and H2, 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 mag netic fieds B = 10² - 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 , being accurate in 2.5%, 5% and 5% respectively, and 15% for the two-electron systems (30% for H2) as compared with the corresponding variational calculations.]]>
y H2, en campos magnéticos intensos son propuestos para estimar la energía de amarre-(ionización) del correspondiente estado base. El estudio se lleva a cabo en el rango de campos magnéticos B = 10² 10(6) a.u. Los modelos estan inspirados (y basados) en la forma cuasi-unidimensional de la función de distribución electrónica, del estado base, que se obtiene mediante cálculos variacionales muy precisos realizados en la aproximación de Born-Oppenheimer en un tratamiento no relativista. Se muestra que los modelos brindan, para los campos magnéticos considerados, una muy buena aproximación a la energía de amarre-(ionización) de los sistemas moleculares de un electrón , con una precision relativa del 2.5%, 5% y 5% respectivamente, y con una precisión relativa del 15% para los sistemas moleculares de 2 electrones (30% para H2) comparadas con los cálculos variacionales correspondientes.]]>
Investigación
Electrostatic models of charged hydrogenic chains in a strong magnetic field
A. Escobar
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Circuito Exterior s/n Ciudad Universitaria, México, D.F., 04510, México.
Recibido el 20 de septiembre de 2010 ]]>
Aceptado el 10 de febrero de 2011
Abstract
Simple one–dimensional electrostatic models of one–(two) electron molecular systems and H2, 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 mag netic fieds B = 102 – 106 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 , being accurate in 2.5%, 5% and 5% respectively, and 15% for the two–electron systems (30% for H2) as compared with the corresponding variational calculations.
Keywords: Hydrogenic chains; strong magnetic field; electrostatic models.
Resumen
Modelos electrostáticos unidimensionales simples de los sistemas moleculares de 1–(2) electrones y H2, en campos magnéticos intensos son propuestos para estimar la energía de amarre–(ionización) del correspondiente estado base. El estudio se lleva a cabo en el rango de campos magnéticos B = 102 106 a.u. Los modelos estan inspirados (y basados) en la forma cuasi–unidimensional de la función de distribución electrónica, del estado base, que se obtiene mediante cálculos variacionales muy precisos realizados en la aproximación de Born–Oppenheimer en un tratamiento no relativista. Se muestra que los modelos brindan, para los campos magnéticos considerados, una muy buena aproximación a la energía de amarre–(ionización) de los sistemas moleculares de un electrón , con una precision relativa del 2.5%, 5% y 5% respectivamente, y con una precisión relativa del 15% para los sistemas moleculares de 2 electrones (30% para H2) comparadas con los cálculos variacionales correspondientes.
I am grateful to A.VTurbiner and J.C.L.Vieyra for providing many remarkable insights on the subject of matter in strong magnetic fields and especially to JCLV for his constant interest in this work. AER was supported in part by a CONACyT grant for PhD studies (México).
References
1. B.B. Kadomtsev and VS. Kudryavtsev, Pis'ma ZhETF15 (1971) 61; Sov. Phys. JETP Lett. 13,9 (1971) 42. [ Links ]
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 mag netic fieds B = 10² - 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 
, being accurate in 2.5%, 5% and 5% respectively, and 15% for the two-electron systems 
and H2, 
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 mag netic fieds B = 102 – 106 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