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The total energies and various bound state properties of the excited $2^1S(L= 0)-$states in two-electron helium atoms, including the ${}^{\infty}$He,${}^4$He and ${}^3$He atoms, are determined to very high numerical accuracy.The convergence of the results obtained for some electron-nuclear andelectron-electron expectation values and, in particular, for theelectron-nuclear and electron-electron cusp values, is discussed. The fieldcomponent of the isotope shift and lowest order QED correction are estimatedfor the $2^1S(L = 0)-$states in the ${}^4$He and ${}^3$He atoms. We also applyour highly accurate methods to numerical computations of the excited$n^1S-$states (for $n$ = 3 and 4) in two-electron atomic systems.

On highly accurate calculations of the excited $n^1S(L = 0)-$states in helium atoms