Atom-solid collisions

It is easily seen by inspection that the biorthogonal basis set definition (3.55) cmnddes with the definifion (3.18) ven in the discussion of the Lanczos method. We recall that the dynamics of operators (liouville equations) or probabilities (Fokker-Planck equations) have a mathematical structure similar to Eq. (3.29) and can thus be treated with the same techniques (see, e.g., Chapter 1) once an appropriate generalization of a scalar product is performed. For instance, this same formalism has been successfully adopted to model phonon thermal baths and to include, in principle, anharmonicity effects in the interesting aspects of lattice dynamics and atom-solid collisions. ... 

Jf(t) which we shall use in this chapter. We must mention, however, that somewhat more complicated forms have been introduced in order to consider some special aspects of the problem. Some of the most notable include that used by Bloss and Hone (which has a core level in the solid and two orbitals on the atom), those which take into account the scattering of atoms with large velocity components parallel to the surface and that recently considered by Kawai et in order to suggest a possible new experimental technique for studying energy levels of atoms in collision with surfaces. 

RELATIVISTIC AND DYNAMIC CONTRIBUTIONS IN ION-ATOM AND ION-SOLID COLLISIONS ... 

From a very general point of view every ion-atom collision system has to be treated as a correlated many-body time-dependent quantum system. To solve this from an ab initio point of view is still impossible. So, one has to rely on various approximations. Nowadays the best method which can be applied to realistic collision systems (which we discuss here) is on the level of the non-selfconsistent time-dependent Hartree-Fock-Slater or, in the relativistic case, the Dirac-Fock-Slater method. Up-to-now no correlation beyond this approximation can be taken into account in the case of 3 or more electrons. (This is in accordance with the definition of correlation given by Lowdin [1] in 1956) In addition no QED contributions, i.e. no correction to the 1/r Coulomb interaction between the electrons, ever have been taken into account, although in very heavy collision systems this effect may become important. This will be discussed in section 5. A short survey of the theory used is followed by our results on impact parameter dependent electron transfer and excitation calculations of ion-atom and ion-solid collisions as well as first results of an ab initio calculation of MO X-rays in such complicated many particle scattering systems. 

From a material-centered point of view, the thermalization of positrons is a process very similar to that of electrons. The initial stage of inelastic collisions and the electromagnetic slowing down process form the usual radiation products. In fluids and molecular or atomic solids, these are excited and ionized molecules, fi-ee radicals, and electrons. In metals, however, plasmon and phonon excitation also play significant roles in the thermalization of positrons. 

The formalism of collisional TCFs can be conveniently applied to interactions involving polyatomics and solid surfaces, using a many-atom description of the collision partners [30,31,35]. Interaction potentials are decomposed into atom-pair, atom-triplet, etc., terms, and the collision can be understood as a sequence of atom-atom encounters by analogy to the three-atom approaches to atom-diatom collisions [36,37]. It is then possible to describe scattering involving polyatomics, solid surfaces and molecules adsorbed at solid surfaces. 

E. Vilallonga and H. Rabitz. Multi-quantum energy transfer into surface Rayleigh, bulk shear and pressure waves by atom-solid surface collisions a discrete-continuum hybrid treatment with applications to He-Pl (III), submitted to J. Chem. Phys. Multi-quantum vibrational energy transfer into adsorbates on solid surfaces by atomic collisions a semiclassical treatment based on dynamical correlations, submitted to J. Chem. Phys. 

Rutherford backscattering is a valuable tool for getting quasi nondestructive depth profiles of thin films on surfaces. Due to their high primary energy, He " ions penetrate into solid surfaces up to ca. 1 pm and emerge back to the vacuum after a binary collision process with a target atom. This collision process follows Eq. (1-49) as ISS, which yields for 0=180° (backscattering)... 

Xe, and Xe. The spin-spin relaxation times T2) have also been measured for liquid and solid Xe. The relaxation of the quadrupolar nuclides are nearly entirely by means of the quadrupolar mechanism (although there is some dipolar contribution to Ne near the melting point), the interaction of the nuclear quadrupole moment with the electric field gradients generated by deformations of the spherical atoms during collisions. The Xe relaxation, on the other hand, is thought to be dominated by the spin-rotation mechanism in the transient diatomic molecule formed in collisions, and He relaxation is by dipolar interactions. ... 

The dynamics of ion surface scattering at energies exceeding several hundred electronvolts can be described by a series of binary collision approximations (BCAs) in which only the interaction of one energetic particle with a solid atom is considered at a time [25]. This model is reasonable because the interaction time for the collision is short compared witii the period of phonon frequencies in solids, and the interaction distance is shorter tlian the interatomic distances in solids. The BCA simplifies the many-body interactions between a projectile and solid atoms to a series of two-body collisions of the projectile and individual solid atoms. This can be described with results from the well known two-body central force problem [26]. 

Figure Bl.23.2. (a) Shadow cone of a stationary Pt atom in a 4 keV Ne ion beam, appearing with the overlapping of ion trajectories as a fiinction of the impact parameter. The initial position of the target atom that recoils in the collision is indicated by a solid circle, (b) Plot of the nonnalized ion flux distribution density across the shadow cone in (a). The flux density changes from 0 inside the shadow cone, to much greater than l in the focusing region, converging to 1 away from the shadow cone edge, (c) Blocking cones...

Parilis E S ef a/1993 Atomic Collisions on Solids (New York North-Holland)... 

The atoms of the gas, by collision with those of the solid, give up energy to them, and we have to find the way in which the energy of the system is distributed between the gas and the solid when there is equilibrium. 

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