FINITE-ELEMENT CALCULATIONS FOR THE S-STATES OF HELIUM

The finite-element method provides a convenient and accurate procedure for the calculation of the expectation values of quantum observable. We calculated energies, wave functions, and expectation values of r1n for n = -1, 1, and 2, and of pidelta(r1) for the singlet n 1S and triplet n 3S states (n = 1,2,3,4) of helium. In contrast to the standard methods with globally defined basis functions, the accuracy of the expectation values of physical observable is comparable to the accuracy of the eigenvalues. The results are-reported here and compared with those of Baker et al. [Relativistic, Quantum Electrodynamic, and Weak Interaction Effects in Atoms, edited by Walter Johnson, Peter Mohr, and Joseph Sucher, AIP Conf. Proc. No. 189 (AIP, New York, 1989); Phys. Rev. A 41, 1247 (1990)], Drake [Nucl. Instrum. Methods Phys. Res. B 31, 7 (1988)], Pekeris [Phys. Rev. 115, 1216 (1959)], Accad et al. [Phys. Rev. A 4, 516 (1971)], and Haftel and Mandelzweig [Phys. Rev. A 38, 5995 (1988)].