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Two Photon Resonant Picosecond Pulse Propagation in Lithium Vapor
The work of this dissertation has been to prove that the coherence of multiphoton excitation can be studied by an appropriately phased and time delayed sequence of pulses. An application of this fundamental study of coherence has been made for the enhancement of third harmonic generation. The coherent recovery of the energy lost to the two photon absorption process enalled a larger propagation distance for the fundamental than in an interaction which is incoherent or coherent, but not using a 90 degree phase shifted pulse pair. Phase matching over this longer propagation distance gave an enhancement of third harmonic generation.
Picosecond Laser-Induced Transient Gratings and Anisotropic State-Filling in Germanium
We present a comparative theoretical study of the transient grating coherent effects in resonant picosecond excitation-probe experiments. Signals in both the probe and conjugate directions are discussed. The effects of recombination, non-radiative scattering and spatial and orientational diffusion are included. The analysis is applied to both a molecular and to a semiconductor model. Signal contributions from concentration and orientational gratings are distinguished and their temporal natures discussed. The theory is used to explain our recent observations in germanium. Included are discussions of picosecond transient grating self-diffraction measurements that can be understood in terms of an orientational grating produced by anisotropic (in k-space) state-filling. Though there have been predictions and indirect experimental evidence for isotropic state-filling in germanium, this is the first direct experimental indication of anisotropic state-filling in a semiconductor.
Measurement of the Rate Coefficients for the Bimolecular and Termolecular Charge Transfer Reactions of He₂⁺ with Ne, Ar, N₂, CO, CO₂, and CH₄
The problem with which this investigation is concerned is that of measuring the rate coefficients for termolecular charge transfer reactions of He2+ in atmospheric pressure afterglows with the minority reacting species. Of particular interest was the discovery that the presence of a third body can change an improbable charge transfer reaction involving He+2 into a very probable one, as in the case of the reaction with argon. For example, in Tables II and II it was shown that less than a 300 torr pressure of helium was required to double the effective rate of reaction of argon with He2+ while over 3000 torr was required for CH4. The sensitivity of the method has been sufficient to detect termolecular components as small as 2 x 10-30 cm /sec and values were found to range widely from 2 x 10 for Ne to 67 x 10-30 cm6/sec for CO2. The size of these termolecular rates not only served to explain specific anomalous efficiencies of the charge transfer process observed in atmospheric pressure lasers but also suggested the general importance of three-body ion-molecule reactions in higher pressure plasmas.
Detection of the Resonant Vibration of the Cellular Membrane Using Femtosecond Laser Pulses
An optical detection technique is developed to detect and measure the resonant vibration of the cellular membrane. Biological membranes are active components of living cells and play a complex and dynamic role in life processes. They are believed to have oscillation modes of frequencies in the range of 1 to 1000 GHz. To measure such a high-frequency vibration, a linear laser cavity is designed to produce a train of femtosecond pulses of adjustable repetition rate. The method is then directly applied to liposomes, "artificial membrane", stained with a liphophilic potential sensitive dye. The spectral behavior of a selection of potential sensitive dyes in the membrane is also studied.
Nonlinear Absorption Techniques and Measurements in Semiconductors
We have conducted a detailed experimental and theoretical study of nonlinear absorption in semiconductors. Experimental measurements were made on a variety of materials at wavelengths of 1.06 and 0.53 microns using a picosecond Nd:YAG laser. Both two- and three-photon processes were investigated. Values of nonlinear absorption coefficients extracted from these measurements show excellent agreement with recent theory and scaling rules. Our theoretical investigation has been carried out for two-, three-,and n-photon absorption, for both continuous and pulsed sources. Expressions are obtained for the transmission of the sample in terms of the incident irradiance for each case. The physical interpretation of these results is discussed. We have also considered the effects of the photogenerated carriers on the measurements. Equations are developed that include linear absorption by these carriers. We have observed severe distortions on the transmitted beam, caused by changes in the refractive index of the material, due to the presence of these carriers. We present a model that accurately describes these effects in terms of the photogenerated carrier density. We have developed several novel techniques for monitoring nonlinear absorption. In particular, we have adapted the photoacoustic technique to the measurement of nonlinear absorption in semiconductors. We have also developed a technique employing irradiance modulation to greatly enhance the sensitivity to nonlinear processes and simultaneously discriminate against linear background signals. A related technique has been used to observe coherent mixing effects in semiconductors with cw, modelocked dye lasers.
Nonlinear Absorption Initiated Laser-Induced Damage in [Gamma]-Irradiated Fused Silica, Fluorozirconate Glass and Cubic Zirconia
The contributions of nonlinear absorption processes to laser-induced damage of three selected groups of transparent dielectrics were investigated. The studied materials were irradiated and non-irradiated fused silica, doped and undoped fluorozirconate glass and cubic zirconia stabilized with yttria. The laser-induced damage thresholds, prebreakdown transmission, and nonlinear absorption processes were studied for several specimens of each group. Experimental measurements were performed at wavelengths of 1064 nm and 532 nm using nanosecond and picosecond Nd:YAG laser pulses. In the irradiated fused silica and fluorozirconate glasses, we found that there is a correlation between the damage thresholds at wavelength λ and the linear absorption of the studied specimens at λ/2. In other words, the laser-induced breakdown is related to the probability of all possible two-photon transitions. The results are found to be in excellent agreement with a proposed two-photon-initiated electron avalanche breakdown model. In this model, the initial "seed" electrons for the formation of an avalanche are produced by two-photon excitations of E' centers and metallic impurity levels which are located within the bandgaps of irradiated Si02 and fluorozirconate glasses, respectively. Once the initial electrons are liberated in the conduction band, a highly absorbing plasma is formed by avalanche impact ionization. The resultant heating causes optical damage. In cubic zirconia, we present direct experimental evidence that significant energy is deposited in the samples at wavelength 532 nm prior to electron avalanche formation. The mechanism is found to be due to formation of color centers (F+ or F° centers) by the two-photon absorption process. The presence of these centers was directly shown by transmission measurements. The two-photon absorption (2PA) process was independently investigated and 2PA coefficients obtained. The accumulated effects of the induced centers on the nonlinear absorption measurements were also considered and the 2PA coefficients were measured using short pulses where this effect …
