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

• Authors: H. Di Rocco , A. Cruzado
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

32.70.-n; 32.70.Jz

Discipline

• 32.70.Jz: Line shapes, widths, and shifts
• 32.70.-n: Intensities and shapes of atomic spectral lines(see also 31.15.-p Calculations and mathematical techniques)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2012
• Volume: 122
• Issue: 4
• Pages: 670-673

Dates

published

2012-10

received

2011-12-20

(unknown)

2012-03-06

(unknown)

2012-05-24

Contributors

author

H. Di Rocco

• Instituto de Física Arroyo Seco (IFAS), Universidad Nacional del Centro de la Pcia. de Buenos Aires Πnto 399, 7000 Tandil, Buenos Aires, Argentina
• Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) Rivadavia 1917, C1033AAJ Buenos Aires, Argentina

author

A. Cruzado

• Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Paseo del Bosque s/n, 1900 La Plata, Buenos Aires, Argentina
• Instituto de Astrofísica de La Plata (IALP-CONICET), Paseo del Bosque s/n, 1900 La Plata, Buenos Aires, Argentina

References

• [1] H.O. Di Rocco, A. Cruzado, Acta Phys. Pol. A 122, 666 (2012)
• [2] H.O. Di Rocco, D.I. Iriarte, J.A. Pomarico, Appl. Spectrosc. 55, 822 (2001)
• [3] J.L. Kielkopf, J. Opt. Soc. Am. 63, 987 (1973)
• [4] R. Ciurylo, J. Domyslawska, R.S. Trawinski, Acta Phys. Pol. A 83, 425 (1993)
• [5] T. Andersen, J. Quant. Spectrosc. Radiat. Transfer 19, 169 (1978)
• [6] Y. Liu, J. Lin, G. Huang, Y. Guo, C. Duan, J. Opt. Soc. Am. B 18, 666 (2001)

Identifiers

DOI

10.12693/APhysPolA.122.670