Propensity rules for excitation of atoms in high-lying doubly excited states by charged-particle impact

For the ¹{P}ᵒ-¹{S}ᵉ$, $¹Pᵒ{{{-}}}¹Dᵉ, ¹{D}ᵉ-¹{S}ᵉ$, and $¹Dᵉ{{{-}}}¹Pᵒ double-electron excitation processes of He in high-lying doubly excited states by charged-particle impact, we have evaluated the Born cross sections using the hyperspherical wave functions. Together with our previous results [Motoyama, Koyoma, and Matsuzawa, Phys. Rev. A 38, 670 (1988); Matsuzawa, Atsumi, and Koyama, ibid. 41, 3596 (1990)], we have theoretically found a set of propensity rules for these excitation processes between the doubly excited states with L{≤}2. These rules indicate that a He atom in a strongly correlated doubly excited state tends to conserve its internal state as a flexible e-He²⁺-e linear triatomic molecule during the excitation processes except for the restriction arising from the Pauli exclusion principle. How the exclusion principle modifies the above-mentioned propensity rules for singlet-singlet optically allowed excitation processes depends on the radial correlation of the initial state. The behaviors of the doubly excited atoms in rotationally and/or vibrationally excited states as the flexible linear triatomic molecule tend to deviate from those predicted by the propensity rules so obtained. This is due to the fact that there are no final states available for the propensity rules to specify because of the restriction arising from the cutoff of the quantum numbers.