The charge transfer (ionization) of hydrogen Rydberg atoms (principal quantum number $n=25-34$) incident at a Cu(100) surface is investigated. Unlike fully metallic surfaces, where the Rydberg electron energy is degenerate with the conduction band of
the metal, the Cu(100) surface has a projected bandgap at these energies, and only discrete image states are available through which charge transfer can take place. Resonant enhancement of charge transfer is observed at hydrogen principal quantum numbers for which the Rydberg energy matches the energy of one of the image states. The integrated surface ionization signals show clear periodicity as the energies of states with increasing $n$ come in and out of resonance with the image states. The velocity dependence of the surface ionization dynamics is also investigated. Decreased velocity of the incident H atom leads to a greater mean distance of ionization and a lower field required to extract the ion. The surface-ionization profiles (signal versus applied field) for `on resonance $n$ values show a changing shape as the velocity is changed, reflecting the restriction of the resonance to a certain range of applied field.
Wavepacket propagation calculations are reported for the interaction of a Rydberg hydrogen atom ($n=2-8)$ with Cu(111) and Cu(100) surfaces (represented by a Chulkov potential), in comparison with a Jellium surface. Both copper surfaces have a projec
ted band gap at the surface in the energy range degenerate with some or all of the Rydberg energies. The charge transfer of the Rydberg electron to the surface is found to be enhanced for $n$ values at which there is a near-degeneracy between the Rydberg energy level and an image state or a surface state of the surface. The enhancement is facilitated by the strong overlap of the surface image-state orbital lying outside the surface and the orbital of the incoming Rydberg atom. These calculations point to the possibility of using Rydberg-surface collisions as a probe of surface electronic structure.
We present a new formalism to calculate phase-space acceptance in a Zeeman decelerator. Using parameters closely mimicking previous Zeeman deceleration experiments, this approach reveals a hitherto unconsidered velocity dependence of the phase stabil
ity which we ascribe to the finite rise and fall times of the current pulses that generate the magnetic fields inside the deceleration coils. It is shown that changing the current switch-off times as the sequence progresses, so as to maintain a constant mean acceleration per pulse, can lead to a constant phase stability and hence a beam with well-defined characteristics. We also find that the time overlap between fields of adjacent coils has an influence on the phase-space acceptance. Previous theoretical and experimental results suggested unfilled regions in phase space that influence particle transmission through the decelerator. Our model provides, for the first time, a means to directly identify the origin of these effects due to coupling between longitudinal and transverse dynamics. Since optimum phase stability is restricted to a rather small parameter range in terms of the reduced position of the synchronous particle, only a limited range of final velocities can be attained using a given number of coils. We evaluate phase stability for different Zeeman deceleration sequences, and, by comparison with numerical three-dimensional particle trajectory simulations, we demonstrate that our model provides a valuable tool to find optimum parameter sets for improved Zeeman deceleration schemes. An acceleration-deceleration scheme is shown to be a useful approach to generating beams with well-defined properties for variable-energy collision experiments. More generally, the model provides significant physical insights applicable to other types of particle decelerators with finite rise and fall time fields.
Zeeman deceleration is an experimental technique in which inhomogeneous, time-dependent magnetic fields generated inside an array of solenoid coils are used to manipulate the velocity of a supersonic beam. A 12-stage Zeeman decelerator has been built
and characterized using hydrogen atoms as a test system. The instrument has several original features including the possibility to replace each deceleration coil individually. In this article, we give a detailed description of the experimental setup, and illustrate its performance. We demonstrate that the overall acceptance in a Zeeman decelerator can be significantly increased with only minor changes to the setup itself. This is achieved by applying a rather low, anti-parallel magnetic field in one of the solenoid coils that forms a temporally varying quadrupole field, and improves particle confinement in the transverse direction. The results are reproduced by three-dimensional numerical particle trajectory simulations thus allowing for a rigorous analysis of the experimental data. The findings suggest the use of a modified coil configuration to improve transverse focusing during the deceleration process.
