The linear dependence of the term energy on quantum defects in ions with completely filled electron shells and its application for calculating parameters of the smooth nonlocal model potential

The energy levels of the valence electrons of free ions with completely filled electron shells are analyzed. A linear correlation between term energies $E_{nl}$ and quantum defects $dn_{nl}$ is assumed to exist at constant values of orbital quantum numbers and ion charges for the Li, Na, Cu, Ag, and Au rows. The empirical dependence of quantum defects $dn_{nl}$ on the principle quantum number $n$ is found. It can be used to estimate unknown term energies. It is also demonstrated that the linear dependences of the smooth nonlocal model pseudopotential parameter $A_{nl}$ of free ions on the term energy $E_{nl}$ is the result of their linear dependences on quantum defects $dn_{nl}$.