Fredholm determinants and inverse scattering problems

The Gel'fand-Levitan and Marchenko formalisms for solving the inverse scattering problem are applied together to a single set of scattering phase-shifts. The result is an identity relating two different types of Fredholm determinant. As an application of the method, an asymptotic formula of high accuracy is derived for a particular Fredholm determinant that determines the level-spacing distribution-function in the theory of random matrices.Research sponsored by the National Science Foundation, Grant No. GP-40768X.     

Intersections of t-reguli,rational curves,and orthogonal Latin squares

The celebrated net-embedding theorem of R.H. Bruck asserts that a net with a large number of parallel classes, i.e., a net with small deficiency, can be embedded in an affine plane. The only known class of examples of unembeddable nets of small deficiency has been constructed by geometry, using partial spreads of PG(3, q). In this note we attempt to generalize that discussion to PG(n, q), with particular emphasis on the case n=5.     

Self-consistent LCAO local density determination of anisotropic compton profile and X-ray structure factors in diamond

Our newly developed fully Self-Consistent Numerical Discrete Variational Method (which exactly treats all non-spherical parts of the crystal potential) yields X-ray scattering factors and anisotropies in the Compton profile of diamond in very good agreement with experiment.     

The ft value for the superallowed Fermi decay 38mK(β+)38Ar

The threshold energy for the reaction ³⁵Cl(α, n)^38mK has been measured to be 6674.8±3.2 keV and the Q-value for the reaction ³⁵Cl(α, p)³⁸Ar to be 837.2±2.4 keV. From the measurements a value of 5021.2±3.4 keV was obtained for the end-point energy of the decay ^38mK(b⁺)³⁸Ar. The half-life was measured as 925.6±0.7ms and hence an “effective” $\text{?t}$ value was calculated, giving the result 3106±10 s with the inclusion of outer radiative corrections to order Z²α³ and 3088±10 s allowing also for calculated charge-dependent effects.     

Molecular simulation and experimental study of substituted polyacetylenes: fractional free volume, cavity size distributions and diffusion coefficients

Glassy, disubstituted acetylene-based polymers exhibit extremely high gas permeabilities and high vapor/gas selectivities, which is quite unusual for conventional glassy polymers such as polysulfone. Diffusion coefficients of poly[1-phenyl-2-[p-(trimethylsilyl)phenyl]acetylene] (PTMSDPA) and poly[diphenylacetylene] (PDPA) were obtained using both molecular simulation and experimental techniques. PTMSDPA, a disubstituted glassy acetylene-based polymer, exhibits higher diffusivity than its desilylated analogue, PDPA. Simulation results are in good agreement with experimental data. Cavity size (free volume) distributions of both polymers are also obtained using an energetic-based algorithm (in't Veld et al., J. Phys. Chem. B 2000, 104, 12028) developed recently. Larger cavities in PTMSDPA contribute to its higher diffusivity, and higher permeability.     

Angle-dependent x-ray magnetic circular dichroism from (Ga,Mn)As: anisotropy and identification of hybridized states

Remarkably anisotropic Mn L2,3 x-ray magnetic circular dichroism spectra from the ferromagnetic semiconductor (Ga,Mn)As are reported. States with cubic and uniaxial symmetry are distinguished by careful analysis of the angle dependence of the spectra. The multiplet structures with cubic symmetry are qualitatively reproduced by calculations for an atomiclike d5 configuration in tetrahedral environment, and show zero anisotropy in the orbital and spin moments within the experimental uncertainty. However, hybridization with the host valence bands is reflected by the presence of a preedge feature with a uniaxial anisotropy and a marked dependence on the hole density.