Gregor Schiwietz

Select scenario quasidipolar ionisation

Technical:

A contour plot of the time-dependent electron density for a hydrogen atom (the target nucleus is shown as a blue solid circle) disturbed by a charged particle (red solid circle with arrow) is displayed. The different colors correspond to an exponential density scale for a density cut in the collision plane (the plane spanned by the impact-parameter and the projectile-velocity vector). The first frame of the animation shows the initial hydrogen-1s electron cloud, a spherically symmetric exponential density distribution.

The density was calculated with our quantum mechanical atomic-orbital (AO) coupled-channel code by solving 172 coupled differential equations for the time-dependent amplitudes. These equations are directly related to the time-dependent Schrödinger equation and each amplitude contains the information on the population as well as the coherence properties for a certain basis state. For this example we have used only single-centered basis states that are (linear combinations of) eigenstates of the unperturbed target Hamiltonian. The coherent superposition of all basis states yields the time-dependent density shown below.

10 keV ANTIPROTON + HYDROGEN collision at an impact parameter of b = 1 a.u.

One may notice four effects during the course of the collision:

1. The (negatively charged) antiproton repels the (negatively charged) electron on the incoming path (z coordinate < 0); the so-called polarization process. One may see that the electron density moves away from the projectile and at intermediate distances a spiral-like structure of the electron density evolves.
2. The dipolar antiproton-proton system does not support bound states for inter-particle distances below 0.64 a.u. For finite velocities and larger impact parameters (1 a.u. in this case) there is still a significant ionization contribution. As can be seen from the animation there is a high transition probability (blowing up of the density) exactly at the distance of closest approach.
3. The antiproton repels the electron also on the outgoing path of the collision. One may see that the electron density near the projectile is very low and that ionized parts of the distribution are preferentially ejected into the backward direction.
4. The remaining target-centered electron density includes also highly excited states and correspondingly, the final density distribution is oscillating.

Selected references on antiprotons interacting with hydrogen and helium atoms:

• "Comprehensive analysis of the stopping power of antiprotons and negative muons in He and H2 gas targets" G. Schiwietz, U.Wille, R.Díez Muino, P.D.Fainstein, and P.L.Grande, J.Phys. B29, 307-321 (1996)
• "Stopping mechanisms of negative heavy particles in gas targets" G. Schiwietz, U.Wille, R.Díez Muino, P.D.Fainstein, and P.L.Grande, NIM B115, 106-110 (1996)