Doorway state approach to optical potential scattering

We extend and apply the doorway state approach in the context of optical potential scattering. This entalls construction of doorway basis states for resolving the transition operator. We focus on analytic solutions to comparatively simple problems in optical potential scattering. Both low and high energy limits are considered, and absorptive interactions are treated; both on- and off-shell partial wave amplitudes are constructed. Further, the full scattering amplitude in the high energy limit is calculated directly in the doorway expansion. With our analytic results, it is possible to identify the physical parameters controlling convergence of the doorway expansion. The same parameters apply over the entire range of cases studied. These parameters are related simply to the target geometry and to the interaction strength. For interactions appropriate to hadron-nucleus scattering, convergence of both on- and off-shell amplitudes is very rapid.     

Eine Erweiterung des Cornu-Diagramms auf den Fall einer teildurchlässigen und phasenschiebenden Halbebene

Cornu's diagram for the graphical evaluation of the intensity distribution in the Fresnel diffraction phenomena behind an opaque half-plane is generalized to the case of diffraction by a half-plane with arbitrary values of transparency and phase-shift.     

Halbdrehungen im Raum

Ohne Zusammenfassung     

Integrated Density of States For Random Metrics on Manifolds

We study ergodic random Schrödinger operators on a coveringmanifold, where the randomness enters both via the potentialand the metric. We prove measurability of the random operators,almost sure constancy of their spectral properties, the existenceof a self-averaging integrated density of states and a Pastur–ubintype trace formula. 2000 Mathematics Subjects Classification35J10, 58J35, 82B44.     

Cationic polymerization of p-substituted α-methylstyrenes. III. Effect of polymerization conditions on tacticity and molecular weight for p-chloro-α-methylstyrene

The cationic polymerization of p-chloro-α-methylstyrene was investigated for the effect of initiator and solvent on polymer tacticity, molecular weight, and molecular weight distribution. The products were generally crystalline polymers of 80–90% syndiotactic content with fairly high molecular weights and broad molecular weight distributions. Tacticities and molecular weight distributions followed similar patterns suggesting that the effect of reaction conditions on ionpair end-group structures was the dominant factor.     

Uniform existence of the integrated density of states for models on $${\mathbb{Z}}^d$$

We provide an ergodic theorem for certain Banach-space valued functions on structures over , which allow for existence of frequencies of finite patterns. As an application we obtain existence of the integrated density of states for associated discrete finite-range operators in the sense of convergence of the distributions with respect to the supremum norm. These results apply to various examples including periodic operators, percolation models and nearest-neighbour hopping on the set of visible points. Our method gives explicit bounds on the speed of convergence in terms of the speed of convergence of the underlying frequencies. It uses neither von Neumann algebras nor a framework of random operators on a probability space.      

Structure of neutron-rich Be and C isotopes

The structure of neutron-rich beryllium isotopes has been investigated using different heavy-ion-induced transfer reactions. In neutron transfer reactions, the population of final states shows a strong sensitivity to the chosen core nucleus, i.e., the target nuclei ⁹Be or ¹⁰Be, respectively. Molecular rotational bands up to high excitation energies are observed with ⁹Be as the core due to its pronounced 2α-cluster structure, whereas only a few states at low excitation energies are populated with ¹⁰Be as the core. For ¹¹Be, a detailed investigation has been performed for the three states at 3.41, 3.89, and 3.96 MeV, which resulted in the most probable spin-parity assignments 3/2⁺, 5/2^?, and 3/2^?, respectively. Furthermore, we have studied particle-hole states of ¹⁶C using the ¹³C(¹²C, ⁹C)¹⁶C reaction and found 14 previously unknown states. Using the ¹²C(¹²C, ⁹C)¹⁵C reaction, five new states were observed for ¹⁵C.     

Algebras of Random Operators Associated to Delone Dynamical Systems

We carry out a careful study of operator algebras associated with Delone dynamical systems. A von Neumann algebra is defined using noncommutative integration theory. Features of these algebras and the operators they contain are discussed. We restrict our attention to a certain C ^*-subalgebra to discuss a Shubin trace formula.     

Structures of the I-, II- and H-methane clathrates and the ice-methane clathrate phase transition from quantum-chemical modeling with force-field thermal corrections

Methane hydrates with the three clathrate structures I, II, and H are studied by quantum-chemical methods. Hybrid density-functional theory B3LYP computations using periodic boundary conditions are combined with force-field methods for the thermal energy effects to calculate energetic, thermodynamic, and structural properties. The pressure dependencies for the crystal structures, lattice energies, and guest molecule interactions are derived. The quantum-chemical geometry optimizations predict too small cell volumes as compared to experimental data, but by including zero-point energy and thermal energy effects, we find the cell volumes increase and the correct densities are obtained. The phase transition from MH-I to ice Ih and methane was computed and found to occur at about 9.7 MPa.