Atomic, Molecular and Optical Physics Commons^™

Reduced Form For The General-State Multicenter Integral From An Integro-Differential Transform, Jack C. Straton

Physics Faculty Publications and Presentations

In a previous paper Gaussian transforms were utilized to obtain the analytically reduced form for the class of multicenter integrals containing a product of hydrogenic orbitals for s states, Yukawa or Coulomb potentials, and plane waves. In the present paper a related transformation is developed for nonspherical functions, leading to the reduced form for multicenter integrals that include hydrogenic orbitals representing states of arbitrary angular momentum.

High-Velocity Limits For The Ratio Of Double To Single Ionisation Of Helium By Projectiles With Electrons, Y. D. Wang, Jack C. Straton, James H. Mcguire, R. D. Dubois

Physics Faculty Publications and Presentations

The ratio of total double to total single ionisation cross sections, R, by high velocity projectiles containing electrons is examined in the first Born approximation. For ionisation of helium by H+, H0 and He0 impact, it is found that t filt H+ < filt Ho < filt Heo . Connection with Bohr's free-collision model for collisions with projectile electrons is given.

Recoil Distributions In Particle Transfer, James H. Mcguire, Jack C. Straton, W. J. Axmann, T. Ishihara, E. Horsdal

Physics Faculty Publications and Presentations

Classical Thomas peaks in various fast second-order particle transfer processes are quantum mechanically broadened by energy nonconservation in the intermediate states of collision. This quantum broadening is considered in observable velocity distributions of recoil particles.

Post-Prior Symmetrical First-Order T Matrix For Charge Transfer, Jack C. Straton, M. D. Girardeau

Physics Faculty Publications and Presentations

The Fock-Tani Hamiltonian is found for systems containing two protons and one electron. It is shown that a post-prior symmetrical T-matrix element for a⁺ + (b⁺ c^-)→(a⁺ c^-)+b⁺ may be found from that of the simpler proton-proton-electron system if a and b are treated as isospin projections of a single type of nucleon. The Coulomb-exchange contribution to the inelastic (isospin flip) scattering of this system gives a first-order T matrix that is completely symmetrical with respect to post and prior interactions and orthogonalizations, a symmetry of the exact …

Analytically Reduced Form For The Class Of Integrals Containing Multicenter Products Of 1s Hydrogenic Orbitals, Coulomb Or Yukawa Potentials, And Plane Waves, Jack C. Straton

Physics Faculty Publications and Presentations

The class of integrals containing the product of N 1s hydrogenic orbitals and M Coulomb or Yukawa potentials with m plane waves is investigated analytically. The results obtained by Straton (1989) are extended and generalized. It is shown that the dimensionality of the entire class can be reduced from 3m to M+N-1.

Fourier Transform Of The Multicenter Product Of 1s Hydrogenic Orbitals And Coulomb Or Yukawa Potentials And The Analytically Reduced Form For Subsequent Integrals That Include Plane Waves, Jack C. Straton

Physics Faculty Publications and Presentations

The Fourier transform of the multicenter product of N 1s hydrogenic orbitals and M Coulomb or Yukawa potentials is given as an (M+N-1)-dimensional Feynman integral with external momenta and shifted coordinates. This is accomplished through the introduction of an integral transformation, in addition to the standard Feynman transformation for the denominators of the momentum representation of the terms in the product, which moves the resulting denominator into an exponential. This allows the angular dependence of the denominator to be combined with the angular dependence in the plane waves.

Reduced-Mass Fock-Tani Representations For A+ + (B+C-) --> (A+C-) + B+ And First-Order Results For {Abc} = {Ppe, Epe, Μpμ, Μdμ, And Μtμ}, Jack C. Straton

Physics Faculty Publications and Presentations

The Fock-Tani transformation in the Jacobi three ⟶ two-body reduced-mass system is carried out and the first-order T matrix is found to be identical to that for the full three-body transformation. The Fock-Tani transformation in the reduced-mass system in which particle b is fixed at the origin is found to give a first-order T matrix with an error of m_c /m_b in the initial momentum wave function. First-order differential and total cross sections are calculated for a⁺ + (b⁺c^-)⟶(a⁺c^-) + b⁺ where |abc|= { …

Fourier Transform Of The Product Of N One-Center Hydrogenic Orbitals, Jack C. Straton

Physics Faculty Publications and Presentations

Integrating the radial part of the Fourier transform of the product of N hydrogenic orbitals results in an associated Legendre function that can be reduced to a finite series of elementary functions. This transform is found to depend on a polynomial in the wave vector k divided by a binomial in k² raised to a power that is the sum of principle quantum numbers. This form facilitates the analytical reduction of integrals arising from orthogonalization corrections in atomic processes. Transforms for the product of orbital pairs (1s,1s) through (1s,3d) are given …

Fock-Tani Transformation And A First-Order Theory Of Charge Transfer, P. C. Ojha, M. D. Girardeau, J. D. Gilbert, Jack C. Straton

