Singly and doubly excited states of the D-dimensional helium atom

Large-order dimensional perturbation theory has proven to be a useful technique for the study of ground and excited states of two-electron atoms. The authors use the 1/D expansion for L = O wave functions to elucidate the evolution between the harmonic (large-D) and physical wave functions, including the transition of the large dimension molecular structure to that of a singly excited state at D = 3. This study is extended to higher angular momentum states by exploiting both approximate and exact interdimensional degeneracies with the S-wave states. They also discuss the relationship between the approximate large dimension quantum numbers introduced by dimensional perturbation theory and the approximate quantum numbers for doubly excited states in three dimensions introduced by Herrick, Lin, Briggs and others