Logarithmic Terms in the Wave Functions of the2S1and2S3States of Two-Electron Atoms

Following our previous attempt to analyze the convergence rate of variational calculations for the ground state of two-electron atoms, the nonconventional terms $\ln (r_1+r_2)$ and ${\left[\ln \right(r_1+r_2\left)\right]}^2$ were inserted into the $2{}_{}{}^1{}_{}{}^{}S$ and $2{}_{}{}^3{}_{}{}^{}S$ states, with the proper exponentials. The convergence of the energy eigenvalues seems to indicate that logarithmic terms are important in these states also.