Diffraction of atoms

The diffraction of atoms by both light waves and material structures plays an important part in atom optics, especially in the development of atomic interferometers, coherent atom beam splitters, etc. 

It is possible to combine the reflection and diffraction of atoms by using a standing evanescent wave (Hajnal and Opat 1989). The required optical wave field can be produced by total internal reflection of a laser beam at the surface of a refractive medium and retroreflecting of the light back along its original path. The evanescent field decreases exponentially in the direction perpendicular to the surface and is 

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Lapshin D, Balykin V, Letokhov V. (1997) Diffraction of atoms by an evanescent wave grating formed by a periodic surface structure. Laser Physics 7 361. 

P.E. Moskowitz, P.L. Gould, S.R- Atlas, D.E. Pritchard Diffraction of an atomic beam by standing-wave radiation. Phys. Rev. Lett. 51, 370 (1983) P.L. Gould, G.A. Ruff, D.E. Pritchard Diffraction of atoms by light The near-resonant Kapitza-Dirac effect. Phys. Rev. Lett. 59, 827 (1986)... 

The Talbot effect plays an important role in atomic interferometry (see Section 7.5). Also, this effect provides an excellent example of near-field atom optics because selfimaging of the grating take place in the near field, where the curvature of the atom wave fronts must be considered (Fresnel diffraction of atomic waves). 

Gould, P. I., Ruff, G.A., and Pritchard, D. E. (1986). Diffraction of atoms by light the near-resonant Kapitza-Dirac effect. Physical Review Letters, 56, 827-830. Goy, P., Raimond, J. M., Gross, M., and Haroche, S. (1983). Observation of cavity-enhanced single-atom spontaneous emission. Physical Review Letters, 50, 1903-1906. 

Hajnal, J. V., and Opat, G. I. (1989). Diffraction of atoms by standing light wave—a reflection grating for atoms. Optics Communications, 71, 119-124. 

The diffraction pattern consists of a small number of spots whose symmetry of arrangement is that of the surface grid of atoms (see Fig. IV-10). The pattern is due primarily to the first layer of atoms because of the small penetrating power of the low-energy electrons (or, in HEED, because of the grazing angle of incidence used) there may, however, be weak indications of scattering from a second or third layer. 

Lennard-Jones J E and Devonshire A F 1936 Diffraction and seiective adsorption of atoms at crystai surfaces Nature 137 1069... 

It is relatively straightforward to detemiine the size and shape of the three- or two-dimensional unit cell of a periodic bulk or surface structure, respectively. This infonnation follows from the exit directions of diffracted beams relative to an incident beam, for a given crystal orientation measuring those exit angles detennines the unit cell quite easily. But no relative positions of atoms within the unit cell can be obtained in this maimer. To achieve that, one must measure intensities of diffracted beams and then computationally analyse those intensities in tenns of atomic positions. 

With XRD applied to bulk materials, a detailed structural analysis of atomic positions is rather straightforward and routine for structures that can be quite complex (see chapter B 1.9) direct methods in many cases give good results in a single step, while the resulting atomic positions may be refined by iterative fitting procedures based on simulation of the diffraction process. 

In this section, we concentrate on the relationship between diffraction pattern and surface lattice [5], In direct analogy with the tln-ee-dimensional bulk case, the surface lattice is defined by two vectors a and b parallel to the surface (defined already above), subtended by an angle y a and b together specify one unit cell, as illustrated in figure B1.21.4. Withm that unit cell atoms are arranged according to a basis, which is the list of atomic coordinates within drat unit cell we need not know these positions for the purposes of this discussion. Note that this unit cell can be viewed as being infinitely deep in the third dimension (perpendicular to the surface), so as to include all atoms below the surface to arbitrary depth. 

Jackson B and Metiu H 1985 An examination of the use of wave packets for the calculation of atom diffraction by surfaces J. Chem. Phys. 83 1952... 

Steinhauer and Gasteiger [30] developed a new 3D descriptor based on the idea of radial distribution functions (RDFs), which is well known in physics and physico-chemistry in general and in X-ray diffraction in particular [31], The radial distribution function code (RDF code) is closely related to the 3D-MoRSE code. The RDF code is calculated by Eq. (25), where/is a scaling factor, N is the number of atoms in the molecule, p/ and pj are properties of the atoms i and/ B is a smoothing parameter, and Tij is the distance between the atoms i and j g(r) is usually calculated at a number of discrete points within defined intervals [32, 33]. 

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