Energies of doubly excited two-electron atoms from interdimensional degeneracies

Abstract

For a two-electron atom, many D=3 states have the same energies as D=5 states of lower angular momentum. Thus the energies of $^{3}$${\mathit{P}}^{\mathit{e}}$, $^{1}$${\mathit{P}}^{\mathit{e}}$, $^{3}$${\mathit{D}}^{\mathit{o}}$, and $^{1}$${\mathit{D}}^{\mathit{o}}$ states for D=3 are respectively identical to those for $^{1}$${\mathit{S}}^{\mathit{e}}$, $^{3}$${\mathit{S}}^{\mathit{e}}$, $^{1}$${\mathit{P}}^{\mathit{o}}$, and $^{3}$${\mathit{P}}^{\mathit{o}}$ states at D=5. We exploit these interdimensional degeneracies to obtain accurate energies for doubly excited 2pnp ${\mathit{P}}^{\mathit{e}}$ states of helium at D=3, with n=2--6, by calculating energy eigenvalues for the singly excited 1s(n-1)s ${\mathit{S}}^{\mathit{e}}$ states at D=5. We also illustrate how some qualitative aspects of double-excitation spectra can be elucidated in terms of interdimensional degeneracies.