Continued fraction approximations to the temperature integral

C. Gutiérrez-Tapia, H. Flores-Llamas

Abstract


The simplest phenomenological model describing thermoluminescence becomes the one-trap-one recombination center model (OTOR). As it is known, the
analysis of thermoluminescence data greatly benefits from separation of a glow
curve into separate glow peaks. The shape of the peaks in thermoluminescence
dosimetry can be represented by the so-called temperature integral. The highly important and close relation between the complementary incomplete gamma function $\Gamma(a,z)$ and the temperature integral in thermoluminescence dosimetry has engaged specialists to pursue a more accurate calculation of $\Gamma(a,z)$. In this work, new approximations for the temperature integral, considering the fast convergence of continued fractions and the straightforward evaluation of the algebraic expressions are obtained. The new reported approximants improve the calculation efficiency of the temperature integral. The simplicity or precision of resent approximations, have a strong effect on values of physical quantities obtained from thermoluminescence data.

Keywords


Complementary incomplete gamma function; continued fractions; temperature integral; approximation

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REVISTA MEXICANA DE FÍSICA, year 67, issue 2, March-April 2021. Bimonthly Journal published by Sociedad Mexicana de Física, A. C. Departamento de Física, 2º Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Apartado Postal 70-348. Tel. (+52)55-5622-4946, https://rmf.smf.mx/ojs/rmf, e-mail: rmf@ciencias.unam.mx. Chief Editor: José Alejandro Ayala Mercado. INDAUTOR Certificate of Reserve: 04-2019-080216404400-203, ISSN: 2683-2224 (on line), 0035-001X (print), both granted by Instituto Nacional del Derecho de Autor. Responsible for the last update of this issue, Technical Staff of Sociedad Mexicana de Física, A. C., Fís. Efraín Garrido Román, 2º. Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Date of last modification, March 1st., 2021.

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