Based on the hyperspherical approach, we have calculated the generalized oscillator strengths and the electron-impact-excitation Born cross sections from the initial $^{1}\mathrm{S}^{\mathrm{e}}$ high-lying doubly excited states to the final $^{1}\mathrm{P}^{\mathrm{o}}$ and $^{1}\mathrm{D}^{\mathrm{e}}$ high-lying doubly excited ones. Together with the previous results on the $^{1}\mathrm{S}^{\mathrm{e}}$${\mathrm{\ensuremath{-}}}^{1}$${\mathrm{S}}^{\mathrm{e}}$ excitation processes, we have found a simple propensity rule that the excitation processes with \ensuremath{\Delta}${n}_{2}$=0 are most likely to take place within each manifold, i.e., the S-S, S-P, or S-D excitation process where ${n}_{2}$ is the radial bending quantum number, i.e., the number of the nodes of the bending vibrational wave functions on the body fixed frame based on the rovibrator model of the doubly excited states. In addition to the propensity rule, \ensuremath{\Delta}${n}_{2}$=0, we have also found a set of propensity rules, i.e., \ensuremath{\Delta}v=\ensuremath{\Delta}T=0 for angular correlation and \ensuremath{\Delta}A=0 for radial correlation according to the rovibrational model where v is the bending vibrational quantum number, T is the vibrational angular momentum, and A is the radial correlation quantum number.This may be interpreted as a result of isomorphism of the surface density plot of the squared channel functions between the initial and final states. The radial propensity rule \ensuremath{\Delta}A=0 seems to dominate over the angular one, i.e., \ensuremath{\Delta}v=\ensuremath{\Delta}T=0 and modifies the latter in the $^{1}\mathrm{S}^{\mathrm{e}}$${\mathrm{\ensuremath{-}}}^{1}$${\mathrm{P}}^{\mathrm{o}}$ excitation processes where both types of the propensity rules are incompatible with one another because of the Pauli exclusion principle for two atomic electrons. This leads to the angular propensity rule \ensuremath{\Delta}v=\ensuremath{\Delta}T=1 for the $^{1}\mathrm{S}^{\mathrm{e}}$${\mathrm{\ensuremath{-}}}^{1}$${\mathrm{P}}^{\mathrm{o}}$ excitation processes, though the propensity rule \ensuremath{\Delta}${n}_{2}$=0 and \ensuremath{\Delta}A=0 remains unchanged. The propensity rule for the S-P excitation is equivalent to the selection rule for photoabsorption by He, as is expected. These propensity rules theoretically demonstrate that the two atomic electrons show remarkable collective behaviors as the result of strongly correlated motion between them, while an incident electron interacts with an atom in the high-lying doubly excited state perturbatively. It has been found that the propensity rule obtained here, i.e., \ensuremath{\Delta}v=\ensuremath{\Delta}T=1 for the S-P excitation is not in agreement with the selection rule observed in the threshold excitation spectra of He by electron impact [P. J. M. van der Burgt et al., J. Phys. B 19, 2015 (1986)] and with the selection rule for the infrared photon absorption by a linear triatomic molecule. The reason for these discrepancies is also discussed.
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Open Access
Jan 1, 1993
G.A Gurzadyan + 1
