Finite-element calculations for the helium atom

We give the explicit form of the Hylleraas-Breit transform in the current paper and apply it to fixed-nucleus problems of heliumlike ions. Employing the relation between the total angular momentum and the Hamilton, the six-dimensional Schrodinger equation is transferred into three-dimensional systems of equations. We use the Lagrange finite-element method to obtain numerical solutions for some low-lying S, 1s2p P-3, and Is3d D-3 states of the helium atom. The relative errors of our approximate energies are: O(10(-8)) a.u. for S states, O(10(-7)) a.u. for Is2p P-3 state and O(10(-5)) a.u. for 1s3d D-3 state. (C) 2003 Wiley Periodicals, Inc.Chemistry, PhysicalMathematics, Interdisciplinary ApplicationsPhysics, Atomic, Molecular & ChemicalSCI(E)EI3ARTICLE1659-6699