Hyperspherical approach to double-electron excitation of He by fast-ion impact

Double-electron-excitation processes of He atoms by proton, antiproton, and ${\mathrm{C}}^{6+}$-ion impact have been theoretically investigated using the second-order Born approximation and the close-coupling method in the energy regime of MeV/u. The semiclassical impact-parameter method with a straight-line-trajectory approximation is employed to describe the collision processes. Hyperspherical wave functions are adopted to take full account of the strongly correlated motion of two atomic electrons in He. For proton and antiproton impact, it is found that the first-order mechanism dominates for excitation to the (2s2p) ${}_{}{}^1{}_{}{}^{}$ ${\mathit{P}}^{\mathit{o}}$ excited state, while the second-order processes play a significant role in excitation to the (2s2s) ${}_{}{}^1{}_{}{}^{}$ ${\mathit{S}}^{\mathit{e}}$, (2p2p${)}^1$ ${\mathit{S}}^{\mathit{e}}$, and (2p2p) ${}_{}{}^1{}_{}{}^{}$ ${\mathit{D}}^{\mathit{e}}$ excited states at a few MeV/u. It should be noted that the doubly excited (2s2p) ${}_{}{}^1{}_{}{}^{}$ ${\mathit{P}}^{\mathit{o}}$ state plays an important role as an intermediate state in these second-order processes in addition to the singly excited 1s2p ${}_{}{}^1{}_{}{}^{}$ ${\mathit{P}}^{\mathit{o}}$ state. It is also found that the difference for the double-electron-excitation processes by proton impact and by antiproton impact is much smaller than that for the double-ionization processes in this energy range. For the ${\mathrm{C}}^{6+}$-ion impact, higher-order mechanisms play more important roles at a few MeV/u. The excitation mechanism is also discussed based on the classification scheme of the correlation quantum numbers, which enables us to obtain a more direct physical insight into the collision mechanism.