Atomic energy levels and Landé<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>g</mml:mi></mml:math>factors: A theoretical study

Abstract

We have developed a relativistic multichannel theory that can be used to calculate the multichannel quantum-defect theory parameters (${\ensuremath{\mu}}_{\ensuremath{\alpha}}, {U}_{i\ensuremath{\alpha}}$) directly from first principles. With the parameters we can calculate the energy levels and Land\'e $g$ factors of Rydberg series based on the multichannel quantum-defect theory. We have performed calculations of excited states for the Ne atom with major configuration $1{s}^{2}2{s}^{2}2{p}^{5}\mathrm{np}$ in ${J}^{\ensuremath{\pi}}={0}^{+}, {1}^{+}, {2}^{+}, \mathrm{and} {3}^{+}$ symmetry. The results are in good agreement with the experimental data. We have also found that the coupling scheme is dependent on the total angular momentum $J$. The $\mathrm{jl}$-coupling scheme is more suitable than the $\mathrm{jj}$-coupling scheme in describing ${J}^{\ensuremath{\pi}}={1}^{+}$ symmetry, whereas the $\mathrm{jj}$-coupling scheme is more suitable than the $\mathrm{jl}$-coupling scheme for ${J}^{\ensuremath{\pi}}={2}^{+}$ symmetry.