Potential energy surfaces in atomic structure: The role of Coulomb correlation in the ground state of helium
| Autor: | Salas, L. D., Arce, J. C. |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Physical Review A 95, 022502 (2017) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevA.95.022502 |
| Popis: | 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 Schr\"odinger 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. Comment: 10 pages, 8 figures |
| Databáze: | arXiv |
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