Scattering of residual gas atoms by fast HCI beams

The scattering of fast ion beams, circulating e.g. in a synchrotron, with the residual gas can lead to desorption when the scattered ions hit the aperture limiting devices of the structure [1]. Here, the impacts of recoiled residual gas particles may be an additional source for desorption. We are thus interested in the scattering of residual gas atoms or molecules by passing fast highly charged ions, focusing on the example of 1 GeV/u U. To make an estimate for the related cross section and the acquired recoil energies we treat the problem as elastic scattering between the nucleus (with charge ZRe) of a residual gas atom and the projectile nucleus (ZP e), neglecting the energy and momentum transfer to the bound electrons of the residual gas atoms or molecules. A classical description with classical trajectories can be employed because the Coulomb parameter η = ZRZP e /(4π 0~cβ) = ZRZP α/β is for the envisaged energies and projectile charges (β = v/c = 0.87, γ = 2, ZP = 92) about unity, or even larger for residual gas atoms heavier than hydrogen [2, 3]. As shown in [4], magnetic field effects and retardation corrections are rather small for relativistic (heavy) ion collisions at such energies (γ = 2) and will be neglected. We then end up with classical scattering with an effective interaction potential V (r) which accounts for the screening of the nuclei by the bound electrons. This can be treated by relativistic classical mechanics. Here closed expressions can be obtained for arbitrary spherically symmetric interactions V (r) [5], if one collision partner remains at rest. As a next step of approximation we thus consider the scattering event in the frame where the heavy projectile (U) is (initially) at rest and treat it as infinitely heavy (mP →∞). Replacing the effective V (r) by the Coulomb potential, i.e. V = κ/r (κ = ZRZP e /(4π 0)) and taking the screening into account only by restricting the allowed impact parameters b to values below a typical screening length λ ≈ 10m, the scattering angle θ(b) can be given explicitly [5] by