Browsing by Author "Frahn, W E"

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    Closed-form description of polarization in elastic and inelastic scattering of light and heavy ions
    (1978) Hill, Timothy Fountain; Frahn, W E
    The present work is an extension of this formalism to vector and tensor polarization in elastic and inelastic scattering of spin-s particles. Moreover, it uses the improved formalism developed by Frahn for the study of elastic and inelastic scattering of heavy ions with zero spin. With regard to inelastic scattering, this implies for instance that Coulomb excitation is included in the theory. This work also uses a modification, due to Kauffmann, of Frahn's formalism, whereby the effects of much stronger real nuclear phase shifts may be included.
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    Direct pion-nucleus interactions in the resonance region
    (1983) Field, Gaynor Mary; Frahn, W E
    The direct reactions of pions with nuclei in the energy region of the πN(3,3) resonance are examined in the eikonal formalism. In particular, the angular and energy dependence of the elastic scattering of πsup(+-) from the calcium isotopes 40Ca, 48Ca is studied, using a detailed phenomenological approach. Excellent agreement is obtained with experimental data. A closely related investigation is also made of the inelastic excitation of low-lying collective states of 40Ca, 48Ca by pions. The resulting one-parameter fits yield deformation lengths which are compared with simple collective model predictions. The total cross-sections for neutral pion scattering from 40Ca, 48Ca in the resonance region are investigated as well, and predictions are made
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    The effect of lattice periodicity on the electronic configuration near a metal surface
    (1976) Andriotis, Antonios N; Wiles, G G; Frahn, W E
    A method is developed for calculating single electron wave functions in a semi-infinite metal. The effect of the lattice periodicity is explicitly taken into account so that the solution in the far interior is consistent with the band structure of the infinite crystal. The solution is sufficiently general to include surface states. The single electron potentials are reconsidered and some new features are discussed. These include the elimination of the singular zero-order Fourier terms of the ion-electron and Hartree potentials which leads to the surface dipole barrier. Also a simple formula is derived for the exchange potential in the zero-order approximation which allows to calculate the exchange potential for wave vectors which have components of velocity parallel to the surface. The method is finally applied to a semi-infinite sodium crystal with a (001) orientation.
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    High-energy approximations to nuclear scattering
    (1973) Schürmann, Bernd; Frahn, W E
    We study high-energy approximations to nuclear scattering. These are based on expansions of the free-particle propagator. We distinguish the eikonal expansion and the Fresnel expansion and interpret their physical meaning in optical terms. A "Fresnel approximation" is defined as a partial sum of the eikonal expansion which describes Fresnel diffraction effects. In Fresnel approximation we derive, by means of a unitary transformation, a closed representation of the scattering amplitude which is formally similar to the corresponding expression irt Glauber's high-energy scattering theory. The corrections to the Glauber model of first order in the reciprocal wave number are given by the second-order eikbnal approximation. These are evaluated explicitly for high energy elastic scattering of protons from light nuclei (⁴He, ¹²C, ¹⁶O).
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    Inelastic nuclear scattering of strongly absorbed particles
    (1967) Potgieter, Johannes Matthys; Frahn, W E
    Closed expressions for differential cross sections are derived from the Austern-Blair theory of inelastic nuclear scattering. These formulae are an extension of the strong absorption model of Frahn and Venter for elastic scattering. AU the well-known features of inelastic angular distributions of composite particles are shown explicitly. These include effects of the multipolarity of the transition, the nuclear interaction, the Coulomb force and the shape of the reflection coefficients in angular momentum space. Analyses of representative sets of experimental data are presented. The results indicate that the Austern-Blair theory. ts remarkably successful in representing the shape of the angular distribution, but tends to underestimate the deformation parameter.
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    Investigating on elastic and inelastic nuclear scattering and polarisation
    (1967) Hahne, Friederich Johannes Wilhelm; Frahn, W E
    Elastic and inelastic scattering of nuclear particles are treated in a partial wave formalism. It is assumed that only a few partial waves having large angular momenta contribute significantly to the scattering amplitude. Parameterised elastic S-matrix elements are used in the Austern-Blair theory to obtain the inelastic S-matrix elements. Relations between elastic and inelastic cross sections and polarisations are derived. The resulting phase rules are discussed. A modification of the Austern-Blair theory makes it possible to describe angular correlation measurements. The theory is compared with optical model and distorted wave Born approximation calculations.
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    A molecular dynamics investigation of a free surface of liquid argon
    (1974) Opitz, Azel Carl Louis; Wiles, G G; Frahn, W E
    A molecular dynamics simulation technique is employed to investigate the equilibrium molecular structure of the liquid-vapour interfacial region for argon at about 124 °K. The density profile through the surface is found to be of a non-monotonic form. The pair distribution function in the surface is also determined and compared to radial distribution functions of the interior liquid. The surface tension and surface energy are also obtained and are found to be in agreement with generally accepted experimental values.
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    Relativistic theory of low energy electron diffraction
    (1973) Feder, Roland; Schaffer, Alfred; Frahn, W E
    In view of investigating the role of spin polarization and further relativistic effects in the diffraction of low energy electrons (LEED) by crystals composed of heavy atoms, a relativistic dynamical theory is developed for calculating LEED intensities and spin polarizations. The presentation of the general framework of solving the boundary value problem for the mixed-representation Dirac equation is followed by the construction of a relativistic KKRZ-type electron-ion-core pseudopotential. The solution of the Dirac equation inside a model crystal that consists of this potential plus a bulk and surf ace optical potential is then derived in an algebraic form. Provision is made for taking into account thermal lattice effects. The computational application of this relativistic LEED theory to the (ool) and the (llo) surface pf tungsten firstly yields intensity results that are found to be in good agreement with experimental data. Secondly, appreciable spin polarization features are predicted, in particular in the specular beam for large angles of incidence on W(ool) at very low energies. It is concluded that measurement of spin polarization in LEED can be expected to be a valuable tool for obtaining additional information about the surface region.
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    A study of nucleon unstable states produced in direct nuclear reactions
    (1974) Hartmann, Kurt Miklos; Frahn, W E
    We study excited states of a nucleus that are unstable against nucleon decay. An expression is derived for the wave function of such an excited nucleus, using the continuum shell-model theory. The bound and resonant states of the shell-model Hamiltonian are treated on an equal footing. The resonant part of this wave function is substituted into the DWBA transition amplitude for stripping reactions. Simple expressions are obtained for the energy spectrum and angular distribution of the uncaptured nucleon(s). Comparison with the corresponding elastic scattering cross section is made and the extraction of· spectroscopic information is discussed. Angular distributions and excitation functions for a number of projectile-target systems are calculated. We also suggest nucleon induced inelastic scattering as an alternative direct reaction mechanism with which these excited states may be studied.
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    Theory of large quantal systems and the quantum theory of measurement
    (1974) Hill, Timothy Fountain; Frahn, W E
    The consistency problem of quantum mechanics may be resolved by regarding any measurement performed on an atomic system as essentially involving an interaction between the atomic system and a macroscopic measuring apparatus and the subsequent behaviour of the apparatus in producing a signal to indicate the result of the measurement. Of central importance in such an approach, therefore, is the study of large quantal systems. Along these lines, two approaches to the consistency problem have been provided; one, by the Italian group of Daneri, Loinger and Prosperi, based on a time-independent ergodic theory of large quantal systems; the other by the Belgian group of George, Prigogine and Rosenfeld, based on a time-dependent theory. In this thesis these two theories are compared and are shown to be equivalent.