The non destructive determination of iodine in soils and biological materials by high energy gamma-photon activation

A non destructive high energy gamma photon activation technique has been developed for the determination of iodine in a wide range of natural materials. Results are presented and compared with those obtained by independent analytical techniques. Studies of the loss of iodine from soils on heating are also presented. The sensitivity and precision of the technique are discussed and its practical aspects described.     

Landau Hamiltonians with Unbounded Random Potentials

We prove the almost sure existence of a pure point spectrum for the two-dimensional Landau Hamiltonian with an unbounded Anderson-like random potential, provided that the magnetic field is sufficiently large. For these models, the probability distribution of the coupling constant is assumed to be absolutely continuous. The corresponding densityg has support equal to , and satisfies , for some > 0. This includes the case of Gaussian distributions. We show that the almost sure spectrum is , provided the magnetic field B0. We prove that for each positive integer n, there exists a field strength B _n , such that for all B>B _n , the almost sure spectrum is pure point at all energies except in intervals of width about each lower Landau level , for m < n. We also prove that for any B0, the integrated density of states is Lipschitz continuous away from the Landau energiesE _n (B). This follows from a new Wegner estimate for the finite-area magnetic Hamiltonians with random potentials.     

Landau Hamiltonians with random potentials: Localization and the density of states

We prove the existence of localized states at the edges of the bands for the two-dimensional Landau Hamiltonian with a random potential, of arbitrary disorder, provided that the magnetic field is sufficiently large. The corresponding eigenfunctions decay exponentially with the magnetic field and distance. We also prove that the integrated density of states is Lipschitz continuous away from the Landau energies. The proof relies on a Wegner estimate for the finite-area magnetic Hamiltonians with random potentials and exponential decay estimates for the finitearea Green's functions. The proof of the decay estimates for the Green's functions uses fundamental results from two-dimensional bond percolation theory.Supported in part by CNRS.Supported in part by NSF grants INT 90-15895 and DMS 93-07438.Unité Propre de Recherche 7061.     

Determination of trace levels of oxygen by gamma-photon activation

A sensitive activation technique for the determination of trace levels of oxygen in a wide range of materials is described with particular emphasis on the γ-irradiation facilities at AERE Harwell and experience of the use of the technique over a number of years. Procedures for removing surface oxygen contamination prior to determination of bulk oxygen concentrations are given, together with details of the radiochemical separation procedures used for a wide range of materials, and examples of the results obtained.     

The use of non-destructive high energy gamma photon activation for trace element survey analysis

An empirical study has been made of the potential of high energy γ photon activation and high resolution γ-ray spectrometry for the survey analysis of trace elements in a variety of materials. Human blood, urine, bone ash, standard glass (NBS, SRM 612) and air particulates, along with synthetic multi-element standards, have been studied following irradiation with γ photons of maximum energy 17–45 MeV. Elements found to be suited to determination by γ activation include Sb, As, Bi, Cd, Cs, Ca, Ce, Cr, Fe, Au, Pb, Mg, Mo, Ni, Nb, Rb, Sr, Tl, Ti, Tm, Zn and Zr. γ spectra, elemental concentrations measured, and/or limits of detection observed, for the matrices studied are given.     

Smoothness of Correlations in the Anderson Model at Strong Disorder

We study the higher-order correlation functions of covariant families of observables associated with random Schr?dinger operators on the lattice in the strong disorder regime. We prove that if the distribution of the random variables has a density analytic in a strip about the real axis, then these correlation functions are analytic functions of the energy outside of the planes corresponding to coincident energies. In particular, this implies the analyticity of the density of states, and of the current-current correlation function outside of the diagonal. Consequently, this proves that the current-current correlation function has an analytic density outside of the diagonal at strong disorder. Submitted: October 8, 2005; Accepted: February 15, 2006     

CR-invariants and the scattering operator for complex manifolds with CR-boundary

Suppose that M is a CR manifold bounding a compact complex manifold X. The manifold X admits an approximate Kähler–Einstein metric g which makes the interior of X a complete Riemannian manifold. We identify certain residues of the scattering operator as CR-covariant differential operators and obtain the CR Q-curvature of M from the scattering operator as well. Our results are an analogue in CR-geometry of Graham and Zworski's result that certain residues of the scattering operator on a conformally compact manifold with a Poincaré–Einstein metric are natural, conformally covariant differential operators, and the Q-curvature of the conformal infinity can be recovered from the scattering operator. To cite this article: P.D. Hislop et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).