K-, L-, and M-Shell X-Ray Production Cross Sections for Beryllium, Aluminum and Argon Ions Incident Upon Selected Elements
Incident 0.5 to 2.5 MeV charged particle beams were used to ionize the inner-shells of selected targets and study their subsequent emission of characteristic x-rays. ⁹Be⁺ ions were used to examine K-shell x-ray production from thin F, Na, Al, Si, P, Cl, and K targets, L-shell x-ray production from thin Cu, An, Ge, Br, Zr and Ag targets, and M-shell x-ray production from thin Pr, Nd, Eu, Dy, Ho, Hf, W, Au, Pb and Bi targets. L-shell x-ray production cross sections were also measured for ²⁷Al⁺ ions incident upon Ni, Cu, Zn, As, Zr, and Pd targets. M-shell x-ray production cross sections were measure for ²⁷Al⁺ and ⁴⁰Ar⁺ ions incident upon Pr, Nd, Gd, Dy, Lu, Hf, Au, Pb, Bi, and U targets. These measurements were performed using the 2.5 MV Van de Graaff accelerator at North Texas State University. The x-rays were detected with a Si(Li) detector whose efficiency was determined by fitting a theoretical photon absorption curve to experimentally measure values. The x-ray yields were normalized to the simultaneously measured Rutherford backscattered (RBS) yields which resulted in an x-ray production cross section per incident ion. The RBS spectrum was obtained using a standard surface barrier detector calibrated for to account for the "pulse height defect." The experimental results are compared to the predictions of both the first Born and ECPSSR theories; each of which is composed of two parts, the direct ionization (DI) of the target electron to the continuum and the capture (EC) of the target electron to the projectile. The first Born describes DI by the Plane-Wave-Born-Approximation (PWBA) and EC by the Oppenheimer-Brinkman-Kramers treatment of Nikolaev (OBKN). ECPSSR expands upon the first Born by using perturbed (PSS) and relativistic (R) target electron wave functions in addition to considering the energy loss (E) of the projectile in …
Picosecond Measurement of Nonlinear Diffusion and Recombination Processes in Germanium
A variation of the excite-and-probe technique is used to measure the picosecond evolution of laser-induced transient gratings that are produced in germanium by the direct absorption of 40 psec optical pulses at 1.06-μm. Grating lifetimes are determined for free carrier densities between 10¹⁸ cm⁻³ and 10²¹ cm⁻³ . For carrier densities less than 10¹⁹ cm⁻³ , a linear diffusion-recombination model for the grating provides a good fit to the experimental data and allows the extraction of the diffusion coefficient and an estimation of the linear recombination lifetime. Above carrier densities of approximately 10²⁰ cm⁻³ , the density dependence of the diffusion coefficient and nonlinear recombination processes must be considered. Numerical solutions to the resulting nonlinear partial differential equation are obtained that allow extraction of information concerning the high density diffusion coefficient and the nonlinear recombination rates.
Electron-Ion Time-of-Flight Coincidence Measurements of K-K Electron Capture, Cross Sections for Nitrogen, Methane, Ethylene, Ethane, Carbon Dioxide and Argon (L-K) Targets
Protons with energies ranging from 0.4 to 2.0 MeV were used to measure K-shell vacancy production cross sections (oVK) for N_2, CH_4, C_2H_4, C_2H_6, and CO_2 gas targets under single collision conditions. An electron-ion time-of-flight coincidence technique was used to determind the ration of the K-K electron capture cross section, OECK, to the K-vacancy production cross section, oVK. These ratios were then combined with the measured values of oVK to extract the K-K electron capture cross sections. Measurements were also made for protons of the same energy range but with regard to L-shell vacancy production and L-K electron capture for Ar targets. In addition, K-K electron capture cross sections were measured for 1.0 to 2.0 Mev 42He^_ ions on CH_4.
Investigation of the Interaction of CO Laser Radiation with n-InSb
The Shubnikov-de Haas magneto-resistance oscillations and photoconductivity were experimentally studied in order to investigate the interaction of CO laser radiation with n-InSb at liquid helium temperatures. The roles of various absorption mechanisms on these effects were considered, particularly near the intrinsic band edge. From these measurements an effective electron temperature Tₑ was defined that increased or decreased under illumination, depending upon the strength of the applied electric field.
The Effect of Intervalence-Band Absorption, Auger Recombination, Surface Recombination, Diffusion and Carrier Cooling on the Picosecond Dynamics of Laser-Induced Plasmas in Germanium
The picosecond optical response of germanium is investigated by performing excitation-probe experiments on a thin, intrinsic-germanium wafer maintained at 135 K. The results of three distinct experiments are reported: (1) the transmission of a single pulse is measured as a function of irradiance, (2) the probe transmission is measured at a fixed time after excitation as a function of the excitation energy, and (3) the transmission of a probe pulse is monitored as a function of time after excitation. These experiments employ 10-picosecond laser pulses at 1.06 um and Stokes-shifted pulses at 1.55-um.
Parametric Studies of Picosecond Laser-Induced Breakdown in Fused Quartz and NaCl
Bulk laser-induced breakdown and self-focusing in single samples of fused quartz and NaCl were examined using picosecond optical pulses at 1.0 ym and 0.5 ym. The results of three separate but related experiments are reported. First the nonlinear index of refraction, n2, of each of the test materials is measured near the respective damage thresholds of the samples. The values of 1*2 were determined by detecting beam distortions in the far field, transmitted laser beam profile caused by the irradiance dependent index of refraction. The experimental traces were compared to theoretical beam profiles generated by a nonlinear propagation code and n2 was extracted from the resulting fits.
Operator Gauge Transformations in Nonrelativistic Quantum Electrodynamics
A system of nonrelativistic charged particles and radiation is canonically quantized in the Coulomb gauge and Maxwell's equations in quantum electrodynamics are derived. By requiring form invariance of the Schrodinger equation under a space and time dependent unitary transformation, operator gauge transformations on the quantized electromagnetic potentials and state vectors are introduced. These gauge transformed potentials have the same form as gauge transformations in non-Abelian gauge field theories. A gauge-invariant method for solving the time-dependent Schrodinger equation in quantum electrodynamics is given. Maxwell's equations are written in a form which holds in all gauges and which has formal similarity to the equations of motion of non-Abelian gauge fields. A gauge-invariant derivation of conservation of energy in quantum electrodynamics is given. An operator gauge transformation is made to the multipolar gauge in which the potentials are expressed in terms of the electromagnetic fields. The multipolar Hamiltonian is shown to be the minimally coupled Hamiltonian with the electromagnetic potentials in the multipolar gauge. The model of a charged harmonic oscillator in a single-mode electromagnetic field is considered as an example. The gauge-invariant procedure for solving the time-dependent Schrodinger equation is used to obtain the gauge-invariant probabilities that the oscillator is in an energy eigenstate For comparison, the conventional approach is also used to solve the harmonic oscillator problem and is shown to give gauge-dependent amplitudes.
