Optical Theorem and the Inversion of Cross Section Data for Atom Scattering from Defects on Surfaces

The information content and properties of the cross section for atom scattering from a defect on a flat surface are investigated. Using the Sudden approximation, a simple expression is obtained that relates the cross section to the underlying atom/defect interaction potential. An approximate inversion formula is given, that determines the shape function of the defect from the scattering data. Another inversion formula approximately determines the potential due to a weak corrugation in the case of substitutional disorder. An Optical Theorem, derived in the framework of the Sudden approximation, plays a central role in deriving the equations that conveniently relate the interaction potential to the cross section. Also essential for the result is the equivalence of the operational definition for the cross section for scattering by a defect, given by Poelsema and Comsa, and the formal definition from quantum scattering theory. This equivalence is established here. The inversion result is applied to determine the shape function of an Ag atom on Pt(111) from scattering data.Comment: 29 pages, 9 Postscript figures, more info available at http://www.fh.huji.ac.il/~dan

He Scattering from Random Adsorbates, Disordered Compact Islands and Fractal Submonolayers: Intensity Manifestations of Surface Disorder

A theoretical study is made on He scattering from three fundamental classes of disordered ad-layers: (a) Translationally random adsorbates, (b) disordered compact islands and (c) fractal submonolayers. The implications of the results to experimental studies of He scattering from disordered surfaces are discussed, and a combined experimental-theoretical study is made for Ag submonolayers on Pt(111). Some of the main theoretical findings are: (1) Structural aspects of the calculated intensities from translationally random clusters were found to be strongly correlated with those of individual clusters. (2) Low intensity Bragg interference peaks appear even for scattering from very small ad-islands, and contain information on the ad-island local electron structure. (3) For fractal islands, just as for islands with a different structure, the off-specular intensity depends on the parameters of the He/Ag interaction, and does not follow a universal power law as previously proposed in the literature. In the experimental-theoretical study of Ag on Pt(111), we use first experimental He scattering data from low-coverage (single adsorbate) systems to determine an empirical He/Ag-Pt potential of good quality. Then, we carry out He scattering calculations for high coverage and compare with experiments. The conclusions are that the actual experimental phase corresponds to small compact Ag clusters of narrow size distribution, translationally disordered on the surface.Comment: 36 double-spaced pages, 10 figures; accepted by J. Chem. Phys., scheduled to appear March 8. More info available at http://www.fh.huji.ac.il/~dani

Solvation Effects on Association Reactions in Microclusters: Classical Trajectory Study of H+Cl(Ar)n

The role of solvent effects in association reactions is studied. Classical trajectory studies of the system H + Cl(Ar)n, (n=1,12) are used to investigate the influence of size, structure and internal energy of the "microsolvation" on the H + Cl association reaction. The following effects of solvating the chlorine in an Arn cluster are found. In the H + ClAr system there is a large "third body" effect. The single solvent atom stabilizes the newly formed HCl molecule by removing some of its excess energy. The cross section found at low energies is a substantial fraction of the gas kinetic cross section. The molecule is produced in highly excited vibrational-rotational states. Some production of long-lived HCl...Ar complexes, with lifetimes of 1 ps and larger, is found for the H + ClAr collisions. Weak coupling stemming from the geometry of the cluster is the cause for long lifetimes. These resonance states decay into HCl + Ar. At low collision energies(E=10 kJ/mol) for H + Cl(Ar)12, the H + Cl association shows a sharp threshold effect with cluster temperature. For temperatures of about T=45 K the cluster is liquidlike, and the reaction probability is high. For T<40 K the cluster is solidlike, and there is no reactivity. This suggests the potential use of reactions as a signature for the meltinglike transition in clusters. At high collision energies (E=100 kJ/mol) H atoms can penetrate also the solidlike Cl(Ar)12 cluster. At this energy, the solid-liquid phase change is found not to increase the reaction probability

Quantum Dynamics of the Photodissociation of Hydrogen Halides in Rare Gas Matrices. I. The Initial State

The present study focusses on the rotational motion of HCl molecules embedded in an Ar matrix. Assuming the HCl molecules to occupy substitutional sites in the fcc lattice, rotational wavefunctions for the vibrational and electronic ground state are obtained. Both the energetics and the spatial structures of the wavefunctions are investigated. While the J=0 and the J=1 state show relatively little matrix effects, all levels for J>1 are split by the crystal field. A possible control of the photodissociation dynamics by selection of rotational states of different spatial orientation is discussed

Structure Determination of Disordered Metallic Sub-Monolayers by Helium Scattering: A Theoretical and Experimental Study

