Potential energy surfaces in atomic structure: The role of Coulomb correlation in the ground state of helium

Abstract

For the $S$ states of two-electron atoms, we introduce an exact and unique factorization of the internal eigenfunction in terms of a marginal amplitude, which depends functionally on the electron-nucleus distances $r_1$ and $r_2$, and a conditional amplitude, which depends functionally on the interelectronic distance $r_{12}$ and parametrically on $r_1$ and $r_2$. Applying the variational principle, we derive pseudoeigenvalue equations for these two amplitudes, which cast the internal Schrödinger equation in a form akin to the Born-Oppenheimer separation of nuclear and electronic degrees of freedom in molecules. The marginal equation involves an effective radial Hamiltonian, which contains a nonadiabatic potential energy surface that takes into account all interparticle correlations in an averaged way, and whose unique eigenvalue is the internal energy. At each point $(r_1,r_2)$, such surface is, in turn, the unique eigenvalue in the conditional equation. Employing the ground state of He as prototype, we show that the nonadiabatic potential energy surface affords a molecularlike interpretation of the structure of the atom, and aids in the analysis of energetic and spatial aspects of the Coulomb correlation, in particular correlation-induced symmetry breaking and quantum phase transition.

arXiv comment10 pages, 8 figures

References in corpus (6)

• Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction
• Effects of symmetry breaking in finite quantum systems
• On the Quantum Theory of Molecules
• Roto-vibrational spectrum and Wigner crystallization in two-electron parabolic quantum dots
• On Factorization of Molecular Wavefunctions
• Unification of the conditional probability and semiclassical interpretations for the problem of time in quantum theory

Cited by in corpus (2)

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