R-3 Repository :: Browsing by Author "Trammell, George T."

Browsing by Author "Trammell, George T."

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A spin-polarized He (2³S₁) metastable atom source for surface research
(1981) Onellion, Marshall; Walters, G. King; Trammell, George T.; Dunning, F. Barry
Surface science has a paucity of probes, particularly for spin-dependent studies. This thesis describes a 2 3S1 He probe, recently developed in this laboratory, that can be used for such investigations. There are three interaction mechanisms such a probe can undergo: resonance ionization/ Auger neutralization, Auger deexcitation, or surface Penning ionization. All are discussed and compared. The important concepts introduced include electronic transitions, factors affecting the interactions, variation of atomic energy levels, and the convolution problem. After introducing these concepts, and describing the resulting physical phenomena, the experimental apparatus is examined. The thesis delineates the rationale for a multi-chamber design and the problems encountered. One diagnostic, a Stern-Gerlach magnet used as a polarization analyzer, is particularly useful and is described in detail. By using the analyzer, we found the beam is approximately 5 percent polarized. Finally, several problems related to the first experiments are discussed.
An investigation of a class of soluble many body problems
(1963) Edwards, Gregg Stanley; Trammell, George T.
This thesis is a report of results so far obtained in an investigation of the properties and characteristics of simple interaction systems whose Hamiltonians are quadratic in their generalized coordinates. The exact solutions of two system types are presented. The first is composed of a simple harmonic oscillator coupled to a uniform lattice of coupled simple harmonic oscillators, or, in the small amplitude approximation, to a beaded string. The second is composed of an arbitrary distribution of oscillators coupled to string. The quantization of linear systems such as those described above is discussed with the result that the solution to the equivalent quantum system in terms of operators is just that of the corresponding classical solution as a function of its initial conditions when these are interpreted as quantum operators. The energy flow along the linear chain is examined in the discussion of the non-exponential decay in dispersive systems. This is compared with the original discussion by Trammell (1956) who pointed out the non-exponential decay of quantum systems and the corresponding behavior of dispersive classical systems.
Classical study of collisions of Rydberg atoms with polar molecules
(1982) Preston, Steven Craig; Lane, Neal F.; Trammell, George T.; Stebbings, Ronald F.
Cross sections for state changing collisions of Rydberg atoms with polar molecules have been calculated using a classical trajectory Monte-Carlo technique. Although the dynamical problem was restricted to two dimensions, useful insights into the full three dimensional system were obtained. For example it was found that at thermal velocities the Rydberg electron can collide with the molecule many times during a angle trajectory. This implies that the impulse approximation, which is commonly used for many Rydberg collision problems, is not valid for this problem, since it cannot account for this effect. Finally, a finite effective range for the dipole interaction was observed, which can be used to make the calculation of three dimensional cross sections more tractable. Without these insights, the three dimensional calculation would have been much more difficult and costly.
Magnetic and chemical effects in x-ray resonant exchange scattering in rare earths and transition metal compounds
(1994) Hamrick, Michael David; Trammell, George T.
The increased availability of synchrotron x-ray sources has facilitated the development of new diffraction techniques based on x-ray resonant exchange scattering (XRES). Resonant electric dipole (E1) and quadrupole (E2) scattering involving virtual transitions between occupied core and empty valence levels is sensitive to the splitting and filling of the valence shells, thus providing information about the spin and orbital distributions of the valence electrons. This sensitivity to electronic properties makes x-ray resonant exchange scattering (XRES) a useful probe of rare earth magnetism as well as effects due to crystal fields (or molecular orbitals) in transition metal compounds. In spiral antiferromagnets, such as holmium, the magnetic sensitivity results in a series of off-Bragg magnetic diffraction peaks. Resonant scattering calculations provide good predictions of the experimental observations, including diffraction conditions, intensities, lineshapes, and polarization dependence. Coefficients giving the magnitude of the scattering are computed for the rare earths. These are then related to effective scattering operators which can be expressed in terms of the angular momentum J in rare earths, making it possible to extend the results of calculations at zero temperature and zero crystal field to finite temperatures and crystal fields. Resonant scattering from transition metal ions in crystal fields includes contributions sensitive to the chemical environment of the ion. The amplitude for E1 resonances exhibits 1- and 2-fold azimuthal patterns in C$\sb1$ and C$\sb2$ symmetries respectively, but cannot distinguish C$\sb3$ and higher order symmetries. E2 amplitudes exhibit these patterns as well as 3- and 4-fold patterns in C$\sb3$ and C$\sb4$ symmetries. The anisotropy in the scattering from a single ion can result in diffraction at Bragg-forbidden reflections which are associated with glide plane or screw axis symmetries in the space group of the crystal. The theory provides a good description of experimental observations in hematite, including the intensity, lineshape, azimuthal pattern, Bragg-forbidden reflection, and scattered polarization.
Magnetic electron emission holography
(1993) Timmermans, Eddy M. E.; Trammell, George T.
