
Accession Number : AD0651912
Title : AN APPROACH TO THE BOUNDSTATE THREEBODY PROBLEM WITH APPLICATION TO THE HELIUMLIKE ATOM.
Descriptive Note : Physical sciences research papers no. 317,
Corporate Author : AIR FORCE CAMBRIDGE RESEARCH LABS L G HANSCOM FIELD MASS
Personal Author(s) : Jasperse,J. R.
Report Date : MAR 1967
Pagination or Media Count : 89
Abstract : A technique is presented for treating a general type of threebody boundstate 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 threebody problem in a special form. Some simple onedimensional applications are examined. The first involves deltafunction pairpotentials including an example where one of the pair interactions is repulsive. The second involves the onedimensional problem of three identical spinless particles interacting through attractive, squarewell potentials. The helium atom is discussed from a threebody point of view. Each orbital is expanded into a complete set of twobody Sturmian functions for the Coulomb potential. For states in atomic helium of the form L=0 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 lowlying states of the heliumlike atoms using this method. In particular, results are reported for the 1s1s(1)S, 1s2s(1)S, and 2s2s(1)S states of He, Li(+), and H().
Descriptors : (*ATOMIC ENERGY LEVELS, INTERACTIONS), (*HELIUM, ATOMIC ORBITALS), (*LITHIUM, ATOMIC ORBITALS), (*HYDROGEN, ATOMIC ORBITALS), POTENTIAL THEORY, WAVE FUNCTIONS, INTEGRALS, GREEN'S FUNCTION, SPECIAL FUNCTIONS(MATHEMATICAL), QUANTUM THEORY, FERMIONS
Subject Categories : Atomic and Molecular Physics and Spectroscopy
Quantum Theory and Relativity
Distribution Statement : APPROVED FOR PUBLIC RELEASE