Twenty-Parameter Eigenfunctions and Energy Values of the Ground States of He and He-Like Ions

Abstract

The nonrelativistic energies of the ground states of ${\mathrm{H}}^{\ensuremath{-}}$, He, ${\mathrm{Li}}^{+}$, ${\mathrm{B}}^{+++}$, ${\mathrm{O}}^{6+}$, ${\mathrm{Ne}}^{8+}$, ${\mathrm{Mg}}^{10+}$ have been calculated by using 20-parameter Hylleraas functions. The coefficients of these functions are listed. The correction due to the motion of the nucleus (mass polarization correction) has been calculated on the basis of these 20-parameter functions. Except for He this correction is found to be quite different from earlier values in the literature. The present status of the problem of the Lamb shift of the ground state of He is briefly discussed.