Negative hydrogenic ion or D center in a quantum wire

Y. C. Lee, J. F. Jan, and W. Z. Lee
Phys. Rev. B 72, 153303 – Published 3 October 2005

Abstract

The negative hydrogenic ion is not only of physical but also historic importance for it is the first quantum mechanical three-body problem that involves the intrinsic electron-electron correlation. Recent advances in nanotechnology have brought the study of this system in a quantum wire into the forefront. The nonanalytic behaviors of the binding energy ϵb2ndelec of the second electron in a negative hydrogenic ion in one dimension and in a quantum wire (QWR) as a function of the Coulombic repulsive strength γ and the wire radius b are first identified. They are then exploited, together with the recognition of the well-known near-infinite (à la Loudon) binding energy of the neutral hydrogenic atom, to set up a model that calculates ϵb2ndelec in a QWR directly, thereby avoiding the pitfalls of a variational approach to this problem. This ϵb2ndelec, found to be 0.4Ryd, is an exact solution for a wire whose radius is nearly zero. For a finite b, it is shown that still ϵb2ndelec0.4Ryd, which is independent of b as long as 0<baBohr due to the inverse square nature of the Coulomb force. Its comparisons with the corresponding cases in three dimensions and two dimensions is discussed.

  • Figure
  • Received 24 June 2005

DOI:https://doi.org/10.1103/PhysRevB.72.153303

©2005 American Physical Society

Authors & Affiliations

Y. C. Lee, J. F. Jan, and W. Z. Lee

  • Physics Department, State University of New York at Buffalo, Amherst, New York 14260, USA

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Issue

Vol. 72, Iss. 15 — 15 October 2005

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