Nonadiabatic quantum molecular dynamics with hopping. II. Role of nuclear quantum effects in atomic collisions

The role of electron-nuclear correlations, i.e., quantum effects in the nuclear motion in atomic collisions with complex targets, is discussed using the recently developed nonadiabatic quantum molecular dynamics with hopping method [Fischer, Handt, and Schmidt, paper I of this series, Phys. Rev. A 90, 012525 (2014)]. It is shown that the excitation process is nearly unaffected by electron-nuclear correlations as long as integral quantities are considered (total kinetic energy loss), whereas the relaxation mechanism of the molecular target is greatly affected (total fragmentation probability). To describe highly differential quantities (kinetic energy loss as a function of the scattering angle), however, the consideration of nuclear quantum effects during the initial excitation process is indispensable, even in collisions where one would expect purely classical behavior of the nuclei due to their small de Broglie wavelength. The calculations reproduce and explain in detail old but still unexplained experimental data of differential energy-loss spectroscopy in $\mathrm{He}+\mathrm{He}$ and $\mathrm{He}+{\mathrm{H}}_2$ collisions.

Figure 1

Overview of the ab initio molecular-dynamics methods used in this work: QMD, NA-QMD, and NA-QMD-H. In the adiabatic limit (i.e., if electronic excitations do not occur in collisions) both nonadiabatic approaches (NA-QMD and NA-QMD-H) should merge into the QMD method (see the text and Paper I).

Figure 2

Kinetic energy loss $\Delta E$ as a function of the impact energy $E_{\mathrm{c}.\mathrm{m}.}$ for collisions of $\mathrm{He}$ with different targets calculated with QMD (green squares), NA-QMD (black squares), and NA-QMD-H (red squares): (a) ${{\mathrm{Na}}_2}^{+}$, (b) ${\mathrm{Na}}_2$, (c) ${\mathrm{N}}_2$, and (d) ${{\mathrm{Na}}_9}^{+}$. The top abscissae denote the corresponding impact velocities $v$. The collision geometries are sketched in the insets. The typical collision scenarios for the labeled impact energy regions I–IV in (a) and (b) are discussed in detail in the text.

Figure 3

Fragmentation probability $P_{\mathrm{F}}$ as a function of the impact energy $E_{\mathrm{c}.\mathrm{m}.}$ for the same collisions as shown in Fig. 2: (a) $\mathrm{He}$ with ${{\mathrm{Na}}_2}^{+}$ and (b) ${\mathrm{Na}}_2$, from QMD (green squares), NA-QMD (black squares), and NA-QMD-H (red squares).

Figure 4

The top panel shows the internuclear distance $R$ of ${\mathrm{N}}_2$ calculated as a function of time $t$ in NA-QMD for three selected impact energies $E_{\mathrm{c}.\mathrm{m}.}$. The bottom panel shows the excitation energies $\Delta E$ [cf. Fig. 2] and fragmentation probabilities $P_{\mathrm{F}}$ predicted by the NA-QMD and NA-QMD-H methods.

Figure 5

Excitation energies, constructed from bare HF one-electron excitations (I) and double-electron (II) excitations calculated using the RHF-HE and UHF methods for (a) the ${\mathrm{H}}_2$ molecule at its equilibrium internuclear distance and (b) the He atom.

Figure 6

Angle-resolved energy-loss spectra for the (a) and (c) $\mathrm{He}+\mathrm{He}$ and (b) and (d) $\mathrm{He}+{\mathrm{H}}_2$ collisions: (a) and (b) results calculated with QMD (green) and NA-QMD (black) and (c) and (d) NA-QMD-H spectra represented (c) by red squares and (d) as a density plot by smoothing the results with localized Gaussian functions. The colors of the density plot range from blue (zero probability) to red (maximum probability). In addition, the black and white lines in (c) and (d), respectively, show experimental peak positions extracted from [41].