Dimensional perturbation theory for the two-electron atom
Perturbation theory in delta = 1/D, where D is the dimensionality of space, is applied to the two-electron atom. In Chapter 1 an efficient procedure for calculating the coefficients of the perturbation series for the ground-state energy is developed using recursion relations between the moments of the coordinate operators. Results through tenth order are presented. The series is divergent, but Pade summation gives results comparable in accuracy to the best configuration-interaction calculations. The singularity structure of the Pade approximants confirms the hypothesis that the energy as a function of delta has an infinite sequence of poles on the negative real axis that approaches an essential singularity at delta = O. The essential singularity causes the divergence of the perturbation series. There are also two poles at delta = 1 that slow the asymptotic convergence of the low-order terms. In Chapter 2, various techniques are demonstrated for removing the effect of these poles, and accurate results are thereby obtained, even at very low order. In Chapter 3, the large D limit of the correlation energy (CE) is investigated. In the limit D ..-->.. infinity it is only 35% smaller than at D = 3. It can be made to vanish in the limit by modifying the Hartree-Fock (HF) wavefunction. In Chapter 4, perturbation theory is applied to the Hooke's-law model of the atom. Prospects for treating more-complicated systems are briefly discussed.
- Research Organization:
- Harvard Univ., Boston, MA (USA)
- OSTI ID:
- 5376093
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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