Theoretical Calculations of thed-,f-, andg-Electron Transition Series

Self-consistent-field calculations of the effective quantum numbers for $\mathrm{nd}$, $\mathrm{nf}$, and $\mathrm{ng}$ electrons for a large number of atomic configurations from $Z=2\mathrm{} \mathrm{to} 126$ have been made using a Hartree plus statistical-exchange method with first-order correlation and relativistic energy corrections. The computed binding energies agree with experimental values where known (67 configurations), with an average deviation of 1.5%. The sudden decreases with increasing $Z$ in the effective quantum numbers of the $d$ and $f$ electrons, which precede the onset of the known transition series, are accurately predicted. An interpretation of these changes in effective quantum number is given in terms of the effective potential. The probable existence of a $7d$, $6f$, or $5g$ transition series beginning at about $Z=122\mathrm{}$ is examined. The computed abrupt decrease in effective quantum number of the $7d$ and $6f$ electrons at $Z=120\mathrm{}$, and of the $5g$ electron at $Z=121\mathrm{}$, indicates the possible participation of all of these electrons in the ground configuration of such elements. Relativistic corrections strongly affect the calculated relative energies of different possible ground configurations of the elements $Z=121\mathrm{} \mathrm{to} 126$.