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Title
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Analytic structure of ground-state energies and wave functions for the inhomogeneous electron liquid in non-relativistic He-like atomic ions with nuclear charge Ze
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Author
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Abstract
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| The ground state of the He atom for fixed nucleus remains intractable so far as regards exact analytic solutions. However, some important results already exist pertaining to its ground-state wave function Psi and corresponding electron density n(r). Here, we extend the existing studies by focussing attention on the non-relativistic series of He-like atomic ions with nuclear charge Z. We then find it instructive to start from the energy E(Z) of such a two-electron spin-compensated problem. This is known to have non-analytic behaviour at a critical Z, say Z(c), equal to 0.911028. A form of Darboux transformation going back at very least to Brandas and Goscinski [E. Brandas and O. Goscinski, Int. J. Quantum Chem. 6, 59 (1972)] is refined somewhat here, and compared with a more intuitive approach of Callan [E. Callan, Int. J. Quantum Chem. 6, 431 (1972)]. The important 1/Z expansion of E(Z) is also invoked. The electron density n(r) and the ground-state wave function Psi are then treated in turn, in a related manner; especially their asymptotic behaviour far from the nucleus. Finally, two exact wave functions for analytically solvable two-Fermion models are shown to sum the infinite series proposed by Fock [V. Fock, Izv. Akad. Nauk SSSR, Ser. Fiz. 18, 161 (1954)]. |
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Language
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English
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Source (journal)
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Physics and chemistry of liquids. - London
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Publication
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London
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2012
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ISSN
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0031-9104
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DOI
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10.1080/00319104.2011.644992
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Volume/pages
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50
:3
(2012)
, p. 389-398
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ISI
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000304271500010
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Full text (Publisher's DOI)
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