\textit{Ab Initio} Calculation of Double Photoexcitation 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 an accurate \textit{ab initio} and 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 a 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 He atoms in an external electric field of $84.4$ \textit{kV/cm}. The effects of dc-field ionization rates on the 1$S^{e}$, 1$P^{o}$, and 1$D^{e}$ states where $n =10-20$ have been identified.