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

Atom Scattering from Disordered Surfaces in the Sudden Approximation: Double Collisions Effects and Quantum Liquids

The Sudden Approximation (SA) for scattering of atoms from surfaces is generalized to allow for double collision events and scattering from time-dependent quantum liquid surfaces. The resulting new schemes retain the simplicity of the original SA, while requiring little extra computational effort. The results suggest that inert atom (and in particular He) scattering can be used profitably to study hitherto unexplored forms of complex surface disorder.Comment: 15 pages, 1 figure. Related papers available at http://neon.cchem.berkeley.edu/~dan

Limited Range Fractality of Randomly Adsorbed Rods

Multiple resolution analysis of two dimensional structures composed of randomly adsorbed penetrable rods, for densities below the percolation threshold, has been carried out using box-counting functions. It is found that at relevant resolutions, for box-sizes, $r$, between cutoffs given by the average rod length and the average inter-rod distance $r_1$, these systems exhibit apparent fractal behavior. It is shown that unlike the case of randomly distributed isotropic objects, the upper cutoff $r_1$ is not only a function of the coverage but also depends on the excluded volume, averaged over the orientational distribution. Moreover, the apparent fractal dimension also depends on the orientational distributions of the rods and decreases as it becomes more anisotropic. For box sizes smaller than the box counting function is determined by the internal structure of the rods, whether simple or itself fractal. Two examples are considered - one of regular rods of one dimensional structure and rods which are trimmed into a Cantor set structure which are fractals themselves. The models examined are relevant to adsorption of linear molecules and fibers, liquid crystals, stress induced fractures and edge imperfections in metal catalysts. We thus obtain a distinction between two ranges of length scales: $r$ where the internal structure of the adsorbed objects is probed, and $< r < r_1$ where their distribution is probed, both of which may exhibit fractal behavior. This distinction is relevant to the large class of systems which exhibit aggregation of a finite density of fractal-like clusters, which includes surface growth in molecular beam epitaxy and diffusion-limited-cluster-cluster-aggregation models.Comment: 10 pages, 7 figures. More info available at http://www.fh.huji.ac.il/~dani/ or http://www.fiz.huji.ac.il/staff/acc/faculty/biham or http://chem.ch.huji.ac.il/employee/avnir/iavnir.htm . Accepted for publication in J. Chem. Phy

The New Censorship: Institutional Review Boards

Do federal regulations on Institutional Review Boards violate the First Amendment? Do these regulations establish a new sort of censorship? And what does this reveal about the role of the Supreme Court

The Administrative Evasion of Procedural Rights

Administrative power does profound harm to civil liberties, and nowhere is this clearer than in the administrative evasion of procedural rights. All administrative power is a mode of evasion, but the evasion of juries, due process, and other procedural rights is especially interesting as it most concretely reveals the administrative threat to civil liberties. In contemporary doctrine, due process and most other procedural rights are understood mainly as standards for adjudication in the courts. Traditionally, however, they were understood, at least as much, to bar adjudication outside the courts. That is, they were understood to block evasions of the courts and their procedural rights. Nonetheless, administrative power evades procedural rights – not only in agency tribunals but also in the courts themselves. The resulting administrative adjudication gives the government ambidextrous paths for enforcement. And it thereby transforms procedural rights from constitutional guarantees into mere options for government power. Turning to theory, this argument about procedural rights is part of a broader thesis about the nature of administrative power. Current doctrine and scholarship presents administrative power as an expression of law, but it makes much more sense to understand it as power – a sort of power that flows in a cascade around pre-existing structures and rights, whether established by the Constitution or the Administrative Procedure Act. Despite its pretense of being administrative “law,” it really is a mode of evasion. Overall, the administrative evasion of procedural rights illustrates how seriously administrative power threatens civil liberties. Whatever one thinks of administrative power as a structural or sociological matter, it is also a civil liberties problem

