AN APPROACH TO THE BOUND-STATE THREE-BODY PROBLEM WITH APPLICATION TO THE HELIUM-LIKE ATOM.
Physical sciences research papers no. 317,
AIR FORCE CAMBRIDGE RESEARCH LABS L G HANSCOM FIELD MASS
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A technique is presented for treating a general type of three-body bound-state problem for situations where the interaction may be written as the sum of three pair potentials. The method is based on the work of Eyges and consists of writing the total wavefunction for the three-body problem in a special form. Some simple one-dimensional applications are examined. The first involves delta-function pair-potentials including an example where one of the pair interactions is repulsive. The second involves the one-dimensional problem of three identical spinless particles interacting through attractive, square-well potentials. The helium atom is discussed from a three-body point of view. Each orbital is expanded into a complete set of two-body Sturmian functions for the Coulomb potential. For states in atomic helium of the form L0 the equations assume a simplified form. For these states, the infinite set of integral equations generated by the expansion is truncated at several orders and solved numerically. Rapid convergence is demonstrated for low-lying states of the helium-like atoms using this method. In particular, results are reported for the 1s1s1S, 1s2s1S, and 2s2s1S states of He, Li, and H-.
- Atomic and Molecular Physics and Spectroscopy
- Quantum Theory and Relativity