Single and double charge transfer in the ${\mathrm{Ne}}^{2+}+\mathrm{He}$ collision within time-dependent density-functional theory

We calculate the charge-transfer cross sections for the ${\mathrm{Ne}}^{2+}+\text{He}$ collision. To this end, we employ Ehrenfest molecular dynamics with time-dependent density-functional theory. The active electrons of the projectile are handled by applying an initial velocity to the Kohn-Sham orbitals via a Galilean boost. The dynamical calculations are performed in an inverse collision framework—the reference frame considers ${\mathrm{Ne}}^{2+}$ to be initially at rest, which ensures numerically converged final-time scattering states. The charge-transfer probabilities are extracted by extending the particle number projection technique to be able to handle the degenerate ${\mathrm{Ne}}^{2+}$ ion. Compared with experimental data available at 10–3000 keV, a fairly good agreement is found for the calculated single- and double-charge transfer cross sections, superior to other theoretical calculations for this ${\mathrm{Ne}}^{2+}+\text{He}$ collision. A time-resolved analysis of the charge-transfer probabilities finds that ionization to the continuum also takes place after the charge transfer has occurred. To account for it, the final scattering states should be followed for a long time, approximately 350 fs, until they stabilize.

Figure 1

The schematic diagram of the simulations, displaying the inverse collision framework. The He atom is treated as the projectile, and the ${\mathrm{Ne}}^{2+}$ ion as the target. The impact parameter is denoted by $b$, and pink arrows point out the incident direction. The whole space is divided into two, the region $V_T$ that contains the target, and its complementary, the region $V_P$ that contains the projectile.

Figure 2

Single- and double-charge transfer cross sections as a function of impact energy. The present results shown by full black circles are calculated by choosing the ${\mathrm{Ne}}^{2+}$ region ($V_T$) to be the whole simulation box. The other scattered symbols are experimental data of Flaks from Refs. [62, 63], Nikilaev from Refs. [64, 65], Winter from Refs. [66, 67], Suk from Ref. [68], Bloemem from Ref. [69], Kusakabe from Ref. [70], and Kase from Ref. [71]. The curves are calculations from Rapp and Francis theory [71, 72], the MOCC method calculations are from Ref. [21], and the results of Friedman are reported in Ref. [73].

Figure 3

Single-electron-capture probability as a function of impact parameter for impact energies at (a) 200–3000 keV and (b) 10–100 keV.

Figure 4

Same as Fig. 3, but for double-electron-capture probability.

Figure 5

The SCT probability as a function of impact parameter and simulation time at 20, 200, and 2000 keV. The entire numerical box is considered to be the ${\mathrm{Ne}}^{2+}$ target region $V_T$.

Figure 6

Snapshots of the electronic density distribution inside the simulation box for 200 keV collisions, for the sequence of time instants displayed in Fig. 5. (top panel) $b=0.2a_0$, (middle panel) $b=3a_0$, (bottom panel) $b=6a_0$. The red dot represents the Ne nucleus. The density values are represented by the colors mapped in the color bar.

Figure 7

The increment of (a) SCT and (b) DCT cross sections calculated at the time instant $t$ relative to the converged ones, e.g., ${\mathrm{\Delta }}_{\mathrm{SCT}\left(\mathrm{DCT}\right)}={\sigma }_{\mathrm{SCT}\left(\mathrm{DCT}\right)}\left(t\right)-{\sigma }_{\mathrm{SCT}\left(\mathrm{DCT}\right)}(t\to \infty )$. The solid curves are shown to guide the eye.