Two‐electron atoms near the one‐dimensional limit
| Autor: | D. J. Doren, D. R. Herschbach |
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| Rok vydání: | 1987 |
| Předmět: | |
| Zdroj: | The Journal of Chemical Physics. 87:433-442 |
| ISSN: | 1089-7690 0021-9606 |
| DOI: | 10.1063/1.453588 |
| Popis: | If the Hamiltonian of a two‐electron atom is generalized in a natural way to arbitrary spatial dimension D, an especially simple case is found in the D=1 limit. While the ground state energy is singular at this point, a scaling argument reduces the problem to a limiting Hamiltonian with only two degrees of freedom in which the Coulombic potentials all reduce to δ functions. Since the singularity at D=1 dominates the energy at nearby dimensions, this limit forms the basis for an expansion in (D−1)/D which is reasonably accurate at D=3. By combining results from this expansion with the 1/D expansion about the D→∞ limit, estimates of the energy at D=3 are obtained with accuracy orders of magnitude better than that of either series alone. The simplicity of the D=1 and large‐D limits and the accuracy of this method allow some qualitative insight into the physical features contributing to correlation effects in small atoms. Analysis of other singularities suggests that the 1/D series has zero radius of converge... |
| Databáze: | OpenAIRE |
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