The boomerang effect in electron-hydrogen molecule scattering as determined by time-dependent calculations

The appearance of oscillations in the energy-dependent cross sections of the vibrational excitation ν=0→ν≥3 of the hydrogen molecule in its electronic ground state as predicted by Mündel, Berman, and Domcke [Phys. Rev. A 32, 181 (1985)] was confirmed in the electron scattering experiments by Allan [J. Phys. B: At. Mol. Phys. 18, L451 (1985)]. These unusual structures were obtained in spite of the extremely short lifetime of H₂^- in its ro-vibrational states. Based on the standard (Hermitian) time-independent scattering calculations, Horáček et al. [Phys. Rev. A 73, 022701 (2006)] associated these oscillations with the boomerang effect. Here, we show the boomerang effect as developed in time, based on our time-dependent nuclear wavepacket (WP) calculations. The nuclear WP dynamics of H₂^- is determined using the non-Hermitian quantum mechanics (NH-QM) which enables the use of the Born-Oppenheimer approximation with complex potential energy surfaces. This NH-QM approach, which enables us the association of the nuclear WP dynamics as obtained from the complex potential energy curve of H₂^- with the evolution of cross section in time, can enlighten the dynamics in other scattering experiments.