Reflection of atoms

Let us consider the possibility of reflection of electrons by an evanescent laser wave formed due to total internal reflection of femtosecond laser pulses from a dielectric-vacuum interface [4] (Fig. lb). Such a laser field was considered elsewhere [7, 8] to effect the mirror reflection of atoms (references to the latest works on the mirror reflection of atoms can be found in Refs. 9 and 10). The light intensity distribution in the evanescent wave in the vacuum may be represented in the form [11]... 

Finally, the structural modifications of elemental boron exhibit complex extended lattices of cages in the solid state, whereas those of metals possess much simpler close-packed atomic lattices. These differences are a direct reflection of atomic properties and result in the respective nonmetallic and metallic behavior. However, boron combines with most other elements including metals. There are a wide range of metal borides known with stoichiometric as well as nonstoi-chiometric atomic ratios. The amazingly varied interpenetration of the two characteristic structural motifs and the subtly balanced competition between the two modes of solid state bonding found in the metal borides constitutes further justification of our theme. This is discussed in some detail in Section II,C. 

Fig. 6.12 (a) Scheme of a gravitooptical trap based on the inelastic reflection of atoms from an evanescent laser wave (EW, evanescent wave), (b) The atomic transitions between hyperfine-structure states responsible for cooling atoms in the trap. (Adapted from Soding et al. 1995.)... 

In the reflection of atoms by an evanescent wave, the amplitude of the light field does not necessarily change adiabatically slowly in comparison with the relaxation of the internal atomic motion. In this case eqn (7.6) for the light gradient (dipole) force acting on the atom is only the zeroth-order term in an expansion of the force in powers of the inverse interaction time (Ol shanii et al. 1992). The next term in the expansion gives rise to a dissipative part in the gradient force. Such nonadiabaticity can happen if the time of interaction of the atom with the field is comparable to 7 F In this case the specular character of the reflection of atoms can be disturbed. 

Balykin, V., Letokhov, V., Ovchinnikov, Yu., and Sidorov, A. (1988a). Quantum-state selective mirror reflection of atoms by laser light. Physical Review Letters, 60, 2137-2140. 

The Tensimetric Reflection of Atomic Order, L. Eyring, J. Solid State Chem., 1,376-385 (1970). 

For each combination of atoms i.j, k, and I, c is defined by Eq. (29), where X , y,. and Zj are the coordinates of atom j in Cartesian space defined in such a way that atom i is at position (0, 0, 0), atomj lies on the positive side of the x-axis, and atom k lies on the xy-plaiic and has a positive y-coordinate. On the right-hand side of Eq. (29), the numerator represents the volume of a rectangular prism with edges % , y ., and Zi, while the denominator is proportional to the surface of the same solid. If X . y ., or 2 has a very small absolute value, the set of four atoms is deviating only slightly from an achiral situation. This is reflected in c, which would then take a small absolute value the value of c is conformation-dependent because it is a function of the 3D atomic coordinates. 

Because th e calculation of m n Iti-ceiiter in tegrals that are in evitable for ah iniiio method is very difficult and time-con sum in g. Ilyper-Chem uses Gaussian Type Orbital (GTO) for ah initio methods. In truly reflecting a atomic orbital. STO may he better than GTO. so HyperC hem uses several GTOs to construct a STO. The number of GTOs depends on the basis sets. For example, in the minimum STO-3G basis set IlyperGhem uses three GTOs to construct a STO. 

Table 11 illustrates the known closed proton and neutron shells and the predicted closed nuclear shells (shown in parentheses) that might be important in stabilising the superheavy elements. Included by way of analogy are the long-known closed electron shells observed in the buildup of the electronic stmcture of atoms. These correspond to the noble gases, and the extra stabiUty of these closed shells is reflected in the relatively small chemical reactivity of these elements. The predicted (in parentheses) closed electronic stmctures occur at Z = 118 and Z = 168. 

Representative chemical shifts from the large amount of available data on isothiazoles are included in Table 4. The chemical shifts of the ring hydrogens depend on electron density, ring currents and substituent anisotropies, and substituent effects can usually be predicted, at least qualitatively, by comparison with other aromatic systems. The resonance of H(5) is usually at a lower field than that of H(3) but in some cases this order is reversed. As is discussed later (Section 4.17.3.4) the chemical shift of H(5) is more sensitive to substitution in the 4-position than is that of H(3), and it is also worth noting that the resonance of H(5) is shifted downfield (typically 0.5 p.p.m.) when DMSO is used as solvent, a reflection of the ability of this hydrogen atom to interact with proton acceptors. This matter is discussed again in Section 4.17.3.7. 

The conecting term in the pressure reflects the diminution in tire impact velocity of atoms at the containing walls of tire gas due to the attraction of the internal mass of gas, and the volume term reflects the finite volume of the molecules. Data for these two constants are shown in Table 3.4. 

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