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

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