Photoconductivity Investigation of Two-Photon Magneto-Absorption, PACRH, and Deep Levels in n-InSb
A high resolution photoconductivity investigation of two 13 -3 photon magneto-absorption (TPMA) in n-InSb (n - 9 x 10 cm ) has been performed. This is the first time that two-photon absorption in a semiconductor has been studied with cw lasers only. With a stable cw CC>2 laser and a highly sensitive sampling and magnetic field modulation technique, a minimum of 4 2 transitions in the TPMA photoconductivity spectra can be observed. Most of these transitions are a result of the usual spherical approximation TPMA selections rules (An =0, ±2; As = 0 for e ⊥ B and Δn = 0; Δs = 0 for e || B) . However, some transitions, in particular several near the TPMA band edge, are not explained by these rules. The TPMA spectra have been found to depend upon crystallographic orientation. This has not been previously observed. The temperature variation of the fundamental energy gap Eg between 2 and 100° K is also obtained from TPMA experiments.
L-shell X-ray production cross sections of ₂₉Cu, ₃₂Ge, ₃₇Rb, ₃₈Sr, and ₃₉Y and M-shell X-ray production cross sections of ₇₉Au, ₈₂Pb, ₈₃Bi, ₉₀Th, and ₉₂U by 70-200 keV protons
L-shell x-ray production cross sections have been measured for thin targets of 29Cu, 32Ge, 37Rb, 38Sr, and 39Y. M-shell x-ray production cross sections have been measured for thin targets of 79Au, 82Pb, 83Bi, 90Th, and 92U. All targets were irradiated with a beam of H+ ions with energies in a range from 70 to 200 keV. Experimental cross sections are compared to other measurements at higher energies and to first Born (Plane Wave Born Approximation for direct ionization and Oppenheimer-Brinkman-Kramers-Nikolaev approximation for electron capture) and the ECPSSR (Energy loss, Coulomb deflection, Perturbed Stationary State calculations with Relativistic effects) theoretical cross sections.
Low-Velocity K-Shell Ionization Cross Sections for Protons, Deuterons and Alpha Particles Bombarding Thin Metal Targets
The purpose of this work was to examine the effect of the use the assumption κω2K/ΕCM «1 in calculating K-shell ionization cross sections in the plane wave Born approximation (PWBA) where κω2K is the observed binding energy of the K-shell and ECM is the energy of the incident particle in the center of mass system. Avoiding this assumption produces a threshold for ionization at Ecm = κω2K. Calculations employing the assumption, which leads to the use of approximate limits of integration, do not go to zero for even the .Lowest values of the incident energy.
Anomalous Behavior in the Rotational Spectra of the v₈=2 and the v₈=3 Vibrations for the ¹³C and ¹⁵N Tagged Isotopes of the CH₃CN Molecule in the Frequency Range 17-95 GHz
The rotational microwave spectra of the three isotopes (^13CH_3^12C^15N, ^12CH_3^13C^15N, and ^13CH_3^13C^15N) of the methyl cyanide molecule in the v_8=3, v_8=2, v_7=1 and v_4=1 vibrational energy levels for the rotational components 1£J£5 (for a range of frequency 17-95 GHz.) were experimentally and theoretically examined. Rotational components in each vibration were measured to determine the mutual interactions in each vibration between any of the vibrational levels investigated. The method of isotopic substitution was employed for internal tuning of each vibrational level by single and double substitution of ^13C in the two sites of the molecule. It was found that relative frequencies within each vibration with respect to another vibration were shifted in a systematic way. The results given in this work were interpreted on the basis of these energy shifts. Large departure between experimentally measured and theoretically predicted frequency for the quantum sets (J, K=±l, ϑ=±1), Kϑ-l in the v_8=3 vibrational states for the ^13c and ^15N tagged isotopes of CH_3CN showed anomalous behavior which was explained as being due to Fermi resonance. Accidently strong resonances (ASR) were introduced to account for some departures which were not explained by Fermi resonance.
The Size Effect on the Galvanomagnetic Properties of a Semiconductor
A theory is developed to explain the dependence of carrier transport in a thin semiconducting film on film thickness, magnetic field strength, and the dominant bulk scattering mechanism. This theory is based on the solution of the linearized Boltzmann equation in relaxation time form. The semiconductor is assumed to be bounded and nondegenerate with spherical energy surfaces and a scalar effective mass, It is also assumed to be flat banded with totally diffuse scattering at the surface. Classical Boltzmann statistics are used for equilibrium. The dependence of the relaxation time on the carrier energy is approximated by a power law equation. The principle improvement over similar theories is the treatment of the dependence of the relaxation time on carrier energy. The power law approximation for this dependence is valid for randomizing and elastic scattering mechanisms.
L- and M-Shell X-Ray Production Cross Sections of Neodymium Gadolinium, Holmium, Ytterbium, Gold and Lead by 25-MeV Carbon and 32-MeV Oxygen Ions
L- and M-shell x-ray production cross sections have been measured for thin solid targets of neodymium, gadolinium, holmium, ytterbium, gold, and lead by 25 MeV 12/6C^q+ (q=4,5,6) and by 32 MeV 16/8O^q+ (q=5,7,8). The cross sections were determined from measurements made with thin targets (< 2.5 μg/cm2). For projectiles with one or two K-shell vacancies, the target x-ray production cross sections were found to be enhanced over those for projectiles without a K-shell vacancy. The sum of direct ionization to the continuum (DI) plus electron capture (EC) to the L, M, N... shells and EC to the K-shell of the projectile have been extracted from the data. The results are compared to the predictions of first Born theories, i.e., plane wave Born approximation for DI and Oppenheimer-Brinkman-Kramers formula of Nikolaev for EC and to the ECPSSR approach that accounts for Energy loss and Coulomb deflection of the projectile as well as for Relativistic and Perturbed Stationary States of inner shell electrons.
