Ab initio study of high-lying doubly excited states of helium in static electric fields: Complex-scaling generalized pseudospectral method in hyperspherical coordinates

We present a complex-scaling (CS) generalized pseudospectral (GPS) method in hyperspherical coordinates (HSC) for $\mathit{ab}$ initio and accurate treatment of the resonance energies and autoionization widths of two-electron atomic systems in the presence of a strong dc electric field. The GPS method allows nonuniform and optimal spatial discretization of the two-electron Hamiltonian in HSC with the use of only a modest number of grid points. The procedure is applied for the first precision calculation of the energies and autoionization widths for the high-lying ${}^1{S}^e$, ${}^1{P}^o$, ${}^1{D}^e$, and ${}^1{F}^o$ ($n=10$–20) doubly excited resonance states of He atoms. In addition, we present a theoretical prediction of the energies and widths of high-lying doubly excited resonance states of ${}^1{P}^o$ ($n=$ 8–15) in external dc electric field strengths of 3.915–10.44 kV/cm. The calculated dc-field perturbed high-lying resonance energies are in good agreement with the latest experimental data.

Figure 1

Quantum defect (real and imaginary part) for the $n=$ 10–20(a) ${}^1{S}^e$ doubly-excited Rydberg states below the $N=2$ threshold.

Figure 2

Quantum defect (real and imaginary part) for the $n=$ 10–20(b) ${}^1{S}^e$ doubly-excited Rydberg states below the $N=2$ threshold. Also shown are the results from Ref. [30] for comparison.

Figure 3

Experimental fluorescence yield spectra [5] and calculated resonance energies $E_r$ for the $n=$ 8–15(a,b) ${}^1{P}^o$ doubly excited Rydberg states below the $N=2$ threshold in dc fields. Here the red (dashed) line and blue (solid) line correspond to ($na$) and ($nb$) series, respectively, and the peaks at the lowest energy correspond to 8(a).

Figure 4

Experimental fluorescence yield spectra [5] and calculated resonance energies $E_r$ for the $n=$ 8–15(a) ${}^1{P}^o$ doubly excited Rydberg states below the $N=2$ threshold in dc fields. Here the red dashed line corresponds to ($na$) series and the peaks at the lowest energy correspond to 8(a).