The $1/Z$-expansion for the Coulomb system of infinitely massive center of charge Z and two electrons is discussed. Numerical deficiency in Baker et al, { \em Phys. Rev. \bf A41}, 1247 (1990) is indicated which continue to raise doubts in correctness of their calculations of the higher order coefficients in $1/Z$-expansion expressed in Refs.[4-5]. It is shown that a minor modification of a few first coefficients found in Ref.[3] allows to calculate the ground state energies at $Z\ =\ 1, 2,\ldots \ 10$ (as well as at $Z > 10$) with a portion of 15th decimal digit in comparison with highly accurate calculations by C. Schwartz and by Nakashima-Nakatsuji. Ground state energies of two-electron ions $Z=11\ (Na^{ 9+})$ and $Z=12\ (Mg^{ 10+})$ are found with 14 decimal digits.
Categories: quant-ph physics.atom-ph physics.chem-ph