CO₂-Laser Induced Hot Electron Magneto-Transport Effects in n-InSb
The effects of optical heating via infrared free carrier absorption on the electron magneto-transport properties of n-InSb at helium temperatures have been studied for the first time. Oscillatory photoconductivity (OPC) type structure is seen in the photon energy dependence of the transport properties. A C0₂ laser (hω = 115 to 135 meV) was used as the optical source. Concentrations between 1 x 10¹⁵ cm⁻³ and 2 x 10¹⁶ cm⁻³ were studied. The conclusions of this study are that the energy relaxation of high energy photoexcited electrons, generated by free carrier absorption of C0₂ laser radiation in degenerate n-InSb at liquid helium temperatures, is by emission of a maximum number of optical phonons, and that this relaxation mechanism produces OPC type structure in the photon energy dependence of the electron temperature of the conduction band electron gas. This structure is seen, therefore, in the transport properties of the sample, including the Shubnikovde Haas effect, the effective absorption coefficient, and the photoconductivity (mobility) response (lower concentrations only). In addition, the highest concentration studied, nₑ = ~2 x 10¹⁶ cm⁻³, sets an experimental lower limit on the concentration at which electron-electron scattering will become the dominant energy relaxation mechanism for the photoexcited electrons, since OPC effects were present in this sample.
Theoretical and Experimental Linewidth Parameters in the Rotational Spectrum of Nitrogen Dioxide
Contributions to the second order collision efficiency function S ⁽²⁾ (b), used in semiclassical perturbation approaches to pressure broadening of microwave and infrared spectra, due to several leading terms, dipole and quadrupole components, in the expansion of the intermolecular interaction energy are derived by method of irreducible spherical tensor operators for molecules of arbitrary symmetry. Results are given explicitly in terms of dipole and quadrupole line strengths. General expressions for dipole moment line strength in the asymmetric rotor basis as well as quadrupole moment line strength for the special case of molecules with two independent quadrupole moment components are derived. Computer programs for calculating linewidth parameters in the rotational spectrum of ¹⁴NO₂ based on Anderson and Murphy and Boggs theories are presented.
Microwave Properties of Hyaluronate Solutions Using a Resonant Microwave Cavity as a Probe
Physiological functions of a biomacromolecule seem to be closely related to its molecular conformations. The knowledge of any conformational changes due to changes in its environment may lead to a proper understanding of its functions. Hyaluronic acid, a biomacromolecule with unusually high molecular weight and some important biological functions is the subject of the present work. A temperature-dependent transition in hyaluronate solution of 120 mg/ml concentration was observed at physiological temperature. It is shown that this temperature-dependent behavior can be related to the orientational polarizability term in the Debye theory of polar molecules in liquids.
Field Dependence of Optical Properties in Quantum Well Heterostructures Within the Wentzel, Kramers, and Brillouin Approximation
This dissertation is a theoretical treatment of the electric field dependence of optical properties such as Quantum Confined Stark (QCS) shifts, Photoluminescence Quenching (PLQ), and Excitonic Mixing in quantum well heterostructures. The reduced spatial dimensionality in heterostructures greatly enhances these optical properties, more than in three dimensional semiconductors. Charge presence in the quantum well from doping causes the potential to bend and deviate from the ideal square well potential. A potential bending that varies as the square of distance measured from the heterostructure interfaces is derived self-consistently. This potential is used to solve the time-independent Schrodinger equation for bound state energies and wave functions within the framework of the Wentzel, Kramers, and Brillouin (WKB) approximation. The theoretical results obtained from the WKB approximation are limited to wide gap semiconductors with large split off bands such as gallium arsenide-gallium aluminum arsenide and indium gallium arsenide—indium phosphide. Quantum wells with finite confinement heights give rise to an energy dependent WKB phase. External electric and magnetic fields are incorporated into the theory for two different geometries. For electric fields applied perpendicular to the heterostructure multilayers, QCS shifts and PLQ are found to be in excellent agreement with the WKB calculations. Orthogonality between electrons and holes gives rise to interband mixing in the presence of an external electric field. On the contrary, intraband mixing between light and heavy holes is not sufficiently accounted for in the WKB approximation.
Inversion-Asymmetry Splitting of the Conduction Band in N-Type Indium Antimonide
The origin of the Shubnikov-de Haas effect, the strain theory developed by Bir and Pikus, and a simple, classical beating-effects model are discussed. The equipment and the experimental techniques used in recording the Shubnikov-de Haas oscillations of n-type indium antimonite are described. The analysis of the experimental data showed that the angular anisotropy of the period of SdH oscillations at zero stress was unmeasurable for low concentration samples as discussed by other workers. Thus the Fermi surfaces of InSb are nearly spherical at low concentration. It was also shown that the Fermi surface of a high concentration sample of InAs is also nearly spherical. The advantages of using the magnetic field modulation and phase sensitive detection techniques in determining the beats are given. The simple, classical beating-effects model is able to explain the experimental beating effect data in InSb. The computer programs used to obtain the theoretical values of the beat nodal position, SdH frequencies, average frequency, the Fermi surface contours, and the energy eigenvalues are given.
Dispersion of the Nonlinear Refractive Index of CS₂ in the Spectral Range of 9-11 μm
The nonlinear refractive index (n2) of room temperature liquid CS2 in the wavelength range of 9 to 11 micrometers is measured. A line tunable hybrid C02 TEA laser and amplifier system is used for the experiments. In these measurements the well known photoacoustic method is utilized to observe the onset of whole beam self-focusing. The photoacoustic signal in a CS2 cell, much longer than the confocal parameter, is monitored. The departure of the acoustic signal from linear growth marks the critical power for the onset of nonlinearity. It is experimentally verified that the phenomenon is power dependent as expected from self-focusing theory. The value of n2 is then calculated from the theoretical model of self focusing. Measurements of the on-axis irradiance transmitted through the nonlinear material as well as the measurements of beam distortion are used to verify the validity of the photoacoustic method. In all the measurements the on-axis intensity was smaller than the calculated threshold intensity for stimulated Brillouin scattering. The back reflection was monitored to make sure that stimulated Brillouin scattering was not playing a role in the phenomenon.
M-Shell X-Ray Production of Gold, Lead, Bismuth, Uranium for Incident Hydrogen, Helium and Fluorine Ions
Incident ¹H⁺ and ⁴He⁺ ions at 0.3-2.6 MeV and ¹⁹F^q⁺ ions at 25, 27 and 35 MeV were used to study the M-shell x-ray production cross sections of Au, Pb, Bi and U. For the incident fluorine ions, projectile charge state dependence of the cross sections were extracted from measurements made with varying target thicknesses ( ~1 to ~300 μg/cm²). The efficiency of the Si(Li) detector was determined by measuring the K-shell x-ray production of various low Z elements and comparing these values to the prediction of the CPSS theory. The experimental results are compared to the prediction of first Born approximation for direct ionization to the continuum and to the OBK of Nikolaev for the electron capture to the K-, L-, M-...shells of the incident ion. Comparison is also made with the ECPSSR theory that accounts for the energy loss, Coulomb deflection, and relativistic effects in the perturbed stationary state theory.
