A finite-element time-dependent approach to proton and antiproton collisions with He atoms Xiaoxu Guan 1 and Klaus Bartschat 2 Department of Physics and Astronomy, Drake University, Des Moines, Iowa 50311, USA Synopsis We have developed a non-perturbative method to describe proton and antiproton collisions with quasi-two electron atoms. All interactions are accounted for through finite-element discrete-variable representations. The initial state is propagated in time using an efficient Arnoldi-Lanczos scheme. Excellent agreement with experiment and another non-perturbative calculation is obtained for the single and double ionization cross sections.
In this work, we have extended our recently developed finite-element discrete-variable representation (FE-DVR) for short-pulse intense laser-atom interactions [3] to treat single and double ionization of He atoms by proton and antiproton impact. The major modification needed concerns the treatment of the timedependent two-body Coulomb interaction between the projectile and the target electrons. Instead of having a time-independent dipole operator that is multiplied by the space-independent electric field of the laser, we now have to account for other multipole terms in the interaction. Additional complications arise from the dependence of the interaction term on the position of the projectile, which we assume to move along a straight-line trajectory. For maximum efficiency, our FE-DVR scheme takes explicit advantage of the reflection symmetry with respect to the collision plane. As an example, Figure 1 shows the cross sections for double ionization of helium by antiproton impact. The present results are in good agreement with the experimental data [4, 5] over a wide range of incident energies, from very slow antiproton impact at 7 keV to a projectile energy as high as 1 MeV. Our predictions are slightly lower than those of Foster et al [2], but the over1 2
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all agreement between these entirely independent approaches is very satisfactory. Despite the size of the errorbars in the latest experimental data, they support the predictions of both calculations regarding the decrease rather than increase of the double ionization cross section towards very low impact energies. Double ionization cross section (Mb)
Collisions of heavy particles, including protons and antiprotons, with helium are of fundamental interest for understanding the dynamics of break-up processes in few-body Coulomb systems. After intensive efforts over the past two decades, satisfactory agreement between the latest experimental data [1] and theoretical predictions from a sophisticated time-dependent finitedifference approach [2] was finally achieved for single ionization of He by antiproton impact.
Present work Foster et al. Hvelplund et al. Knudsen et al.
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Fig. 1. Cross section for double ionization of helium by antiproton impact. This work is supported by the US National Science Foundation via grant no. PHY-0757755 and the Teragrid allocations TG-PHY090031 and TGPHY080044N.
References [1] Knudsen H, et al. 2008 Phys. Rev. Lett. 101 043201. [2] Foster M, Colgan J, and Pindzola M S 2008 Phys. Rev. Lett. 100 033201. [3] Guan X, Bartschat K, and Schneider B I 2008 Phys. Rev. A 77 043421. [4] Hvelplund P, et al. 1994 J. Phys. B 27 925. [5] Knudsen H, et al. 2009 Nucl. Instr. and Meth. B 267 244.
