\textit{Ab Initio} Calculation of Double Photoexcitation of Rydberg Resonance States of Helium below the $N $=2 Threshold in a Strong DC Electric Field

We present a complex-scaling (CS)-generalized pseudospectral (GPS) method in hyperspherical coordinates (HSC) for \textit{ab initio }accurate treatment of the electron structure and quantum dynamics of two-electron systems. The GPS method allows non-uniform and optimal spatial discretization of the two-electron Hamiltonian in HSC with the use of only very modest number of grid points. The procedure is applied for the precision calculation of the energies and widths of doubly-excited Rydberg resonance states as well as the ionization rates of the He atom in an external dc electric field of 84$.$4 \textit{kV/cm}. The effects of dc-field ionization rates on the 1S$^{e}$, 1P$^{o}$, and 1D$^{e}$ states for $n $= 10-20 have been identified and studied in detail.