Double Excitation of Atoms by Electron Impact

The electron-impact double-excitation cross sections for several states of lithium, beryllium, magnesium, and calcium are calculated using the Born-Oppenhemier scattering approximation. The energy dependence of the total cross sections and the angular dependence of the differential cross sections for these parity-unfavored transitions are reported. The maximum values of the total cross sections for excitation of the lowest states (np)²³Pg of beryllium, magnesium and calcium are found to be comparable in magnitude to those for single excitations in the same energy range (~πa₀²). Those for the (np)(3d)¹Dᵤ and ³Dᵤ excitations are found to be of the order of 10^-1πa₀² for magnesium and 10^-2πa₀² for beryllium. The highly excited ($1s$) (2p)²⁴Pg state of lithium has a maximum cross section of 4×10^-5πa₀². The highly excited (1s)(2p)²⁴Pg for all these transitions are proportional to sin²θ and so they vanish in the forward and backward directions. The polarization of the dipole radiation emitted by these doubly excited states is described. Target wave functions are constructed using the Hartree-Fock method. For the ¹Sg→³Pg transition in magnesium and calcium, pseudopotential methods were also used to construct the target wave functions. The resulting cross sections agree closely with those computed with Hartree-Fock orbitals.