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

Abstract

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 ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}^{e}$, ${}^{1}\phantom{\rule{-0.16em}{0ex}}{P}^{o}$, ${}^{1}\phantom{\rule{-0.16em}{0ex}}{D}^{e}$, and ${}^{1}\phantom{\rule{-0.16em}{0ex}}{F}^{o}$ ($n=10$--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 ${}^{1}\phantom{\rule{-0.16em}{0ex}}{P}^{o}$ ($n=$ 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.