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Scanning Tunneling Microscopy of Homo-Epitaxial Chemical Vapor Deposited Diamond (100) Films

Description: Atomic resolution images of hot-tungsten filament chemical-vapor-deposition (CVD) grown epitaxial diamond (100) films obtained in ultrahigh vacuum (UHV) with a scanning tunneling microscope (STM) are reported. A (2x1) dimer surface reconstruction and amorphous atomic regions were observed on the hydrogen terminated (100) surface. The (2x1) unit cell was measured to be 0.51"0.01 x 0.25"0.01 nm2. The amorphous regions were identified as amorphous carbon. After CVD growth, the surface of the epitaxial films was amorphous at the atomic scale. After 2 minutes of exposure to atomic hydrogen at 30 Torr and the sample temperature at 500° C, the surface was observed to consist of amorphous regions and (2x1) dimer reconstructed regions. After 5 minutes of exposure to atomic hydrogen, the surface was observed to consist mostly of (2x1) dimer reconstructed regions. These observations support a recent model for CVD diamond growth that is based on an amorphous carbon layer that is etched or converted to diamond by atomic hydrogen. With further exposure to atomic hydrogen at 500° C, etch pits were observed in the shape of inverted pyramids with {111} oriented sides. The temperature dependence of atomic hydrogen etching of the diamond (100) surface was also investigated using UHV STM, and it was found that it was highly temperature dependent. Etching with a diamond sample temperature of 200° C produced (100) surfaces that are atomically rough with no large pits, indicating that the hydrogen etch was isotropic at 200° C. Atomic hydrogen etching of the surface with a sample temperature of 500° C produced etch-pits and vacancy islands indicating an anisotropic etch at 500° C. With a sample temperature of 1000° C during the hydrogen etch, the (100) surface was atomically smooth with no pits and few single atomic vacancies, but with vacancy rows predominantly in the direction of the dimer ...
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Date: May 2000
Creator: Stallcup, Richard E.

Microstructure and Electronic Structures of Er-Doped Si Nano-particles Synthesized by Vapor Phase Pyrolysis

Description: Si nanoparticles are new prospective optoelectronic materials. Unlike bulk Si cry-stals, Si nanoparticles display intriguing room-temperature photoluminescence. A major challenge in the fabrication of Si nanoparticles is the control of their size distribution. The rare-earth element Er has unique photo emission properties, including low pumping power, and a temperature independent, sharp spectrum. The emission wavelength matches the transmission window of optical fibers used in the telecommunications industry. Therefore, the study of Er-doped Si nanoparticles may have practical significance. The goals of the research described in this dissertation are to investigate vapor phase pyrolysis methods and to characterize the microstructure and associated defects, particles size distributions and photoluminescence efficiencies of doped and undoped Si nanoparticles using analytical transmission electron microscopy, high resolution electron microscopy, and optical spectroscopy. Er-doped and undoped Si nanoparticles were synthesized via vapor-phase pyrolysis of disilane at Texas Christian University. To achieve monodisperse size distributions, a process with fast nucleation and slow growth was employed. Disilane was diluted to 0.48% with helium. A horizontal pyrolysis oven was maintained at a temperature of 1000 °C. The oven length was varied from 1.5 cm to 6.0 cm to investigate the influence of oven length on the properties of the nanoparticles. The Si nanoparticles were collected in ethylene-glycol. The doped and undoped Si nanoparticles have a Si diamond cubic crystal structure. Neither Er precipitation, Er oxides or Er silicides were detected in any of the samples. The Er dopant concentration was about 2 atom% for doped samples from the 3.0 and 6.0 cm ovens as determined by quantitative analysis using X-ray energy dispersive spectroscopy. The average Si nanoparticle size increases from 11.3 to 15.2 nm in the doped samples and from 11.1 to 15.7 nm in the undoped samples as the oven length increases from 1.5 to 6.0 cm. HREM data ...
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Date: May 2000
Creator: Chen, Yandong

