Regular series of doubly excited states inside two-electron continua: Application to $2s^2$-hole states in neon above the Ne${}^{2+}\hspace{0.5em}1s^{2}2s^{2}2p^4$ and $1s^{2}2s2p^5$ thresholds

We report results of many-electron calculations that predict the presence of a regular series of autoionizing doubly excited states (DESs) of ${}^1{P}^o$symmetry embedded inside one- as well as two-electron continua of neon, in the range of excitation 105.9–121.9 eV above the ground state. The limit of 121.9 eV represents the two-electron ionization threshold (TEIT) labeled by Ne${}^{2+}$ $1s^{2}2p^6$ ${}^{1}S$. The wave functions of these unstable states and their properties are computed according to the theoretical framework, which is explained and justified in the text. Their formal structure is $({\psi }_{\mathrm{core}}){}^{1}S\otimes \Phi (\overrightarrow{r_1},\overrightarrow{r_2}){}^1{P}^o$, where both ${\psi }_{\mathrm{core}}$ and $\Phi ({\mathrm{r⃗}}_1,{\mathrm{r⃗}}_2)$ are correlated wave functions, the latter being represented reasonably accurately by a self-consistently obtained superposition of $\mathrm{nsnp}$ and $\mathit{np}(n+1)d$ configurations $n$$=$3–7. By fitting the calculated lowest energies at each value of $n$, (five states), an effective hydrogenic formula is obtained, which gives the whole energy spectrum up to the TEIT. The autoionization widths are small and decrease with excitation energy. Oscillator strengths for the excitation of these narrow resonance states by absorption of one photon are also small. Because of their electronic structure, these states are compared to ${}^1{P}^o$ DESs in He, which were found in the 1980s to constitute a regular ladder with wave-function characteristics that tend to those of the so-called Wannier state at threshold. In the present case, the presence of the core and the concomitant interactions do not permit the emergence of such geometrical features.

Figure 1

The part of the Ne spectrum, which is relevant to the $2s^2$-hole DESs of ${}^1{P}^o$symmetry, labeled by $(1s^{2}2p^6)\mathrm{nsnp}$ configurations. The energies for the thresholds are experimental (NIST tables). The predicted excitation energies of the DESs are obtained as explained in the text.