Energies of the Ground States of He,Li+, andO6+

Abstract

A complete 14-parameter calculation for the ground state of He and similar 10-parameter calculations for the ground states of ${\mathrm{Li}}^{+}$ and ${\mathrm{O}}^{6+}$ have been carried out. In addition, using the four most important of eleven terms, which were tried individually as fifteenth parameters, an 18-parameter calculation for He has been carried out but without minimizing against the scale parameter $k$. Similar 12-parameter calculations were carried out for ${\mathrm{Li}}^{+}$ and ${\mathrm{O}}^{6+}$ using the two most important terms beyond the tenth in the He calculation. As a result, the 18-parameter nonrelativistic ionization potential of He is found to be 198311.4 ${\mathrm{cm}}^{-1\mathrm{}}$. The series of 6, 10, 14, 18 parameter values appears to converge to ${198312.}_3$ ${\mathrm{cm}}^{-1\mathrm{}}$ with an error of less than 2 ${\mathrm{cm}}^{-1\mathrm{}}$. Adding the relativistic corrections yields ${198310.}_4$ ${\mathrm{cm}}^{-1\mathrm{}}$ which agrees to 0.1 ${\mathrm{cm}}^{-1\mathrm{}}$ with the latest experimental value. Considering the uncertainties of the theoretical and experimental values, the magnitude of the Lamb shift of the ground state of He (compared to ${\mathrm{He}}^{+}$) must be less than 3 ${\mathrm{cm}}^{-1\mathrm{}}$ which does not contradict present theoretical estimates. Similar agreements but within wider limits of error are found for the 12-parameter energy values of the ground states of ${\mathrm{Li}}^{+}$ and ${\mathrm{O}}^{6+}$.