\textit{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 new complex-scaling (CS) generalized pseudospectral (GPS) method in hyperspherical coordinates (HSC) for \textit{ab initio} and accurate treatment of the resonance energies and autoionization widths of two-electron atomic systems in the presence of strong dc electric field. The GPS method allows non-uniform 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 to 20) doubly-excited resonance states of He atoms. In addition, we present the first 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.