Excitation Energies of 1s² ns (6≤n≤9) States for Lithium-Like Systems from Z=11 to 20

The non-relativistic energies of 1s² ns (6≤n≤9) states for the lithium-like systems from Z = 11 to 20 are calculated by using a full-core-plus-correlation (FCPC) method. The relativistic and mass-polarization effects on the energy are calculated by the first-order perturbation corrections. The correction from the quantum-electrodynamics effect is also included using effective nuclear charge. Based on these results and the quantum defect theory, the quantum defects of 1s² ns series for these ions, as a function of energy, are determined. The comparisons between the ionization potentials for 1s² ns states (6≤n≤9) obtained by the FCPC method and the semi-empirical method are carried out. The results show that their agreement is very well and the energies of all discrete states (n≥10) below the ionization threshold of this series for the ions can be predicted by using their quantum defects.