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The $1/Z$-expansion for the Coulomb system of infinitely massive center ofcharge Z and two electrons is discussed. Numerical deficiency in Baker et al,{\em Phys. Rev. \bf A41}, 1247 (1990) is indicated which continue to raisedoubts 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 modificationof a few first coefficients found in Ref.[3] allows to calculate the groundstate energies at $Z\ =\ 1, 2,\ldots \ 10$ (as well as at $Z > 10$) with aportion of 15th decimal digit in comparison with highly accurate calculationsby C. Schwartz and by Nakashima-Nakatsuji. Ground state energies oftwo-electron ions $Z=11\ (Na^{9+})$ and $Z=12\ (Mg^{10+})$ are found with 14decimal digits.

On 1/Z expansion for two-electron systems