata (IALP-CONICET), Paseo del Bosque s/n, 1900 La Plata, Buenos Aires, Argentina |

Received: December 20, 2011; revised version March 6, 2012; in final form May 24, 2012 |

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Assuming that V(x) ≈ (1 - μ) G_{1} (x) + μ L_{1} (x) is a very good approximation of the Voigt function, in this work we analytically find μ 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 μ 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 μ as a function, not only of a, but also of x. Kielkopf first proposed μ (a, x) based on numerical arguments. We find that the Voigt function calculated with the expression μ (a, x) we have obtained in this paper, deviates from the exact value less than μ(a) does, specially for high |x| values. |

DOI: 10.12693/APhysPolA.122.670 PACS numbers: 32.70.-n, 32.70.Jz |