Hybrid orbital and numerical grid representation for electronic continuum processes: Double photoionization of atomic beryllium

Abstract

A general approach for ab initio calculations of electronic continuum processes is described in which the many-electron wave function is expanded using a combination of orbitals at short range and the finite-element discrete-variable representation (FEM-DVR) at larger distances. The orbital portion of the basis allows efficient construction of many-electron configurations in which some of the electrons are bound, but because the orbitals are constructed from an underlying FEM-DVR grid, the calculation of two-electron integrals retains the efficiency of the primitive FEM-DVR approach. As an example, double photoionization of beryllium is treated in a calculation in which the $1{s}^{2}$ core is frozen. This approach extends the use of exterior complex scaling (ECS), successfully applied to helium and ${\mathrm{H}}_{2}$, to calculations with two active electrons on more complicated targets. Integrated, energy-differential and triply-differential cross sections are exhibited, and the results agree well with other theoretical investigations.