Oscillatory structure

Using the accurate theoretical model, the physical origin of the intriguing oscillatory structure of the DCS can be traced. One striking feature that emerges from the scattering calculations is the occurrence of very... 

In conclusion, we have demonstrated that the DCS for the H + D2 —> HD + H reaction exhibits pronounced oscillatory structures in the backward scattering direction both in experimental and in theory. The physical origin of this structure has been traced to the opening of a sequence of quantized transition state thresholds. 

Figure 5 shows the 3-dimensional reconstructed attractors and their projections on canonical planes. The reconstructed phase portraits do not exhibit a defined structure, i.e., it is not toroidal or periodic. As matter of fact, the oscillatory structure is only observed in the Poincare map. The Poincare map is often used to observe the oscillatory structure in dynamical systems. The... 

In the presence of large amount of micelles, the total force between surfaces may oscillate due to the occurrence of oscillatory structural forces. Structural... 

PA. Kralchevsky and N.D. Denkov Analytical Expression for the Oscillatory Structural Surface Force. Chem. Phys. Lett. 240, 385 (1995). 

The production of stable anions by low-energy electron impact has been studied by ESD [22,41,43,44,122,147,154,156,157,166-219] and charge-trapping [154,156,217,220-236] experiments. Below 20 eV, the desorption of stable anions from condensed systems is attributed to DEA, which produces oscillatory structures in the anion yield functions, and... 

Kralchevsky P, Denkov ND (1995) Analytical expression for the oscillatory structural surface force. Chem Phys Lett 240 385-392... 

If the delay time is made very long, an oscillatory structure may be observed in case the sensitivity is high enough. 

We have scanned up to -120 ps and seen no oscillatory structure whatsoever. 

Ion-impact excitation has been widely studied in the rare gases260 270 and for alkali metal ion-atom collisions.271 280 In many cases excitation functions have been measured (i.e., total cross sections as a function of initial relative translational energy), and in some instances the angular dependencies of the differential cross sections for inelastic scattering have been determined. The most striking feature of the results from these experiments is the oscillatory structure that is evident in many of the... 

The oscillatory structure just mentioned has been clearly demonstrated to result from quantum-mechanical phase-interference phenomena. The necessary condition264,265 for the occurrence of oscillatory structure in the total cross section is the existence in the internuclear potentials of an inner pseudocrossing, at short internuclear distance, as well as an outer pseudo-crossing, at long internuclear distance. A schematic illustration of this dual-interaction model, proposed by Rosenthal and Foley,264 is shown in Fig. 37. The interaction can be considered to involve three separate phases, as discussed by Tolk and et al. 279 (1) the primary excitation mechanism, in which, as the collision partners approach, a transition is made from the ground UQ state to at least two inelastic channels U, and U2 (the transition occurs at the internuclear separation 7 , the inner pseudocrossing, in Fig. 37), (2) development of a phase difference between the inelastic channels,... 

Figure 37. Schematic illustration of dual-interaction model for ion-impact excitation resulting in oscillatory structure in total cross section see text.279...

The most striking feature of the broadening is the pronounced oscillatory structure at n 20. While the structure is also present in the shift data, it is there not so pronounced. Oscillations in the self shift and broadening similar to those... 

Theoretical analysis of sheeting in the drainage of thin liquid films has been conducted in [359]. Sheeting dynamics and hole formation (i.e. black spot formation) was described by non-linear hydrodynamic stability analysis based on the equilibrium oscillatory structural component of disjoining pressure. The effect of stepwise thinning, accompanied by formation of holes , was described qualitatively. It is rather arguable whether the term holes for a black spot is appropriate since in 1980 holes in NBF were described as lack of molecules. The use the same term for two different formations is at least confusing. Besides, to have a hole in a CBF is almost as to have a hole in the sea water . 

Stratification of asymmetric aqueous films from NaDoS, CTAB and a commercial surfactant (alpha-olefin sulphonate) solutions at C > Ccmc on a decane substrate have been studied by Bergeron and Radke [236], They found three transitions by thickness in the metastable multilayer films. They observed also stratified CTAB aqueous films on glass. The n(/i) isotherms of stratified films were analysed considering also the oscillatory structural component of disjoining pressure. 

The two components of each of the compound-specific complex functions e or h define the optical properties of a medium completely. The availability of both of the related components renders possible to derive the underlying oscillatory structure as well as to calculate the spectra of the medium to be expected with any well-defined experimental technique. 

One finds that the oscillatory structure of dti (r) observed in Fig. 5.1 is completely due to the density correction Av r, dens), as can be gleaned from Fig. 5.3 . As expected, the functional correction Avx(r,fctl) is only relevant for the high density small-r regime, i.e. the innermost orbitals. In this regime, however, the Av r) from the LDA is rather different from the exact OPM result. In order to demonstrate that both components of Avj (r) contribute to the error of the LDA it is again advantageous to consider Hg Similar to the situation for AE the exact Avx r,fctl) vanishes. As is clear from Fig. 5.4 the LDA does not reproduce the exact Av ir). In particular, Av r,fctl) does not vanish but is of the same order of magnitude as the exact Avjr, dens). 

As indicated before, the strongest quantum effects are observed with slow ions, and produce an oscillatory structure of the low velocity stopping powers. A nice account of this phenomenon was given by Briggs and Pathak [30] who considered the interaction between slowly moving ions and the individual electrons of the medium considered as an electron gas (representing the conduction or valence electron.s in the solid) and applied the methods of quantum-scattering theory. 

One-color NeNePo spectra of Ag measured at 385 nm and an anion temperature of 20 K are shown in Fig. 5 [212]. Trace A (top right) shows the (uncorrected) mass selected Ag yield as function of the delay time between the pump and probe pulses from —4.9 ps to +4.9 ps in steps of 20 fs. Trace A shows a pronounced oscillatory structure, characterized by a period of about 740 fs. The intensity of the maxima decreases for larger delay times and additional, weaker structures are observed at delay times >2.8 ps overlapping the 740-fs... 

Further evidence of the formation of transient anions in the condensed phase Is provided by resolving the vibrational structure of the state of N2 In the v=l, 2, and 3 decay channels In the solid. From this result, shown In Fig. 5b, we can estimate (j4) the average vibrational energy (0.29 eV) and the lifetime (a 3x10" 5 sec.) of the resonance. These values, are close to those found in the gas phase (0.27 eV and 3.5xl0"l5 sec (30), respectively). Furthermore, the shift in the energy of the oscillatory structure... 

The term cosO-jR b) in Eq. (14) introduces oscillatory structure into the momentum density. Using the orientation of the axes defined in Fig. 1,... 

As before, the exponential introduces oscillatory structure with period IuIRab-However, a key difference from homonuclear systems ca = Cg) is that the diffraction features no longer lead to any nodal planes, simply becau% Ca Cb-... 

Figure 2a shows contours of (/>5(p) at R v 2.35 bohr, which is close to the equilibrium geometry. Orbital (j>s now takes the form of a distorted H(ls) function which extends over the boron centre, but which makes relatively little use of the boron basis functions. Accordingly, much of the oscillatory structure disappears from the p-space electron density. 

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