Dynamic screening and two-center effects in neutral and partially dressed ion-atom collisions

In collisions involving projectiles with bound electrons, partial or total screening of their nuclear charge must be considered. Accordingly, a projectile dynamic effective charge, as a function of the collision momentum transfer, is included in the state-of-the-art continuum distorted wave with eikonal initial state model. This correction, applied in the exit channel, recovers a two-center description from collisions with neutral projectiles. Also, an improvement of both target and projectile ionization double differential cross sections is achieved, especially at the binary encounter and electron capture to the continuum peaks. The results calculated by our analytical model are shown in accordance with previous theoretical and experimental work.

Figure 1

Single ionization DDCS at $\theta ={15}^{\circ }$ calculated for different charge corrections in comparison with bare projectiles. (a) He ionization by the impact of ${\mathrm{He}}^{+}$ in comparison with same energy ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{2+}$ impacts. (b) Electron emission for 500-keV/u H $+$ He, in comparison with 500-keV/u ${\mathrm{H}}^{+} +$ He. ${\nu }_0{\xi }_0$ stands for the use of the asymptotic charge in both channels; ${\nu }_0{\xi }_K$ means that the dynamic charge is applied in the final channel while the asymptotic one is used in the initial channel; ${\nu }_K{\xi }_0$ is exactly the opposite as the previous case and ${\nu }_K{\xi }_K$ indicates that the dynamic effective charge was included in both initial and final channels.

Figure 2

He ionization DDCS as a function of the emission angle for fixed energies corresponding to soft collisions, the ECC cusp, and ${45}^{\circ }$ binary encounter peak. Continuous lines are for dressed projectile impact, within the ${\nu }_0{\xi }_0$ or ${\nu }_0{\xi }_K$ cases (see Fig. 1 caption). Dashed lines are for bare projectile impacts. LR stands for the long-range interaction, i.e., the perturbation potential due to the short-range interaction is not taken into account.

Figure 3

Theoretical and experimental results for 200-keV/u He $+$ Ar at $0^{\circ }$. “T ion” and “P ion” are our calculated target ionization and projectile electron loss, respectively. In panel (a) all calculations are for the ${\nu }_0{\xi }_0$ case while in panel (b) all calculations are for the ${\nu }_0{\xi }_K$ one. The experimental results are from [11]. Dotted lines are both multiplied by a factor of 0.3 to fit experiments.

Figure 4

Analysis of those electrons emitted from the projectile and detected in the laboratory frame at ${170}^{\circ }$ with energy from 1 to 100 eV. (a) Energy and emission-angle Lorentz transformations from the laboratory frame to the projectile one as a function of the detected energy. Contained in the projectile frame emission energy curve is the value of the projectile ionization DDCS at that energy. (b) Target and projectile ionization DDCS for the reversed collision system of Fig. 5, 440-keV/u He $+ {\mathrm{Li}}^{+}$, at $5^{\circ }$.

Figure 5

Experimental and theoretical DDCS for 440-keV ${\mathrm{Li}}^{+} +$ He at fixed emission angles of (a) ${10}^{\circ }$, (b) ${52}^{\circ }$, (c) ${120}^{\circ }$, and (d) ${170}^{\circ }$. On the left panel of each figure the calculations use the asymptotic net charge in both initial and final channel, ${\nu }_0{\xi }_0$, while in the right panel we have the ${\nu }_0{\xi }_K$ case, i.e., a net charge in the initial channel distortion and a dynamic effective charge in the final channel distortion. Experimental data are from [18].