Core Electrons in the Electronic Stopping of Heavy Ions

Electronic stopping power in the $\mathrm{keV}/\AA$ range is accurately calculated from first principles for high atomic-number projectiles and the effect of core states is carefully assessed. The energy loss to electrons in self-irradiated nickel is studied using real-time time-dependent density functional theory. Different core states are explicitly included in the simulations to understand their involvement in the dissipation mechanism. The core electrons of the projectile are found to open additional dissipation channels as the projectile velocity increases. Almost all of the energy loss is accounted for, even for high projectile velocities, when core electrons as deep as $2s^{2}2p^6$ are explicitly treated. In addition to their expected excitation at high velocities, a flapping dynamical response of the projectile core electrons is observed at intermediate velocities. The empirical reference data are well reproduced in the projectile velocity range of 1.0–12.0 a.u. (1.5–210 MeV).

Figure 1

Electronic stopping power (${\mathcal{S}}_e$) for a Ni projectile in a Ni crystal as a function of velocity. For reference, both the nuclear (dashed, black curve) and the electronic (solid, blue curve) stopping powers from SRIM [50] are presented. Open triangles (maroon) show calculated ${\mathcal{S}}_e$ for a Ni10 projectile in a Ni10 host, solid squares (red) for a Ni16 projectile in a Ni16 host, filled circles (indigo) for Ni18 in Ni18, open circles (orange) for Ni26 in Ni18, and open squares (green) for Ni26 in Ni26.

Figure 2

Instantaneous energy expectation values for the propagating Kohn-Sham states $⟨{\psi }_n^{\mathrm{KS}}(t)|H_{\mathrm{KS}}|{\psi }_n^{\mathrm{KS}}(t)⟩$ as a function of projectile position (relative to the unperturbed Fermi energy). The red curves show $2p^6$ states of the projectile. The black curves show the rest of the projectile states and the host states below the Fermi energy. The blue curves indicate as the states cross above the Fermi energy. The inset in the top panel shows the length scale of the initial transient, due to the initial velocity kick.

Figure 3

Fourier transform of the energy of the $2p$ states (red curves of Fig. 2) in time (left panel, frequency expressed in energy units) and space (right panel).

Figure 4

The contour plot of $2p$ orbital of the projectile. The orbital at the initial position appears clipped because the projectile is initially placed at (011) plane of the supercell. The orbital is plotted for three different projectile velocities starting from the same initial position with three subsequent projectile positions as it travels through the Ni crystal.