Multi-Channel Inverse Scattering Problem on the Line: Thresholds and Bound States

We consider the multi-channel inverse scattering problem in one-dimension in the presence of thresholds and bound states for a potential of finite support. Utilizing the Levin representation, we derive the general Marchenko integral equation for N-coupled channels and show that, unlike to the case of the radial inverse scattering problem, the information on the bound state energies and asymptotic normalization constants can be inferred from the reflection coefficient matrix alone. Thus, given this matrix, the Marchenko inverse scattering procedure can provide us with a unique multi-channel potential. The relationship to supersymmetric partner potentials as well as possible applications are discussed. The integral equation has been implemented numerically and applied to several schematic examples showing the characteristic features of multi-channel systems. A possible application of the formalism to technological problems is briefly discussed.Comment: 19 pages, 5 figure

Beyond the Shade of the Oak Tree: The Recent Growth of Johannine Studies

The recent growth within Johannine studies has developed as a result of several factors. First, the discovery of the Dead Sea Scrolls led to an appreciation of the Jewishness of John’s origin. Second, new approaches to John’s composition have emerged, followed by a larger set of inquiries as to the Johannine tradition’s relation to parallel traditions. This has been accompanied by a fourth interest: the history of the Johannine situation. Fifth, new literary studies have posed new horizons for interpretation, and sixth, theories continue to abound on the identity of the Beloved Disciple. A seventh development involves new ways of conceiving John’s theological features, leading to an eighth: reconsidering John’s historical features and re-envisioning its historical contributions in new perspective

Predictions of total and total reaction cross sections for nucleon-nucleus scattering up to 300 MeV

Total reaction cross sections are predicted for nucleons scattering from various nuclei. Projectile energies to 300 MeV are considered. So also are mass variations of those cross sections at selected energies. All predictions have been obtained from coordinate space optical potentials formed by full folding effective two-nucleon (NN) interactions with one body density matrix elements (OBDME) of the nuclear ground states. Good comparisons with data result when effective NN interactions defined by medium modification of free NN t matrices are used. Coupled with analyses of differential cross sections, these results are sensitive to details of the model ground states used to describe nuclei

A NEW LITHOGRAPHIC TECHNIQUE FOR THE MANUFACTURE OF HIGH RESOLUTION ZONE PLATES FOR SOFT X-RAYS

Une technique de lithographie utilisant un microscope électronique à balayage en transmission est en développement. Cette technique est capable de dessiner avec précision sur des petites surfaces, des motifs dont l'épaisseur des lignes est inférieure à 50 nm. On décrit la méthode et on discute de ses applications à la fabrication de composants d'optique pour la diffraction des rayons-X mous.A lithographie technique using a Scanning Transmission Electron Microscope is being developed. This technique is capable of drawing accurate patterns, with line widths much less than 50 nm, over small areas. The method is described and its application to the manufacture of diffractive optical components for soft X-rays is discussed

THE EFFECTS OF MANUFACTURING INACCURACIES ON THE IMAGING PROPERTIES OF ZONE PLATES

Tous les procédés utilisés pour réaliser des lentilles à zone de Fresnel pour rayons X mous présentent des imperfections de fabrication qui affectent les images. On discute les erreurs possibles en microlithographie par microscopie électronique à balayage en transmission et on en conclut que ce procédé peut être utilisé en donnant une précision suffisante.Any process for making soft X-ray zone plates will have associated manufacturing errors which will affect the imaging properties. The errors possible in a lithographic manufacturing technique using a scanning transmission electron microscope are discussed, and it is concluded that sufficiently accurate zone plates may readily be made