Nested Well Plasma Traps

Description: Criteria for the confinement of plasmas consisting of a positive and negative component in Penning type traps with nested electric potential wells are presented. Computational techniques for the self-consistent calculation of potential and plasma density distributions are developed. Analyses are presented of the use of nested well Penning traps for several applications. The analyses include: calculations of timescales relevant to the applications, e.g. reaction, confinement and relaxation timescales, self-consistent computations, and consideration of other physical phenomenon important to the applications. Possible applications of a nested well penning trap include production of high charge state ions, studies of high charge state ions, and production of antihydrogen. In addition the properties of a modified Penning trap consisting of an electric potential well applied along a radial magnetic field are explored.
Date: August 2000
Creator: Dolliver, Darrell

The Stopping of Energetic Si, P and S Ions in Ni, Cu, Ge and GaAs Targets

Description: Accurate knowledge of stopping powers is essential for these for quantitative analysis and surface characterization of thin films using ion beam analysis (IBA). These values are also of interest in radiobiology and radiotherapy, and in ion- implantation technology where shrinking feature sizes puts high demands on the accuracy of range calculations. A theory that predicts stopping powers and ranges for all projectile-target combinations is needed. The most important database used to report the stopping powers is the SRIM/TRIM program developed by Ziegler and coworkers. However, other researchers report that at times, these values differ significantly from experimental values. In this study the stopping powers of Si, P and S ions have been measured in Ni, Cu, Ge and GaAs absorbers in the energy range ~ 2-10 MeV. For elemental films of Ni, Cu and Ge, the stopping of heavy ions was measured using a novel ERD (Elastic Recoil Detection) based technique. In which an elastically recoiled lighter atom is used to indirectly measure the energy of the incoming heavy ion using a surface barrier detector. In this way it was possible to reduce the damage and to improve the FWHM of the detector. The results were compared to SRIM-2000 predictions and other experimental measurements. A new technique derived from Molecular Beam Epitaxy (MBE) was developed to prepare stoichiometric GaAs films on thin carbon films for use in transmission ion beam experiments. The GaAs films were characterized using X-ray Photoelectron Spectroscopy (XPS) and Particle Induced X-ray Emission (PIXE). These films were used to investigate the stopping powers of energetic heavy ions in GaAs and to provide data for the calculation of Bethe-Bloch parameters in the framework of the Modified Bethe-Bloch theory. As a result of this study, stopping power data are available for the first time for Si and P ions ...
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Date: December 2001
Creator: Nigam, Mohit

Space-Charge Saturation and Current Limits in Cylindrical Drift Tubes and Planar Sheaths

Description: Space-charge effects play a dominant role in many areas of physics. In high-power microwave devices using high-current, relativistic electron beams, it places a limit on the amount of radiation a device can produce. Because the beam's space-charge can actually reflect a portion of the beam, the ability to accurately predict the amount of current a device can carry is needed. This current value is known as the space-charge limited current. Because of the mathematical difficulties, this limit is typically estimated from a one-dimensional theory. This work presents a two-dimensional theory for calculating an upper-bound for the space-charge limited current of relativistic electron beams propagating in grounded coaxial drift tubes. Applicable to annular beams of arbitrary radius and thickness, the theory includes the effect introduced by a finite-length drift tube of circular cross-section. Using Green's second identity, the need to solve Poisson's equation is transferred to solving a Sturm-Liouville eigenvalue problem, which is easily solved by elementary methods. In general, the resulting eigenvalue, which is required to estimate the limiting current, must be numerically determined. However, analytic expressions can be found for frequently encountered limiting cases. Space-charge effects also produce the fundamental collective behavior found in plasmas, especially in plasma sheaths. A plasma sheath is the transition region between a bulk plasma and an adjacent plasma-facing surface. The sheath controls the loss of particles from the plasma in order to maintain neutrality. Using a fully kinetic theory, the problem of a planar sheath with a single-minimum electric potential profile is investigated. Appropriate for single charge-state ions of arbitrary temperature, the theory includes the emission of warm electrons from the surface as well as a net current through the sheath and is compared to particle-in-cell simulations. Approximate expressions are developed for estimating the sheath potential as well as the transition to space-charge ...
Date: August 2000
Creator: Stephens, Kenneth Frank

