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

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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 r₁ and r₂, and a conditional amplitude, which depends functionally on the interelectronic distance r₁₂ and parametrically on r₁ and r₂. 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 (r₁,r₂), 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.