Energy Levels of a Helium Atom

D. T. Aznabayev^{a, b}, A. K. Bekbaev^{a, b}, I. S. Ishmukhamedov^{a, b}, and V. I. Korobov^a

^aJoint Institute for Nuclear Research, Dubna, Moscow oblast, 141980 Russia

^bAl-Farabi Kazakh National University, Almaty, 050038 Kazakhstan

e-mail: aznabaev@theor.jinr.ru

Abstract—The nonrelativistic ionization energy levels of a helium atom are calculated for S, P, and D states.
The calculations are based on the variational method of “exponential” expansion. The convergence of the cal-
culated energy levels is studied as a function of the number of basis functions (N). This allows us to claim that
the obtained energy values (including the values for the states with a nonzero angular momentum) are accurate
to 20 significant digits.

DOI: 10.1134/S1547477115050040

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