Energies of the ground states of He, Li⁺, and O⁶⁺

Abstract

A complete 14-parameter calculation for the ground state of He and similar 10-parameter calculations for the ground states of Li⁺ and O⁶⁺ 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 Li⁺ and O⁶⁺ 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 cm^-1. The series of 6, 10, 14, 18 parameter values appears to converge to 198312.₃ cm^-1 with an error of less than 2 cm^-1. Adding the relativistic corrections yields 198310.₄ cm^-1 which agrees to 0.1 cm^-1 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 He⁺) must be less than 3 cm^-1 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 Li⁺ and O⁶⁺.