Effects induced by nuclear motion on the ground state energies of Helium and 1s-Helium isoelectronic series from Lithium to Xenon

The non-relativistic energy magnitudes for the ground state of He and He isoelectronic series with atomic number Z = 3 ÷ 54, are calculated. Calculations are performed using an explicitly correlated trial wave-functions of the generalized Hylleraas type. We have developed a variational procedure that allows solving the two-particle Schroedinger equation for a practically unlimited number of parameters in a series of trial wave-functions along the positive degrees of Hylleraas coordinates. Non-conventional optimization methods are developed and particularly applied nonlinear programming is used to solve the problem. The contributions to the energy for various parameters is analyzed. The so-called mass-corrections and mass-polarizations to the non-relativistic energy is also studied. The obtained results are compared to existing experimental data and available data given by other authors. One should note that up to now such data have been computed only for atomic numbers Z = 2 ÷ 12. Behavior of the ground state energy versus Z, the effects of mass corrections and mass polarizations, as well as the contribution of these effects in formation of the electron system energies, are investigated.