Physics Faculty Publications and Presentations

A unitary (Fock-Tani) transformation of the second-quantized Hamiltonian breaks the interaction into its component parts, e.g., elastic scattering, inelastic scattering, rearrangement interaction, etc. The interaction for a particular process is ‘‘weaker’’ than the overall interaction; this is reflected in certain orthogonality corrections which appear in a perturbation expansion of the T-matrix element. As a result, the internuclear potential makes a negligible contribution of order m_e/m_p to the first-order amplitude for charge transfer. We find very good agreement with experimental and the best available theoretical results for the total cross section for the reaction p+H(1s)→H(1s)+p for …

The Application Of Exact Electrodiffusion Theory To Ion Transport Across Lipid Bilayer Membranes, Scott Cohen

Dissertations and Theses

The question of how ions interact with each other and with the potential energy barrier in thin lipid bilayer membranes has interested investigators for several years. The application of electrodiffusion theory to the study of this question is the central theme of this work. We have calculated current-voltage curves for barriers of various shapes and heights, in each case by means of numerically integrating the exact electrodiffusion equation as well as this same equation in the constant field approximation. We have also calculated the total charge in the membrane for the same conditions under which we have calculated the current-voltage …

Electrostatic Tem Studies Of Magnetic Domains In Thin Iron Films, Hideaki Karamon

Dissertations and Theses

An electron microscope with electrostatic lenses was used for high resolution studies of magnetic domains in thin iron films.

Observation methods used to determine the directions of local magnetization in iron thin films were the Lorentz method and the Foucault method.

We studied how Bloch line-crosstie pairs and crosstie main walls behave in applied, in-plane magnetic fields. We found that crosstie main walls remain unchanged until crosstie density goes nearly to zero when the field is applied perpendicular to the main wall. A twisted type of domain appears where crossties disappear.

Effective Force Constant Ratios: Iron In Iridium And Rhodium, Dennis Munsterman

Dissertations and Theses

Classical methods of analyzing heat capacity data for the characteristic moments of the frequency distribution are applied to iridium and rhodium. Impurity moments are determined from high and low temperature f values. These moments are combined by modern theory to estimate the magnitude of the host-host to host-impurity force constant ratio. Ratios of the various host moments are also examined.

The Dynamics Of An Hcp Crystal With A Substitutional Defect, Pramod C. Karulkar

Dissertations and Theses

We examine the problem of the dynamics of a hexagonal close packed crystal with a single substitutional impurity. The effects of the mass and the force constant changes due to the introduction of the impurity atom are taken into account assuming nearest neighbor interactions under the harmonic approximation. Using Green’s function and group theoretical methods, the equations of motion for the perturbed normal modes are obtained in an exact form. The calculations are performed by allowing for very general force constant changes which can have noncentral as well as central contributions. Further, by assuming central forces, we simplify the equations …

Evidence For The Existence Of Two Stable Sites For Cobalt Impurity Atoms In Aluminum, Arun Venkatachar

Dissertations and Theses

Using Fe⁵⁷Mössbauer spectroscopy, two alternative sites occupied by cobalt (10^-4 at. % ) impurity atoms in aluminum have been isolated. The substitutional site A is the stable position after annealing the sample above 840 K, followed by a rapid quench. The impurity atoms in site A are characterized by a single line Mössbauer spectrum (indicative of a cubic environment), a room-temperature f = 0.502 (r. m. s. displ. 0.071 A) and an I. S. (reI. to Fe) = -0.421 mm/sec. For anneals below 770 K the cobalt atoms migrate to site B, which is characterized by a …

Crystal Structure Determination Of Β-Lactoglobulin From Electron Micrographs, Richard Roeter

Dissertations and Theses

Often electron micrographs exhibit a repeating structure. Sometimes this repeating structure satisfies the definition of a crystal in that it has a three dimensional repeating structure. If the unit cell structure of this repeating structure can be determined it can be used to help categorize different sections of a particular sample. In some cases, the use of optical diffraction analysis of electron micrographs with repeating structure is a method of determining the unit cell structure.

Samples of β-Lactoglobulin were prepared for viewing in the electron microscope using both the crystalline material and carbon replicas of the crystal surface. Because the …

Investigation Of The Alpha-Sub-Gamma Phase In Alnico 6, Cortez Samuel

Dissertations and Theses

The purpose of this research project was to study the αᵧ phase in Alnico 6. Other phases were studies for comparison. Also the effect of an applied magnetic field on the formation of the αᵧ phase was investigated.

Three single crystals of Alnico 6 were heat treated for one hour--one at 1250°C, one at 1000°C, and one at 800°C--and water-quenched. The microstructure of each sample was observed with the optical microscope, and X-ray diffraction patterns were taken to determine the crystal structure of the phases present.

Several single crystal samples of Alnico 6 were heat treated at 1000°C and furnace-cooled. …

Electron Optical Study Of A Secondary Electron Multiplier, Chang Min Shen

Dissertations and Theses

Electron orbital theory was applied to the design of the geometrical structure of an electron multiplier for an image intensifier. A special structure satisfying production requirements was studied. Electron optical calculations consisted of determining the potential distribution and tracing the electron trajectories. Liebmann's procedure was used to solve Laplace's equation with constant potentials on the multiplier electrodes as boundary conditions. The trajectories were determined by solving the equation of motion in an electrostatic field using a Runge-Kutta procedure. The initial conditions for the trajectories were the initial energies, initial positions, and the initial directions of the secondary electrons. The plotted …