A Collisional Mechanism in the Ion-Solid Interaction Which Enhances Scattering Yields Near 180⁰
In the course of experiments using uniaxial double alignment channeling to investigate radiation damage in single crystals, an anomalously large ion-scattering yield from the near surface of disordered or simulated disordered solid targets was observed. The chronology of the discovery of this new ion-solid effect and its explanation are presented along with experiments detailing the dependence of the new effect upon ion type and energy, as well as target atomic number and density. Targets included a spectrum of polycrystalline elemental targets in a range Z = 29 to Z = 82. Also, the influence of the effect upon scattering yields from an aligned Au(110) single crystal is demonstrated.
Formation of Supersaturated Alloys by Ion Implantation and Pulsed-Laser Annealing
Supersaturated substitutional alloys formed by ion implantation and rapid liquid-phase epitaxial regrowth induced by pulsed-laser annealing have been studied using Rutherford-backscattering and ion-channeling analysis. A series of impurities (As, Sb, Bi, Ga, In, Fe, Sn, Cu) have been implanted into single-crystal (001) orientation silicon at doses ranging from 1 x 10^15/cm2 to 1 x 10^17/cm2. The samples were subsequently annealed with a Ω-switched ruby laser (energy density ~1.5 J/cm2, pulse duration 15 x 10-9 sec). Ion-channeling analysis shows that laser annealing incorporates the Group III (Ga, In) and Group V (As, Sb, Bi) impurities into substitutional lattice sites at concentrations far in excess of the equilibrium solid solubility. Channeling measurements indicate the silicon crystal is essentially defect free after laser annealing. The maximum Group III and Group V dopant concentrations that can be incorporated into substitutional lattice sites are determined for the present laser-annealing conditions. Dopant profiles have been measured before and after annealing using Rutherford backscattering. These experimental profiles are compared to theoretical model calculations which incorporate both dopant diffusion in liquid silicon and a distribution coefficient (k') from the liquid. It is seen that a distribution coefficient (k') far greater than the equilibrium value (k0) is required for the calculation to fit the experimental data. In the cases of Fe, Zn, and Cu, laser annealing causes the impurities to segregate toward the surface. After annealing, none of these impurities are observed to be substitutional in detectable concentrations. The systematics of these alloys systems are discussed.
Phase Transition Studies in Polar and Nonpolar Liquids at Microwave Frequencies
A resonant microwave cavity technique was employed to study the dielectric behavior of some polar and non-polar liquids near the phase transition temperatures at microwave frequencies of 7.2, 9.2 and 10.1 GHz. The Slater perturbation equations for a resonant microwave cavity are briefly discussed to show that the above technique can be used to determine both the real and imaginary parts of dielectric response. Abrupt changes in dielectric response were observed near the phase transition temperatures for the polar liquids studied in this investigation. The dielectric relaxation phenomenon in liquids has been treated as a chemical rate process and the abrupt change in the dielectric response of the liquids near phase transition temperatures is shown to be related to the dramatic changes in the free energy of activation of the molecules. Some values of the free energy of activation were deduced for the various compounds from data obtained in this investigation.
Target Thickness Dependence of Cu K X-Ray Production for Ions Moving in Thin Solid Cu Targets
Measurements of the target thickness dependence of the target x-ray production yield for incident fast heavy ions are reported for thin solid Cu targets as a function of both incident projectile atomic number and energy. The incident ions were F, Al, Si, S, and CI. The charge state of the incident ions was varied in each case to study the target x-ray production for projectiles which had an initial charge state, q, of q = Z₁, q = Z₁ - 1, and q < Z₁ - 1 for F, Al, Si, and S ions and q = Z₁ - 1 and q < Z₁ - 1 for C1 ions. The target thicknesses ranged from 2 to 183 ug/cm². In each case the Cu K x-ray yield exhibits a complex exponential dependence on target thickness. A two-component model which includes contributions to the target x-ray production due to ions with 0 and 1 K vacancies and a three-component model which includes contributions due to ions with 0, 1, and 2 K vacancies are developed to describe the observed target K x-ray yields. The two-component model for the C1 data and the three-component model for the F, Al, Si, S, and C1 data are fit to the individual data for each projectile, and the cross sections for both the target and projectile are determined. The fits to the target x-ray data give a systematic representation of the processes involved in x-ray production for fast heavy ions incident on thin solid targets.
Nonlinear Optical Properties of GaAs at 1.06 micron, picosecond Pulse Investigation and Applications
The author explores absorptive and refractive optical nonlinearities at 1.06 [mu]m in bulk, semi-insulating, undoped GaAs with a particular emphasis on the influence of the native deep-level defect known as EL2. Picosecond pump-probe experimental technique is used to study the speed, magnitude, and origin of the absorptive and refractive optical nonlinearities and to characterize the dynamics of the optical excitation of EL2 in three distinctly different undoped, semi-insulating GaAs samples. Intense optical excitation of these materials leads to the redistribution of charge among the EL2 states resulting in an absorptive nonlinearity due to different cross sections for electron and hole generation through this level. This absorptive nonlinearity is used in conjunction with the linear optical properties of the material and independent information regarding the EL2 concentration to extract the cross section ratio [sigma][sub p]/[sigma][sub e] [approx equal]0.8, where [sigma][sub p](e) is the absorption cross section for hole (electron) generation from EL2[sup +] (EL2[sup 0]). The picosecond pump-probe technique can be used to determine that EL2/EL2[sup +]density ratio in an arbitrary undoped, semi-insulating GaAs sample. The author describes the use of complementary picosecond pump-probe techniques that are designed to isolate and quantify cumulative and instantaneous absorptive and refractive nonlinear processes. Numerical simulations of the measurements are achieved by solving Maxwell equations with the material equations in a self-consistent manner. The numerical analysis together with the experimental data allows extraction of a set of macroscopic nonlinear optical parameters in undoped GaAs. The nonlinearities in this material have been used to construct three proof-of-principle nonlinear optical devices for use at 1.06 [mu]m: (1) a weak beam amplifier, (2) a polarization rotation optical switch, and (3) optical limiters.
Development and Application of a Nonlinear Optical Characterization Technique
This dissertation reports a sensitive single beam experimental technique for measuring nonlinear refraction and nonlinear absorption in a wide variety of materials. The experimental setup is described and a comprehensive theoretical analysis including cases where nonlinear refraction and nonlinear absorption are also presented.
