Electrostatic models of charged hydrogenic chains in a strong magnetic field

A. Escobar

Abstract


Simple one-dimensional electrostatic models of one-(two) electron molecular systems H$_2^{+}$, H$_3^{2+}$, H$_4^{3+}$ and H$_2$, H$_3^{+}$, H$_4^{2+}$ in a strong magnetic field are proposed to estimate the binding-(ionization) energy of the corresponding ground states. The study is carried out in the range of magnetic fieds $B=10^2-10^6\,$ a.u. The models are inspired (and based) on the quasi one-dimensional form of the ground state electronic distribution function which is obtained by precise variational calculations in the Born-Oppenheimer approximation in a non-relativistic framework. It is shown that the models give, for all magnetic fields considered, a very good description of the binding-(ionization) energy of the one-electron molecular systems H$_2^{+}$, H$_3^{2+}$, H$_4^{3+}$, being accurate in $2.5%$, $5%$ and $5%$ respectively, and $15%$ for the two-electron systems H$_3^{+}$, H$_4^{2+}$ ($30%$ for H$_2$) as compared with the corresponding variational calculations.

Keywords


Hydrogenic chains; strong magnetic field; electrostatic models

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REVISTA MEXICANA DE FÍSICA, year 67, issue 1, January-February 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, January 4, 2021.

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