Vermeule Unbound

My book asks Is Administrative Law Unlawful? Adrian Vermeule answers “No.” In support of his position, he claims that my book does not really make arguments from the U.S. Constitution, that it foolishly denounces administrative power for lacking legislative authorization, that it grossly misunderstands this power and the underlying judicial doctrines, and ultimately that I argue “like a child.” My book actually presents a new conception of administrative power, its history, and its unconstitutionality; as Vermeule has noted elsewhere, it offers a new paradigm. Readers therefore should take seriously the arguments against the book. They also, however, should recognize that the book unavoidably has provoked a strong reaction. The question here, therefore, is whether Vermeule’s heated denunciation is more revealing about the book or about the difficulty of defending administrative power

Trivial Rights

In the summer of 1789, when the House of Representatives was formulating the amendments that became the Bill of Rights, Theodore Sedgwick of Massachusetts argued against enumerating the right of assembly. The House, he urged, might have gone into a very lengthy enumeration of rights; they might have declared that a man should have a right to wear his hat if he pleased, that he might get up when he pleased, and go to bed when he thought proper ... [Was] it necessary to list these trifles in a declaration of rights, under a Government where none of them were intended to be infringed

A Constitutional Right of Religious Exemption: An Historical Perspective

Did late eighteenth-century Americans understand the Free Exercise Clause of the United States Constitution to provide individuals a right of exemption from civil laws to which they had religious objections? Claims of exemption based on the Free Exercise Clause have prompted some of the Supreme Court\u27s most prominent free exercise decisions, and therefore this historical inquiry about a right of exemption may have implications for our constitutional jurisprudence. Even if the Court does not adopt late eighteenth-century ideas about the free exercise of religion, we may, nonetheless, find that the history of such ideas can contribute to our contemporary analysis. The historical evidence concerning religious liberty in eighteenth-century America is remarkably rich and consequently can reveal analytical difficulties and solutions to which we should be attentive when formulating our modern constitutional law

Our Unruly Administrative State

One of the perennial academic rituals of administrative “law” is to explain its compatibility with the rule of law. As surely as seasons pass, academics muster their formidable intellectual resources to reassure us, and themselves, that in pursuing administrative power, they have not abandoned the rule of law. A more immediate justificatory project might be to explain the constitutionality of the administrative state. But notwithstanding valiant efforts, its constitutionality remains in doubt. So a fallback measure of its legitimacy seems valuable. From this perspective, even if the administrative state is not quite constitutional, it can enjoy legitimacy under traditional common law ideas about the rule of law. Jurisprudence thus comes to the aid of aspirations for legality. But can the rule of law rescue the legitimacy of administrative power? The historical difficulty is that the rule of law is not an old common law ideal. The other difficulty, based in contemporary realities, is that administrative power is unruly. It is so unruly that it cannot easily be fit under any rubric of law or even rules

Early Prerogative and Administrative Power: A Response to Paul Craig

What does English experience imply about American constitutional law? My book, Is Administrative Law Unlawful?, argues that federal administrative power generally is unconstitutional. In supporting this conclusion, the book observes that eighteenth-century Americans adopted their constitutions not only with their eyes on the future, but also looking over their shoulder at the past – especially the English past. This much should not be controversial. There remain, however, all sorts of questions about how to understand the English history and its relevance for early Americans. In opposition to my claims about American law, Paul Craig lobs three critiques from across the pond. His two main arguments concern the English history of prerogative and administrative power – though in addition, he makes a conceptual point about the distinction between legislative and judicial power. It will be seen that Craig\u27s account repeatedly misunderstands the history and even the conceptual framework. Nonetheless, his article usefully draws attention to some important issues. This is therefore a good occasion not simply to respond, but more broadly to explore three important questions about early prerogative and administrative power. First, how can one distinguish absolute prerogative power and administrative power in seventeenth- and eighteenth-century England? Second, how did the English resolve the tensions between their inherited types of administrative power and their constitutional principles? Third, how did Americans resolve the tensions between their inherited types of administrative power and their constitutional principles