Picosecond Dynamics of Free-Carrier Populations, Space-Charge Fields, and Photorefractive Nonlinearities in Zincblende Semiconductors

Description: Generally, nonlinear optics studies investigate optically-induced changes in refraction or absorption, and their application to spectroscopy or device fabrication. The photorefractive effect is a nonlinear optical effect that occurs in solids, where transport of an optically-induced free-carrier population results in an internal space-charge field, which produces an index change via the linear electrooptic effect. The photorefractive effect has been widely studied for a variety of materials and device applications, mainly because it allows large index changes to be generated with laser beams having only a few milliwatts of average power.Compound semiconductors are important photorefractive materials because they offer a near-infrared optical response, and because their carrier transport properties allow the index change to be generated quickly and efficiently. While many researchers have attempted to measure the fundamental temporal dynamics of the photorefractive effect in semiconductors using continuous-wave, nanosecond- and picosecond-pulsed laser beams, these investigations have been unsuccessful. However, studies with this goal are of clear relevance because they provide information about the fundamental physical processes that produce this effect, as well as the material's speed and efficiency limitations for device applications.In this dissertation, for the first time, we time-resolve the temporal dynamics of the photorefractive nonlinearities in two zincblende semiconductors, semi-insulating GaAs and undoped CdTe. While CdTe offers a lattice-match to the infrared material HgxCd1-xTe, semi-insulating GaAs has been widely used in optoelectronic and high-speed electronic applications. We use a novel transient-grating experimental method that allows picosecond temporal resolution and high sensitivity. Our results provide a clear and detailed picture of the picosecond photorefractive response of both materials, showing nonlinearities due to hot-carrier transport and the Dember space-charge field, and a long-lived nonlinearity that is due to the EL2 midgap species in GaAs. We numerically model our experimental results using a general set of equations that describe nonlinear diffraction and ...
Date: August 1999
Creator: Stark, Thomas S.

A Comprehensive Model for the Rotational Spectra of Propyne CH₃CCH in the Ground and V₁₀=1,2,3,4,5 Vibrational States

Description: The energy states of C₃ᵥ symmetric top polyatomic molecules were studied. Both classical and quantum mechanical methods have been used to introduce the energy states of polyatomic molecules. Also, it is shown that the vibration-rotation spectra of polyatomic molecules in the ground and excited vibrational states can be predicted by group theory. A comprehensive model for predicting rotational frequency components in various v₁₀ vibrational levels of propyne was developed by using perturbation theory and those results were compared with other formulas for C₃ᵥ symmetric top molecules. The v₁₀=1,2,3 and ground rotational spectra of propyne in the frequency range 17-70 GHz have been reassigned by using the derived comprehensive model. The v₁₀=3 and v₁₀=4 rotational spectra of propyne have been investigated in the 70 GHz, and 17 to 52 GHz regions, respectively, and these spectral components assigned using the comprehensive model. Molecular constants for these vibrationally excited states have been determined from more than 100 observed rotational transitions. From these experimentally observed components and a model based upon first principles for C₃ᵥ symmetry molecules, rotational constants have been expressed in a form which enables one to predict rotational components for vibrational levels for propyne up to v₁₀=5. This comprehensive model also appears to be useful in predicting rotational components in more highly excited vibrational levels but data were not available for comparison with the theory. Several techniques of assignment of rotational spectra for each excited vibrational state are discussed. To get good agreement between theory and experiment, an additional term 0.762(J+1) needed to be added to Kℓ=1 states in v₁₀=3. No satisfactory theoretical explanation of this term has been found. Experimentally measured frequencies for rotational components for J→(J+1)=+1 (0≤J≤3) in each vibration v₁₀=n (0≤n≤4) are presented and compared with those calculated using the results of basic perturbation theory. The v₉=2 rotational ...
Date: December 1986
Creator: Rhee, Won Myung

K-, L-, and M-Shell X-Ray Production Cross Sections for Beryllium, Aluminum and Argon Ions Incident Upon Selected Elements

