Nonvariational calculation of the relativistic, finite-size, and QED corrections for the 2 (1)S excited state of the helium atom.

Abstract

Relativistic and QED corrections are calculated by using a direct solution of the Schroedinger equation for the 2 [sup 1][ital S] excited state of the helium atom obtained with the correlation-function hyperspherical-harmonic method. Our extremely accurate nonvariational results for relativistic, QED, and finite-size corrections coincide exactly (up to 0.000 03 cm[sup [minus]1]) with the values obtained in precision variational calculations of Drake [Nucl. Instrum. Methods Phys. Res. B 5, 2207 (1988)] and Baker, Hill, and Morgan [in [ital Relativistic], [ital Quantum] [ital Electrodynamic] [ital and] [ital Weak] [ital Interaction] [ital Effects] [ital in] [ital Atoms], edited by Walter Johnson, Peter Mohr, and Joseph Sucher, AIP Conf. Proc. No. 189 (AIP, New York, 1989), p. 123] for both infinite and finite nuclear masses. This confirms that a discrepancy of 0.0033 cm[sup [minus]1] between theory and experiment is not a result of an inaccuracy of variational wave functions, but is rooted in our inadequate knowledge of the QED operators. A better understanding of the different QED contributions to the operators (such as, for example, a more precise estimate of the Bethe logarithm) is therefore needed to explain the discrepancy.