An algebraic approach to multiparameter spectral theory

Root subspaces for multiprameter eigenvalue problems are described using coalgebraic techniques. An algorithm is given to construct bases for the root subspaces.

     

Measurement of gamow-teller strength for 176Yb --> 176Lu and the efficiency of a solar neutrino detector

We report a 0 degrees 176Yb(p,n)176Lu measurement at IUCF where we used 120 and 160 MeV protons and the energy dependence method to determine Gamow-Teller (GT) matrix elements relative to the model independent Fermi matrix element. The data show that there is an isolated concentration of GT strength in the low-lying 1(+) states making the proposed Low Energy Neutrino Spectroscopy detector (based on neutrino captures on 176Yb) sensitive to pp and 7Be neutrinos and a promising detector to resolve the solar neutrino problem.     

The diffraction of elastic waves by an imperfect fusion bond

We consider diffraction by a semi-infinite crack located alonga fusion interface between two differing elastic media. Twotypes of crack, namely open and partially closed cracks, areinvestigated. An open crack is modelled by a stress-free contactboundary condition and a partially closed crack is modelledby a spring contact boundary condition. For the latter, thejump in the stress across the crack is assumed to be proportionalto the jump in the displacement across the crack. This situationarises in, for example, a K-weld where the fine grain of theparent material (for example, ferritic or forged austeniticsteel) is in stark contrast with the coarse-grained weld metal(for example, austenitic weld metal). In the metal weld thedirection of the grain axis varies through the metal. However,diffraction is a local phenomenon and so the austenitic steelis assumed to have a zonal axis so that it may be modelled bya transversely isotropic composite. The ferritic or forged austeniticsteel will be modelled as an isotropic material.     

Irreducible Semigroups of Matrices with Eigenvalue One

We study groups and semigroups of n x n matrices with the property that each matrix has a fixed point, i.e., 1 is an eigenvalue of each matrix. We show that for n=3 and $n\geq 5$ there are irreducible matrix groups and irreducible semigroups of nonnegative matrices with this property. In fact, for n = 3 we determine the structure of any such semigroup. We also present additional hypotheses implying reducibility.     

Second Root Vectors for Multiparameter Eigenvalue Problems of Fredholm Type

A class of multiparameter eigenvalue problems involving (generally) non self-adjoint and unbounded operators is studied. A basis for the second root subspace, at eigenvalues of Fredholm type, is computed in terms of the underlying multiparameter system. A self-adjoint version of this result is given under a weak definiteness condition, and Sturm-Liouville and finite-dimensional examples are considered.

     

Density functional calculation of the 2D potential surface and deuterium isotope effect on 13C chemical shifts in picolinic acid N-oxide. Comparison with experiment

2D free energy surfaces V = V(rOH, rO...O) for the intramolecular H-bond in the title compound were calculated by the DFT method and used in the calculation of primary and secondary chemical shifts of the compound dissolved in chloroform and acetonitrile. Solvent effects were accounted for by the SCRF/PCM method. The corresponding two-dimensional chemical shift surfaces with included solvent reaction field were obtained using the Continuous Set of Gauge Transformations approach at the B3LYP/6-311+G(2d,2p) level of theory. The chemical shifts were estimated as quantum averages along the two internal coordinates in the hydrogen bond and along several vibrational levels according to the Boltzmann distribution at room temperature. Fairly good agreement between the experimental and calculated isotope effects was obtained. 1D and 2D NMR spectra of solutions of picolinic acid N-oxide and its deuterated analogue were recorded and assigned.     

Root vectors for geometrically simple two-parameter eigenvalues

A class of two-parameter eigenvalue problems involving generally nonselfadjoint and unbounded operators is studied. A basis for the root subspace at a geometrically simple eigenvalue of Fredholm type is computed in terms of the underlying two-parameter system. Comparison with Faierman's work on two-parameter boundary value problems of Sturm-Liouville type is given as an application.

     

Breakup of 8B and the 7Be(p, γ)8B reaction

The calculated rate of events in some of the existing solar neutrino detectors is directly proportional to the rate of the ⁷Be(p, γ)⁸B reaction measured in the laboratory at low energies. However, the low-energy cross sections of this reaction are quite uncertain as various measurements differ from each other by 30–40%. The Coulomb dissociation process which reverses the radiative capture by the dissociation of ⁸B in the Coulomb field of a target, provides an alternate way of accessing this reaction. While this method has several advantages (like large breakup cross sections and flexibility in the kinematics), the difficulties arise from the possible interference by the nuclear interactions, uncertainties in the contributions of the various multipoles and the higher order effects, which should be considered carefully. We review the progress made so far in the experimental measurements and theoretical analysis of the breakup of ⁸B and discuss the current status of the low-energy cross sections (or the astrophysical S-factor) of the ⁷Be(p, γ)⁸B reaction extracted therefrom. The future directions of the experimental and theoretical investigations are also suggested. Work supported by EPSRC, UK, grant nos J/95867 and L/94574.