Computer Simulations of Mechanical Behavior of Polymer Liquid Crystals
In this dissertation molecular dynamics simulations of behavior of polymer liquid crystals (PLC's) under tensile deformation have been performed. PLC's composed of random or block copolymers of rigid and flexible segments have been studies. Systems of fully flexible chains have been simulated for comparison. Stress-strain relations and fracture mechanics have been investigated.
Fluorine K-Shell X-Ray Cross Section Measurements for ⁷Li, ¹⁰B, ¹²C, ¹⁴N, and ¹⁶O Ions on Ultra-Clean, Ultra-Thin Yf₃ Solid Target Foils
In this study, procedures were developed to produce ultra-clean, ultra-thin target foils and to remove x-ray interference from electron bremsstrahlung and low energy K-shell x-rays from contaminant elements.
A New Method for Measuring the Nuclear Hexadecapole Interaction in Some Solids
A new method for measuring the nuclear hexadecapole interaction (HDI) in solids based on NMR quadrupole echoes is described. Theoretical values of the shifts of the quadrupole echo times caused by the HDI are given for two pulse and three pulse echoes in a nuclear spin 5/2 system. The method is applied to 1271 in an almost strain free crystal of KI and a hexadecapole coupling frequency (e2M16m16/h) of 630 Hz was found. Here e is the electronic charge, em16 is the fourth gradient of the external electric potential at the nuclear site, eM16 is the hexadecapole moment and h is the Planck constant. This HDI is smaller than previously measured values in solids (42.6 MHz for 1 81 Ta in TaF 5, 66.6 MHz for 175Lu in Lu(NO3 )3*4H 20), but not as small as an atomic beam result of 151 Hz for 165Ho in atomic Ho. The method described here may be used to search for the HDI in other cubic crystals. A double resonance (1151n, 31P) multiple pulse method was unsuccessfully used to search for the 1151n HDI in a single crystal of InP.
Novel Semi-Conductor Material Systems: Molecular Beam Epitaxial Growth and Characterization
Semi-conductor industry relies heavily on silicon (Si). However, Si is not a direct-band gap semi-conductor. Consequently, Si does not possess great versatility for multi-functional applications in comparison with the direct band-gap III-V semi-conductors such as GaAs. To bridge this gap, what is ideally required is a semi-conductor material system that is based on silicon, but has significantly greater versatility. While sparsely studied, the semi-conducting silicides material systems offer great potential. Thus, I focused on the growth and structural characterization of ruthenium silicide and osmium silicide material systems. I also characterized iron silicon germanide films using extended x-ray absorption fine structure (EXAFS) to reveal phase, semi-conducting behavior, and to calculate nearest neighbor distances. The choice of these silicides material systems was due to their theoretically predicted and/or experimentally reported direct band gaps. However, the challenge was the existence of more than one stable phase/stoichiometric ratio of these materials. In order to possess the greatest control over the growth process, molecular beam epitaxy (MBE) has been employed. Structural and film quality comparisons of as-grown versus annealed films of ruthenium silicide are presented. Structural characterization and film quality of MBE grown ruthenium silicide and osmium silicide films via in situ and ex situ techniques have been done using reflection high energy electron diffraction, scanning tunneling microscopy, atomic force microscopy, cross-sectional scanning electron microscopy, x-ray photoelectron spectroscopy, and micro Raman spectroscopy. This is the first attempt, to the best of our knowledge, to grow osmium silicide thin films on Si(100) via the template method and compare it with the regular MBE growth method. The pros and cons of using the MBE template method for osmium silicide growth are discussed, as well as the structural differences of the as-grown versus annealed films. Future perspectives include further studies on other semi-conducting silicides material systems in terms …
Effects of Quantum Coherence and Interference
Quantum coherence and interference (QCI) is a phenomenon that takes place in all multi-level atomic systems interacting with multiple lasers. In this work QCI is used to create several interesting effects like lasing without inversion (LWI), controlling group velocity of light to extreme values, controlling the direction of propagation through non-linear phase matching condition and for controlling the correlations in field fluctuations. Controlling group velocity of light is very interesting because of many novel applications it can offer. One of the unsolved problems in this area is to achieve a slow and fast light which can be tuned continuously as a function of frequency. We describe a method for creation of tunable slow and fast light by controlling intensity of incident laser fields using QCI effects. Lasers are not new to the modern world but an extreme ultra-violet laser or a x-ray laser is definitely one of the most desirable technologies today. Using QCI, we describe a method to realize lasing at high frequencies by creating lasing without inversion. Role of QCI in creating correlations and anti-correlations, which are generated by vacuum fluctuations, in a three level lambda system coupled to two strong fields is discussed.
An Electro- Magneto-static Field for Confinement of Charged Particle Beams and Plasmas
A system is presented that is capable of confining an ion beam or plasma within a region that is essentially free of applied fields. An Artificially Structured Boundary (ASB) produces a spatially periodic set of magnetic field cusps that provides charged particle confinement. Electrostatic plugging of the magnetic field cusps enhances confinement. An ASB that has a small spatial period, compared to the dimensions of a confined plasma, generates electro- magneto-static fields with a short range. An ASB-lined volume thus constructed creates an effectively field free region near its center. It is assumed that a non-neutral plasma confined within such a volume relaxes to a Maxwell-Boltzmann distribution. Space charge based confinement of a second species of charged particles is envisioned, where the second species is confined by the space charge of the first non-neutral plasma species. An electron plasma confined within an ASB-lined volume can potentially provide confinement of a positive ion beam or positive ion plasma. Experimental as well as computational results are presented in which a plasma or charged particle beam interact with the electro- magneto-static fields generated by an ASB. A theoretical model is analyzed and solved via self-consistent computational methods to determine the behavior and equilibrium conditions of a relaxed plasma. The equilibrium conditions of a relaxed two species plasma are also computed. In such a scenario, space charge based electrostatic confinement is predicted to occur where a second plasma species is confined by the space charge of the first plasma species. An experimental apparatus with cylindrical symmetry that has its interior surface lined with an ASB is presented. This system was developed by using a simulation of the electro- magneto-static fields present within the trap to guide mechanical design. The construction of the full experimental apparatus is discussed. Experimental results that show the characteristics of …
The Effects of Residual Gases on the Field Emission Properties of ZnO, GaN, ZnS Nanostructures, and the Effects of Light on the Resistivity of Graphene
In this dissertation, I present that at a vacuum of 3×10-7 Torr, residual O2, CO2, H2 and Ar exposure do not significantly degrade the field emission (FE) properties of ZnO nanorods, but N2 exposure significantly does. I propose that this could be due to the dissociation of N2 into atomic nitrogen species and the reaction of such species with ZnO. I also present the effects of O2, CO2, H2O, N2, H2, and Ar residual gas exposure on the FE properties of GaN and ZnS nanostructure. A brief review of growth of ZnO, GaN and ZnS is provided. In addition, Cs deposition on GaN nanostructures at ultra-high vacuum results in 30% decrease in turn-on voltage and 60% in work function. The improvement in FE properties could be due to a Cs-induced space-charge layer at the surface that reduces the barrier for FE and lowers the work function. I describe a new phenomenon, in which the resistivity of CVD-grown graphene increases to a higher saturated value under light exposure, and depends on the wavelength of the light—the shorter the wavelength, the higher the resistivity. First-principle calculations and theoretical analysis based on density functional theory show that (1) a water molecule close to a graphene defect is easier to be split than that of the case of no defect existing and (2) there are a series of meta-stable partially disassociated states for an interfacial water molecule. Calculated disassociation energies are from 2.5 eV to 4.6 eV, that match the experimental observation range of light wavelength from visible to 254 nm UV light under which the resistivity of CVD-grown graphene is increased.