An approach based on He scattering is used to develop an atomic-level structural model for an epitaxially grown disordered sub-monolayer of Ag on Pt(111) at 38K. Quantum scattering calculations are used to fit structural models to the measured angular intensity distribution of He atoms scattered from this system. The structure obtained corresponds to narrowly size-dispersed compact clusters with modest translational disorder, and not to fractals which might be expected due to the low surface temperature. The clusters have up to two layers in height, the lower one having few defects only. The relations between specific features of the angular scattering distribution, and properties such as the cluster sizes and shapes, the inter-cluster distance distribution etc., are discussed. The results demonstrate the usefulness of He scattering as a tool for unraveling new complex surface phases.Comment: 5 pages, 3 figures, to appear in Surf. Sci. Lett. Related papers available at http://neon.cchem.berkeley.edu/~dani/He-papers.htm

A Simplified Approach to Optimally Controlled Quantum Dynamics

A new formalism for the optimal control of quantum mechanical physical observables is presented. This approach is based on an analogous classical control technique reported previously[J. Botina, H. Rabitz and N. Rahman, J. chem. Phys. Vol. 102, pag. 226 (1995)]. Quantum Lagrange multiplier functions are used to preserve a chosen subset of the observable dynamics of interest. As a result, a corresponding small set of Lagrange multipliers needs to be calculated and they are only a function of time. This is a considerable simplification over traditional quantum optimal control theory[S. shi and H. Rabitz, comp. Phys. Comm. Vol. 63, pag. 71 (1991)]. The success of the new approach is based on taking advantage of the multiplicity of solutions to virtually any problem of quantum control to meet a physical objective. A family of such simplified formulations is introduced and numerically tested. Results are presented for these algorithms and compared with previous reported work on a model problem for selective unimolecular reaction induced by an external optical electric field.Comment: Revtex, 29 pages (incl. figures

Explaining Horizontal and Vertical Cooperation on Public Services in Michigan: The Role of Local Fiscal Capacity

Michigan local governments engage in a wide range of cooperative activities. Little is known, however, about what factors motivate local governments to engage in intergovernmental cooperation and how local government officials choose among various forms of collaboration. We develop and test a theory of intergovernmental cooperation that explains differences in the factors that lead local governments to engage in horizontal cooperation with other local units versus vertical cooperation with county or state governments. Our primary focus is on fiscal capacity: we hypothesize that limited fiscal capacity leads many local governments, especially townships, to work collaboratively with state or county actors to provide government services. Local governments with greater fiscal capacity, especially cities, are stronger potential partners and so are more likely to collaborate with other local governments using horizontal arrangements. We expect other factors, such as population characteristics, local and regional economic factors, federal or state mandates, and the existence of collaborative partners, to matter as well. We test these hypotheses with survey data collected in 2005 by the Citizens Research Council of Michigan on the mode of service provision employed by 460 Michigan local governments across 115 service categories. We find strong support for our propositions about the linkage between local fiscal capacity and intergovernmental cooperation on public services

Inversion of Randomly Corrugated Surfaces Structure from Atom Scattering Data

The Sudden Approximation is applied to invert structural data on randomly corrugated surfaces from inert atom scattering intensities. Several expressions relating experimental observables to surface statistical features are derived. The results suggest that atom (and in particular He) scattering can be used profitably to study hitherto unexplored forms of complex surface disorder.Comment: 10 pages, no figures. Related papers available at http://neon.cchem.berkeley.edu/~dan

The Curse of Copying , 7 J. Marshall Rev. Intell. Prop. L. 296 (2008)

The concept of “copying” has long been involved with various aspects of intellectual property law, particularly in regard to patents and trademarks. In the absence of legally determined exclusive rights, “copying” is permitted, and is in fact, encouraged. However, because the term “copying” carries an undercurrent of disapproval and unfavorable practices, it is a favorite of patentees looking to portray an accused infringer in the most negative light, especially before a jury. Hence, the curse of “copying.” This article will review the current state of “copying” by addressing the substantive precedent in areas where “copying” has traditionally had a substantive effect—willfulness of any accused infringing conduct and obviousness of the patented invention. With respect to “copying” and willful infringement, this article outlines two important considerations that the precedent is weak upon—“‘copying’ what?” and “‘copying’ when?” Lifting the curse requires care and some courage at trial, in view of a precedential framework that is less than favorable to the accused infringer and the pejorative impact the term “copying” will likely have on the jury and the court. These issues will be discussed and suggestions are advanced throughout as to how one might lift the curse once it is pronounced