Distance of Excited-State Formation in Ion-Surface Collisions

Abstract

We present the first numerical results of a multichannel theory for resonant charge exchange in ionsurface scattering at grazing incidence. The time-dependent Schrodinger equation describing resonant exchange can be solved in the adiabatic approximation for the slow perpendicular motion. As an initial application the state dependence of the distance of formation in the H(« SB *2) following specular reflection of protons at a gold surface is determined. PACS numbers: 34.50.Fa, 34.50.Pi, 34.70.+e, 79.20.Rf Charge-exchange processes in ion-surface scattering at small grazing angles (0:<5 O ) provide the unique opportunity to study collision processes under unusual conditions not easily accessible by other means: Projectile ions reflected specularly at clean surfaces undergo an array of extremely soft collisions at the surface layer with distances of closest approach selected by the normal component of the projectile velocity. An even more interesting feature is that the electron capture from the conduction band of the metal into atomic orbitals is simultaneously characterized by two different time (or velocity) scales: a fast motion of the projectile (i?j|^u F ) in the surface plane and the near-adiabatic motion along the surface normal (v ± <^v^) where the characteristic internal velocity of the target electrons is the Fermi velocity vp. Both low-and high-energy methods therefore must be combined to describe inelastic electronic processes near the surface at intermediate velocities.The technique of ion-surface scattering at grazing incidence has recently been used in a large number of investigations in a broad range of different subfields such as the polarization characteristics of excited atomic manifolds, 1 " 3 the production of nuclear spin polarization, 4 surface channeling, 5 and the diagnostics of surface magnetic order. 6 For the understanding of the production mechanism of excited states itself as well as its application as a potential tool of surface diagnostics, detailed knowledge of the distance dependence of the formation process is required.As a first application of a new multichannel treatment of resonant charge transfer we calculate the formation distance from the surface of all substates H(/i~2,/m) following p -* Au collisions at intermediate projectile speeds (i? = l a.u.). The quantization axis is chosen to coincide with the surface normal. The gold surface is described by a (nearly) free-electron jellium model. The motion of the proton can be quite accurately approxi-mated by a classical trajectory since the de Broglie wavelength A, d is small compared to characteristic distances in the target or projectile. In the following we will be concerned only with the outward portion of the trajectory of the receding ion which is taken as a straight line. Deviations near the turning point as well as the inward portion are irrelevant for the formation of excited states for reasons to be discussed below. The electron transfer from a conduction-band state 0* to an atomic orbital <f>j is then governed by a...

One-electron matrix elements in the theory of ion–metal-surface scattering

“…(7) and (8) are related [64] by (A3) where q =~q~, and a"is defined by Eq. (42). It is therefore sufficient to consider explicitly the function (A4) i.e.…”

“…and E. by setting K*= I dq, J*. (q, } and K =I dqJ, (q), (34) (42) where the functions J. *(q, }and J.…”

Theory of emission-angle-dependent Auger transitions in ion-atom collisions

“…The essential difference between this equation and that of the classical paper by Fano (1961), for instance, is that in the above expression we suppose that the matrix element (Tfl VIITl) and the energies E, and E, depend explicitly on time, while the linewidth remains unchanged. Under these conditions the amplitude in equation (3.1) no longer represents a rigorous solution; rather it can be regarded as an adiabatic approximation (Bargdorfer and Kupfer 1986).…”

Analysis of some beam-foil molecular-effect data

“…The excitation energy differences in question are approximately lo-' eV (Hashkin and Stoner 1975). If such a value is used as an upper limit for AE, a lower limit of 3 x lo-" s is obtained for T. During such a time interval, the projectiles used would move approximately m. This is much longer than any foil-projectile interaction time is assumed to be (Zimny et al 1986, Burgdorfer andKupfer 1986), illustrating that we deal not only with an enhanced probability for electron capture at the back of the foil, but also with a redistribution of the level population taking place downstream from the foil. However, any interaction on one ion caused by the presence of the accompanying ion will have ceased much earlier than 3 x s (Frischkorn and Groeneveld 1983), ruling out once more the role of the accompanying particle, in consistency with Baudinet-Robinet et a1 (1986).…”