Synthesis, Characterization, Structural, and Optical Properties of Zinc Oxide Nanostructures Embedded in Silicon Based Substrates
Structural and optical properties of ZnO nanostructures synthesized by low energy ion implantation technique were examined. ZnO molecular ions were implanted into Si/SiO2 substrates at room temperature and then furnace annealed under different temperatures and environments. In all as-implanted samples only Zn nanostructures with varying diameters distributed into the Si/SiO2 matrices were observed. No trace of ZnO was found. The distributions of Zn nanostructures in Si/SiO2 closely matched results from Stopping and Range of Ions in Matter (SRIM) simulations. During annealing at 750 oC, Zn diffused both toward and away from the surface of the substrate and combine with oxygen to form ZnO nanostructures. At higher annealing temperatures ZnO bonding started to break down and transfer to zinc silicate (Zn2SiO4), and at 900 oC the ZnO was completely converted into Zn2SiO4. The average sizes of Zn/ZnO nanostructures depended on the ion fluence. If the fluence increased the average sizes of nanostructures also increased and vice versa. For room temperature photoluminescence (RT-PL), band-edge emission in the ultraviolet (UV) region was observed from all samples annealed at 700 oC/750 oC and were slightly blue shifted as compare to bulk ZnO. Donor-bound exciton (D,X) and acceptor-bound exciton (A,X) transitions were observed in low temperature photoluminescence (PL). The lifetime of both donor-bound excitonic emission (D, X) and acceptor-bound excitonic emission (A, X) were found to be in the picosecond (ps) range.
Synthesis Strategies and a Study of Properties of Narrow and Wide Band Gap Nanowires
Various techniques to synthesize nanowires and nanotubes as a function of growth temperature and time were investigated. These include growth of nanowires by a chemical vapor deposition (CVD) system using vapor-liquid-solid (VLS) growth mechanism and electro-chemical synthesis of nanowires and nanotubes. Narrow band gap InSb Eg = 0.17 eV at room temp) nanowires were successively synthesized. Using a phase diagram, the transition of the nanowire from metallic- semiconducting- semi-metallic phase was investigated. A thermodynamic model is developed to show that the occurrence of native defects in InSb nanowires influenced by the nanowire growth kinetics and thermodynamics of defect formation. Wide band gap ZnO (Eg = 3.34 eV) and In2O3 (3.7 eV) were also synthesized. ZnO nanowires and nanotubes were successfully doped with a transition metal Fe, making it a Dilute Magnetic Semiconductor of great technological relevance. Structural and electronic characterizations of nanowires were studied for different semiconducting, metallic and semi-metallic nanowires. Electron transport measurements were used to estimate intrinsic material parameters like carrier concentration and mobility. An efficient gas sensing device using a single In2O3 nanowire was studied and which showed sensitivity to reducing gas like NH3 and oxidizing gas like O2 gas at room temperature. The efficiency of the gas sensing device was found to be sensitive to the nature of contacts as well as the presence of surface states on the nanowire.
How Cooperative Systems Respond to External Forces
Cooperative interactions permeate through nature, bringing about emergent behavior and complexity. Using a simple cooperative model, I illustrate the mean field dynamics that occur at the critical point of a second order phase transition in the framework of Langevin equations. Through this formalism I discuss the response, both linear and nonlinear, to external forces. Emphasis is placed on how information is transferred from one individual to another in order to facilitate the collective response of the cooperative network to a localized perturbation. The results are relevant to a wide variety of systems, ranging from nematic liquid crystals, to flocks and swarms, social groups, and neural networks.
Room Temperature Gold-Vacuum-Gold Tunneling Experiments
An experiment has been completed which demonstrated quantum mechanical tunneling of electrons between two gold electrodes separated in vacuum. The tunneling current between the gold electrodes has been measured, for fixed voltages of 0.1 and 0.01 volts, as the electrode spacing was varied from a distance of approximately 2.0 nm down to a point where the electrodes touched. Current-voltage characteristics for fixed electrode spacing in the direct tunneling region have also been measured. Numerical calculations of the tunneling current based on the free-electron model of the electrodes and the barrier, an image-potential reduced barrier, and a WKB approximation for the tunneling probability have been performed and compared with Simmons' theory and with the experimental results. Within experimental error the results indicate that an image potential reduced barrier with the modifications suggested by Lang and Kohn gives a close approximation to the true barrier for metal-vacuum-metal tunneling. For the first time, the work function of the electrodes in a tunneling experiment has been deduced from experimental parameters independent of the tunneling device.
Theoretical Cross Section for Light Scattering from Superfluid Helium-4
The finite lifetime of the bound roton pair is included in the theoretical light scattering cross section to explain the shape of the peak in the observed Raman light scattering cross section in He II. A model Hamiltonian is used to describe interactions between quasiparticles for the helium system. The equation of motion for the bound roton pair state, which is taken to be a collective mode of quasiparticle pairs, is solved. The cross section for light scattering is then derived using Fermi's Golden Rule with the bound roton pair as the final state. Since the bound roton pair can decay into two free phonons, a phenomenological width r is included in the cross section. The peak position and shape of the observed cross section are both fitted using a binding energy of εB = 0.37 K for the bound roton pair.
