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

Assuming that V (x) ≈ (1 − µ) G₁(x) + µL₁(x) is a very good approximation of the Voigt function, in this work we analytically find µ from mathematical properties of V (x). G₁(x) and L₁(x) represent a Gaussian and a Lorentzian function, respectively, with the same height and HWHM as V (x), the Voigt...

Descripción completa

Detalles Bibliográficos
Autores principales: Di Rocco, Héctor Oscar, Cruzado, Alicia
Formato: Articulo
Lenguaje:Inglés
Publicado: 2012
Materias:
Astronomía
Voigt function
Gaussian function
Lorentzian function
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/128257
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-128257
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Astronomía
Voigt function
Gaussian function
Lorentzian function
spellingShingle Astronomía
Voigt function
Gaussian function
Lorentzian function
Di Rocco, Héctor Oscar
Cruzado, Alicia
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
topic_facet Astronomía
Voigt function
Gaussian function
Lorentzian function
description Assuming that V (x) ≈ (1 − µ) G₁(x) + µL₁(x) is a very good approximation of the Voigt function, in this work we analytically find µ from mathematical properties of V (x). G₁(x) and L₁(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.
format Articulo
Articulo
author Di Rocco, Héctor Oscar
Cruzado, Alicia
author_facet Di Rocco, Héctor Oscar
Cruzado, Alicia
author_sort Di Rocco, Héctor Oscar
title 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
title_short 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
title_full 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
title_fullStr 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
title_full_unstemmed 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
title_sort 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
publishDate 2012
url http://sedici.unlp.edu.ar/handle/10915/128257
work_keys_str_mv AT diroccohectoroscar thevoigtprofileasasumofagaussianandalorentzianfunctionswhentheweightcoefficientdependsonthewidthsratioandtheindependentvariable
AT cruzadoalicia thevoigtprofileasasumofagaussianandalorentzianfunctionswhentheweightcoefficientdependsonthewidthsratioandtheindependentvariable
AT diroccohectoroscar voigtprofileasasumofagaussianandalorentzianfunctionswhentheweightcoefficientdependsonthewidthsratioandtheindependentvariable
AT cruzadoalicia voigtprofileasasumofagaussianandalorentzianfunctionswhentheweightcoefficientdependsonthewidthsratioandtheindependentvariable
bdutipo_str Repositorios
_version_ 1764820452183638017

Ejemplares similares