I show that the difference in 'spin up' and 'spin down' angular intensities of electrons emitted from inner core levels of atoms in a magnetic crystal is a spin hologram. Its inverse 'pictures' the component of the spins in the neighborhood of the emitter in the direction that the detected electrons are spin analyzed. Measuring the spin difference in three orthogonal directions determines a vector hologram which gives an image of the atomic spin vectors. I develop the theory and illustrate the feasibility and potential of this novel technique by means of model calculations. Furthermore, I give a detailed treatment of the elastic scattering processes that are responsible for the spin holograms, and study the effect of multiple scattering and self-interference which could cause complications.
Multinuclei coherent effects on the widths and energy shifts on low energy neutron resonance
(1993) Hu, Xiaomin; Trammell, George T.
The exponentially decaying semi-stationary states of an assembly of identical classical radiators can have decay rates and resonant frequencies significantly different from that of an isolated radiator. These coherent effects on classical radiators emitting classical waves apply also to the particle processes in quantum limits, leading to the superradiant and subradiant modes with widths(decay rates) greatly enhanced or suppressed and resonant energies significantly shifted. The purpose of this thesis is to investigate these coherent effects on slow neutron-heavy nuclei interaction. A simple field model is introduced to show the coherent effects on the decay rates and resonant energies of two identical decaying states and on the neutron widths and resonant energies of neutron-two nuclei scattering. The latter case is also obtained by multiple scattering theory and is extended to a more general case of neutron-N nuclei scattering. The coherent effects on neutron width near Bragg angle in a crystal are also investigated.
Quasielastic neutron scattering study of water in agarose gels
(1980) Trantham, Eugene Clark; Rorschach, Harold E.; Estle, Thomas L.; Trammell, George T.
The differential cross section for the scattering of thermal neutrons from a solid or liquid contains information about the thermal motion of the nuclei. Measurement of the line shape in liquids for small energy transfer can be interpreted in terms of the mechanism of the diffusive motion and is refered to as the Quasielastic Neutron Scattering (QNS) technique. QNS has been used in this investigation to study the effect of macromolecules on the physical properties of water. A pilot study on the aqueous agarose gel system which made use of a triple axis spectrometer at the Oak Ridge National Laboratory has been completed. Studies have been conducted on the scattering intensity vs. energy transfer as a function of gel concentration and momentum transfer. The concentration dependence was studied by preparing gels of 4%, 9%, 15%, and 2% agarose by weight in H2O. The momentum transfer was studied for values of the scattered wave vector in the range .7A^-1 to 1.9A^-1. The contribution of the agarose to the scattering was determined by measuring the quasielastic spectrum of a 2% agarose in D2O gel. This allowed the scattering contribution of the water to be separated from that of the agarose. These data were analysed using the "bound-free" model for the distribution of correlation times in water. In this model, one fraction is assumed to be identical to pure water and the remaining fraction is assumed to be tightly bound to the agarose macromolecules. This analysis gave an estimate for the "bound" fraction in the 2% HgO gel of 21% +/- 4%. This result is in good agreement with previous nuclear magnetic resonance studies of the diffusion coefficient in agarose gels.
Resonant gamma-ray optics
(1965) Hannon, James Patrick; Trammell, George T.
This thesis treats the coherent interaction of light quantum with a crystal, taking proper account of the mutual interactions of the individual scatterers. Of particular interest is the case of resonant scattering. Using the Feynman approach to quantum electrodynamics, we first develop the general ideas with one- and two-particle systems. The major results are then presented in sections V and VI. [see PDF for formulas] In section V we derive a general quantum expression governing the coherent optical properties of an N particle system: In section VI we use these results to treat resonant optics. It is found that at certain well defined frequencies and angles, the interactions among the resonators can lead to a greatly enhanced coherent width, and therefore to suppression of incoherent processes such as inelastic scattering and absorption. It will be shown that for certain conditions, this width enhancement causes anomolously high transmission or reflection.
Scattering operator for elastic and inelastic resonant x-ray scattering
(1994) Luo, Jin; Trammell, George T.; Hannon, James P.
I have shown that in the fast collision approximation, the scattering operator for resonant x-ray scattering can be expressed in terms of simple spin-orbital moment operators M$\sp{(k)}$(l,s) of the valence shell involved in the resonance. Using these operators, one not only can determine the thermal expectation values of the various spin-orbit multipole moments in the valence shell through the coherent elastic scattering and absorption, but also can obtain the moment-moment correlation functions (Van Hove scattering function S(q,$\omega$)) among the various atoms of the scattering sample from the coherent elastic and inelastic scattering. We have applied the effective scattering operators to the x-ray magnetic scattering in ${La\sb{2-x}Sr\sb{x}CuO\sb4}$ high temperature superconductors, and obtained the relations between the scattering cross-section and the Van Hove scattering function, and the instantaneous correlation function of the spins in these materials. This theory is applicable to the analysis of a broad range of resonant x-ray elastic and inelastic scattering and absorption experiments involving rare earth, actinide and transition elements.