A Theoretical Investigation of Bound Roton Pairs in Superfluid Helium-4
The Bogoliubov theory of excitations in superfluid helium is used to study collective modes at zero temperature. A repulsive delta function shell potential is used in the quasiparticle excitation energy spectrum to fit the observed elementary excitation spectrum, except in the plateau region. The linearized equation of motion method is used to obtain the secular equation for a collective mode consisting of a linear combination of one and two free quasiparticles of zero total momentum. It is shown that in this case for high-lying collective modes, vertices involving three quasiparticles cancel, and only vertices involving four quasiparticles are important. A decomposition into various angular momentum states is then made. Bound roton pairs in the angular momentum D-state observed in light-scattering experiments exist only for an attractive coupling between helium atoms in this oversimplified model. Thus, the interaction between particles can be reinterpreted as a phenomenological attractive coupling between quasiparticles, in order to explain the Raman scattering from bound roton pairs in superfluid helium.
A Study of L-Shell X-Ray Production Cross Sections Due to [Hydrogen-1], [Helium-4], and [Lithium-7] Ion Bombardment of Selected Thin Rare Earth and ₈₂Pb Targets
Thin target L-Shell x-ray production cross sections for protons incident on ₆₂Sm and ₇₀Yb in the energy range of 0.3 to 2.4 MeV/amu, alpha particles incident on ₆₂Sm, ₇₀Yb, and ₈₂Pb in the energy range of 0.15 to 4.8 MeV/amu, and lithium ions incident on ₅₈Ce, ₆₀Nd, ₆₂Sm, ₆₆Dy, ₆₇Ho, ₇₀Yb, and ₈₂Pb in the energy range of 0.8 to 4.4 MeV/amu have been measured. The cross section data have been compared to the planewave Born approximation (PWBA) and the PWBA modified to include binding energy and Coulomb deflection effects. The Lα₁,₂ x-ray production cross sections are best represented by the PWBA modified to include both the binding energy and Coulomb deflection effects (PWBA-BC) over the entire incident ion, incident energy, and target ranges studied. However, the Lγ₁ and Lγ₂,₃,₍₆₎ x-ray production cross sections are best represented by the PWBA except at the lower ion energies, where both the PWBA and PWBA-BC are in disagreement with the data. The comparison of Lα₁,₂/Lγ₂,₃,₍₆₎ ratios to theory reveals that the PWBA-BC does not predict the inflection point substantiated by the data, and the agreement between the data and the PWBA-BC becomes worse as the atomic number of the incident ion increases. Comparison of the PWBA modified to include binding energy effects CPWBA-B) and the PWBA modified to include Coulomb deflection effects (PWBA-C) to the Lα₁,₂, Lγ₁, and the Lγ₂,₃ cross sections for protons, alpha particles, and lithium ions incident on ₇₀Yb indicates that the PWBA-C overestimates the magnitude of the data but does describe the shape of the L₁-associated cross section while the PWBA-B underestimates the magnitude of the data but fails to predict the proper shape of the L₁-associated data. In order to evaluate the ability of the PWBA and the presently accepted modifications to the PWBA to fit the experimental …
K-Shell Ionization Cross Sections of Selected Elements from Fe to As for Proton Bombardment from 0.5 to 2.0 MeV
The problem with which this investigation is concerned is that of making experimental measurements of proton-induced K-shell x-ray production cross sections and to study the dependence of these cross sections upon the energy of the incident proton. The measurements were made by detection of the characteristic x-rays emitted as a consequence of the ionization of the K-shell of the atom. The method for relating this characteristic x-ray emission to the x-ray production cross section is discussed in this work.
The Shubnikov-de Haas Effect in N-Type Indium Antimonide
The Shubnikov-de Haas effect is an oscillation in the electrical resistivity or conductivity of a metal, semimetal, or semiconductor as a function of changing magnetic field which occurs at low temperatures. The effect is caused by the quantization of the momentum and energy of the charge carriers by the magnetic field. Since the nature of the oscillation depends strongly on the energy band structure of the material in which it is measured, the effect could be quite useful as an investigative tool. Its usefulness has been limited, however, by the uncertainty as to the functional form of the relationship between the measured oscillations and the parameters characterizing the material. One purpose of the present study is to extend the usefulness of the Shubnikov-de Haas effect by experimentally determining the functional form appropriate for a material such as n-type indium antimonide. The second purpose of the study is to determine values for the parameters which characterize the band structure of indium antimonide. The curve fitting procedure is found to be a powerful tool for investigating band structure. All computer programs used in processing the data, fitting the data, and comparing the results with the Kane model are given.
Density Profile of a Quantized Vortex Line in Superfluid Helium-4
The density amplitude of an isolated quantum vortex line in superfluid 4He is calculated using a generalized Gross-Pitaevskii (G-P) equation. The generalized G-P equation for the order parameter extends the usual mean-field approach by replacing the interatomic potential in the ordinary G-P equation by a local, static T matrix, which takes correlations between the particles into account. The T matrix is a sum of ladder diagrams appearing in a diagrammatic expansion of the mean field term in an exact equation for the order parameter. It is an effective interaction which is much softer than the realistic interatomic Morse dipole-dipole potential from which it is calculated. A numerical solution of the generalized G-P equation is required since it is a nonlinear integro-differential equation with infinite limits. For the energy denominator in the T matrix equation, a free-particle spectrum and the observed phonon-roton spectrum are each used. For the fraction of particles in the zero-momentum state (Bose-Einstein dondensate) which enters the equation, both a theoretical value of 0.1 and an experimental value of 0.024 are used. The chemical potential is adjusted so that the density as a function of distance from the vortex core approaches the bulk density asymptotically. Solutions of the generalized G-P equation are not very dependent on the choice of energy denominator or condensate fraction. The density profile is a monotonically increasing function of the distance from the vortex core. The core radius, defined to be the distance to half the bulk density, varies from 3.7 A to 4.7 A, which is over three times the experimental value of 1.14 A at absolute zero.
K-Shell Ionization Cross Sections For Elements Se To Pd: 0.4 To 2.0 MeV
K-Shell ionization cross section for protons over the energy range of 0.4 to 2.0 MeV have been measured on thin targets of the elements Se, Br, Rb, Sr, Y, Mo and Pd. Total x-ray and ionization cross sections for the K-shell are reported. The experimental values of the ionization cross sections are compared to the non-relativistic plane-wave Born approximation, the binary-encounter approximation, the constrained binary-encounter approximation, and the plane-wave Born approximation with corrections for Coulomb-deflection and binding energy effects.
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