Semiempirical determination of the atom-surface interaction

We discuss three methods of determining V(z), the lateral average (G = 0 Fourier component) of the atom-surface interaction, from the bound state spectrum found in beam scattering. One method uses the Rydberg-Klein-Rees technique, which yields the width of the potential (i.e., separation of classical turning points) as a function of energy. This method incorporates also the known asymptotic form V ～ ?C₃z^?3, whereC₃ is derived from the polarizability and dielectric function of atom and solid, respectively. The second method uses a hybrid potential, constructed from a Morse potential with shifted zero of energy connected to the asymptotic form,?C₃z^?3, requiring continuity of V and $\text{d}\text{V}\text{d}\text{z}$. The third potential is a Lennard-Jones 3–9 interaction. Results are presented for H and He scattering from LiF and NaF.     

Six-dimensional Dirac equation

The Dirac equation in six-dimensional relativity (three space and three time) is considered and shown to correspond to particles which have spatial spin-1/2 and temporal spin-1/2. Explicit forms of the spinor transformation are found. Plane wave solutions are obtained and their properties are given in terms of spatial and temporal spins and helicities. An expression is found for the charge conjugation operator.     

Giant resonances in f-p shell nuclei studied by inelastic scattering of 80 MeV 3He ions

Spectra of ⁴⁸Ti, ⁵⁶Fe, ⁵⁹Co and ⁶⁰Ni have been investigated for excitation energies of 10–20 MeV by inelastic scattering of 80 MeV ³He particles. Broad peaks with excitation energies of about $\text{63±1 A}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>3</mtext>}}\text{MeV}$ and FWHM of 6 MeV have been observed. Much narrower satellite peaks occur at excitation energies about $\text{51±1 A}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>3</mtext>}}\text{MeV}$. The angular distributions of the sum of these peaks were compared to extended optical model DWBA calculations which confirm the predominant L = 2 character of the GR. A tentative assignment of L = 2 or 4 was made for the 13.5 MeV satellite peak in ⁵⁶Fe. We see no definite evidence for the presence of an L = 1 GR component.     

High resolution proton magnetic resonance spectra of heterocyclics 1,4-benzodithiin and 1,4-benzodioxin

The proton magnetic resonance spectra of 1,4-benzodithiin and 1,4-benzodioxin have been fully analyzed. The effects of the substituent heteroatoms on the chemical shifts of the various protons in the two molecules have been discussed.     

A method for predicting the stability characteristics of three-term homogeneous recurrence relations

A simple method is presented which determines the numerical stability or instability in the computation of any solution of a three-term homogeneous linear difference equation of order m in terms of the size of a single parameter. The method is illustrated by application to a second order and to a third order difference equation. Excellent agreement with predictions is reported.     

A reduced gradient method for quadratic programs with quadratic constraints and lp-constrained lp-approximation problems

A dual algorithm is developed for solving a general class of nonlinear programs that properly contains all convex quadratic programs with quadratic constraints and l_p-constrained l_p-approximation problems. The general dual program to be solved has essentially linear constraints but the objective function is nondifferentiable when certain variables equal zero. Modifications to the reduced gradient method for linearly constrained problems are presented that overcome the numerical difficulties associated with the nondifferentiable objective function. These modifications permit ‘blocks’ of variables to move to and away from zero on certain iterations even though the objective function is nondifferentiable at points having a block of variables equal to zero.     

An improved acousto-optical light modulator

A simplification of the conventional acousto-optical light modulator and deflector arrangement is presented. The collimating lens, modulator, and focusing lens are combined into one unit — a modulator whose faces are curved rather than plane.     

On causal dynamics without metrisation: Part II

An interpretation of an ordering relation as an operator is constructed by appeal to the notion of homotopy. A metric-free definition of a causal ordering is given, after carefully investigating, by means of the notion of ordered sets, what is crucial to the notion of causality. A metric-free condition is derived that a causal ordering operator must satisfy, and a concrete realisation is found to exist that embodies the paraphernalia of Minkowski space with Zeeman's fine topology. Moreover, it is seen that a coordinate space used to give a cartography to causally related events must have at least a hyperbolic metric.This work was undertaken and completed whilst the author was at the Post Office Research Station, Dollis Hill, London, N.W.2.     

Far infrared spectrum of acrylonitrile

Two bands in the far infrared spectrum of acrylonitrile have been studied under moderately high resolution. Accurate band centers are obtained and the rotational constants are analyzed in terms of Coriolis coupling between the in-plane and out-of-plane bending modes.