Short range order in lattice dynamics and the feasibility of exafs measurements
(1985) Laaksonen, Reima Tapani; Wang, C. C.; Trammell, George T.; Miettinen, Hannu E.
We studied theoretically the kinetics of a bcc lattice near the critical temperature. Our motivation is to examine the feasibility of using the recently developed time-resolved EXAFS technique to study the lattice dynamics. We derived the kinetic equations using the quasi-chemical approximation and keeping the number of particles constant and allowing only atom-vacancy exchange process. We solved these equations for a relaxation process following a sudden temperature change. Our calculations show that the long-range order exhibits critical slowing-down, as expected. Also the non-linear coupling between short- and long-range order was observed. Because of this non-linear coupling the relaxation of the short-range also slows down near the critical temperature. Our results put stringent conditions on possible experiments.
The charge migration in biomolecules
(1972) Leung, Huen Kwong; Trammell, George T.
The one-dimensional polyconjugated chains of biomolecules are chosen for study. The band theory of the pi-electrons in polymers is reviewed and the experimental results of electric conduction in biomolecular systems are discussed. The migation of charges, especially that of holes which is considered to be important in both conduction phenomena and physical processes of radiation damage, .is studied in a simplified mode]. We use the Wannier function to represent the access charge, say a hole, made initially at some localized region and the time evolution is described by the time - dependent Wannier function. It is shown that the hole or the access electron in the polyconjugated chain of a protein or a DNA macromolecule, will spread out after some time duration t > To , where To~ 10 to the -15 sec for most cases. And the r.m.s. velocity of spreading is approximately equal to the group velocity in the band conduction, it is estimated that vrms = 10 to the 6th ~10 to the 7th cm/sec. The probability of finding the access charge at n unit cells away from the initial place is Pn = |Jn (2Bt/h)|2 where is the Bessel function of first kind and of order n. The effects neglected in this simplified treatment and their expected importances for intra-molecular charge transfer processes are discussed briefly.
The hindered rotation of orbitally-singlet diatomic molecules in ionic crystals
(1982) Das, Pulak Kumar; Estle, Thomas L.; Trammell, George T.; Kilpatrick, John E.
The hindered rotation of orbitally—singlet diatomic molecules in ionic crystals at sites of symmetry has been studied using the Hindered Rotor model. The static crystalline field due to the crystal is expanded in terms of spherical harmonics and symmetrized to transform like the totally symmetric representation of the group. The rotational wave functions are also expanded in terms of spherical harmonics up to about t = 2 and symmetrized to transform like any one of the ten irreducible representations of the ^ group. The eigenvalues are calculated in terms of the molecular moment of inertia for various values of the parameters characterizing the hindering potential.
Theory of elastic x-ray resonant exchange scattering in lanthanides and actinides
(1990) Hamrick, Michael David; Trammell, George T.
Resonant X-ray scattering has been observed in lanthanides and actinides. The observed scattering is sensitive to magnetization, but it arises primarily from electric, rather than magnetic, multipole transitions. The magnetic sensitivity is due to "exchange" effects and to spin-orbit correlations in one or both of the levels involved in the resonance. "Exchange" effects include the exclusion principle, which permits transitions only to vacant orbitals in partially filled shells, and exchange splitting in band states. The elastic scattering amplitude contains terms dependent on the direction of the magnetic moment up to quadratic order for E1 transitions and up to quartic order for E2 transitions. In coherent scattering of X-rays from spiral antiferromagnets, the magnetic sensitivity results in the formation of resonant magnetic satellites associated with the Bragg peaks. This effect provides a new type of probe for the investigation of magnetic structures.
Theory of thermal neutron scattering by nuclear spin waves
(1977) Word, Robert E.; Trammell, George T.
Neutron spectrometers having the capability of resolving the energy of the slow neutron with an error of less than 1^-7 ev have been constructed within recent years, making it possible to measure dynamical processes of correspondingly finer energies. This thesis investigates coupled electronic-nuclear spin waves which are coupled by the hyperfine interaction. The differential cross section and scattered state polarization for the scattering of thermal neutrons from systems described by the Suhl-Nakamura Hamiltonian are developed in the Van Hove correlation function formalism; the relevant correlation functions for the Suhl-Nakamura system are computed.1 The implications of these calculations for the feasibility of detecting nuclear spin wave modes in neutron scattering experiments are discussed.
Use of neutron resonant scatterers as phasors to study molecular dynamics
(1989) Lu, Fan; Trammell, George T.
Neutron resonant scattering in the epithermal regime provides a potential tool for studying molecular dynamics. The theory is established by expressing the scattering function in terms of the Fourier and Laplace transforms of correlation functions which relate to the different positions of two coherent scatterers at different times. The correlation between resonant and non-resonant scatterers is especially useful in solving the scattering "phase" problem and obtaining further dynamic information. The theory is applied to the dynamic study of polyhedron and macro molecules in the linear regime (harmonic).

Browsing by Author "Trammell, George T."

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