Ground-State Energy Eigenvalues and Eigenfunctions for an Electron in an Electric-Dipole Field

Journal Article · Sat Oct 05 00:00:00 UTC 1968 · Physical Review

DOI: https://doi.org/10.1103/physrev.174.81 · OSTI ID:4842114

Turner, J. E. ^[1]; Anderson, V. E. ^[1]; Fox, Kenneth ^[1]

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1. Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Ground-state energy eigenvalues and eigenfunctions are obtained by a variational method for an electron in the field of a finite, stationary, permanent electric dipole. The dipole moments studied cover the range from the minimum value required for binding (D_min =0.6393 ea₀) to D =400 ea₀, where the system is equivalent to the hydrogen atom perturbed slightly by a distant stationary negative charge. The eigenvalues obtained agree with those reported by Wallis, Herman, and Milnes, who determined them by another method in the range D =0.84ea₀ to 30⁢ea₀. The normalized eigenfunctions display the manner in which the electronic charge density changes from that of the hydrogen atom at very large D to a flat distribution approaching that which is characteristic of a zero-energy continuum state as the minimum moment is approached from above. Optimized variational wave functions for different values of D are presented for use in other calculations. Contour maps and profiles of electronic charge density are shown for a number of values of D. Mean values of the powers -1, 1, and 2 of the distances of the electron from the dipole charges are also calculated.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: US Atomic Energy Commission (AEC)
• Grant/Contract Number: W-7405-ENG-26
• NSA Number: NSA-23-012993
• OSTI ID: 4842114
• Report Number(s): ORNL--4297
• Journal Information: Physical Review, Journal Name: Physical Review Journal Issue: 1 Vol. 174; ISSN 0031-899X
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English