Low and high Z asymptotics along atomic isoelectronic sequences: configurations with npn′p open shells. (18th February 2019) - Katriel, Jacob
Abstract: The energy levels corrresponding to configurations that involve two p electrons outside a closed shell, or outside a closed shell plus an additional s -type electron, are revisited. The six levels that arise for two inequivalent p orbitals outside a closed shell can be split into two triples, 3 P < 1 D < 1 S and 1 P < 3 D < 3 S, to be referred to as normal and inverted, respectively. While the weighted average energy of the normal triple is higher than that of the inverted triple, they sometimes (but not always) intertwine, i.e. 3 S > 3 P . Examining the relative ordering of the latter two states along isoelectronic sequences, they are (sometimes) found to depend on the nuclear charge, Z . For equivalent p electrons only the normal triple is allowed by the Pauli principle. Effects of configurations that, neglecting relativistic effects, are asymptotically degenerate at 1 Z → 0, when present, are systematically examined. At the low Z end of the isoelectronic sequence a critical charge, Z c, is approached at which the binding energy of the outermost electron vanishes. For an open shell with two inequivalent p electrons it was shown that Z c = N − 1, where N is the total number of electrons. The quantum defects of the outermost p electron in the various states formed out of such configurations have been examined, confirming an asymptotic integrality conjecture, lim Z → N − 1 δ np = N p, where N p is the number of occupied or partly occupied p orbitals in the remaining N − 1 electron system. For pairs of states belonging to a common configuration, whose difference of energies is Δ E, we consider the ratio Δ E Z 2 versus Z, that typically obtains a maximum at some Z > N − 1 . Below this maximum the interelectronic repulsion is higher in the lower energy state, since − Z 3 ∂ ∂ Z Δ E Z 2 is equal to the difference between these interelectronic repulsions. A common thread of the treatment of the various issues considered is the anchoring of our analyses in the asymptotic behaviour of the features considered as Z → ∞ and as Z → Z c .