Description: 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 ...
Date: December 1986
Creator: Price, Jack Lewis

The Rotational Spectra of Propyne in the Ground, V₁₀=1, V₁₀=2, and V₉=1 Vibrational States

Description: The problem of a vibrating-rotating polyatomic molecule is treated, with emphasis given to the case of molecules with C_3v symmetry. It is shown that several of the gross features of the rotational spectra of polyatomic molecules in excited vibrational states can be predicted by group theoretical considerations. Expressions for the rotational transition frequencies of molecules of C_3v symmetry in the ground vibrational state, singly excited degenerate vibrational states, and doubly excited degenerate vibrational states are given. The derivation of these expressions by fourth order perturbation theory as given by Amat, Nielsen, and Tarrago is discussed. The ground and V_10=1 rotational spectra of propyne have been investigated in the 17 to 70 GHz, and 17 to 53 GHz regions, respectively, and compared with predictions based on higher frequency measurements. The V_9=1 and V_10=2 rotational spectra of propyne have been investigated and assigned for the first time. A perturbation of the V_9=1 rotational spectra for K=-l has been discovered and discussed.
Date: August 1985
Creator: Ware, John Matthew

Nonlinear Absorption Techniques and Measurements in Semiconductors

Description: 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.
Date: August 1985
Creator: Woodall, Milton Andrew

Microwave Spectra of ¹³C Isotopic Species of Methyl Cyanide in the Ground, v₈=1 and v₈=2 Vibrational States

Description: The problem of the quadrupole interaction occurring in a vibrating-rotating C₃v symmetric top molecule has been studied in detail. The quadrupole interaction has been treated as another perturbation term to a general frequency expression accounting for the vibrating-rotating interaction of the molecule so that a complete frequency formula is obtained for both interactions, and from which hyperfine spectral components are predicted and measured. The hyperfine transitions in the ground, and v₈=1 and v₈=2 excited vibrational states of the ¹³C isotopes of methyl cyanide have been investigated in the frequency range 17-72 GHz, primarily in the low J transitions (0≤J≤3). The study of the ground state of isotope i3CH3i3CN, and the v₈=1, v₈=2 excited vibrational states for all the isotopes have been conducted here for the first time. A substantial perturbation has been discovered and discussed at the ΔJ=3→4 transitions within the Kl=1 sets in the v₈=1 mode for isotopes ¹³CH₃CN and CH₃¹³CN. A total of 716 hyperfine transitions have been assigned from measurements, only 7 of which have been measured previously. A total of 84 molecular constants have been reported; 70 of these constants are derived for the first time from microwave data.
Date: May 1988
Creator: Tam, Hungsze

Nonlinear Absorption Initiated Laser-Induced Damage in [Gamma]-Irradiated Fused Silica, Fluorozirconate Glass and Cubic Zirconia

Description: 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 ...
Date: August 1988
Creator: Mansour, Nastaran

Experimental Determination of the Scattering Cross-section of Ogives and Prolate Spheroids at Microwave Frequencies

Description: Because of the great difficulty of obtaining exact numerical values of cross-section, and because of the inherent uncertainties in interpreting and evaluating the approximate methods, accurate experimental cross-section data would be extremely useful to the radar engineer. It was with this purpose in mind that the present long-range research program in microwave scattering was undertaken. Of immediate interest were the scattering properties of the prolate spheroid, the ogive (formed by rotating the minor segment of a circle around the chord), and, for comparison, the long cylinder.
Date: 1956
Creator: Rhoads, Wayne C.

Ion Beam Synthesis of Binary and Ternary Transition Metal Silicide Thin Films

Description: Among the well-known methods to form or modify the composition and physical properties of thin films, ion implantation has shown to be a very powerful technique. In particular, ion beam syntheses of binary iron silicide have been studied by several groups. Further, the interests in transition metal silicide systems are triggered by their potential use in advanced silicon based opto-electronic devices. In addition, ternary silicides have been by far less studied than their binary counterparts despite the fact that they have interesting magnetic and electronic properties. In this study, we investigate ion beam synthesis of Fe-Si binary structures and Fe-Co-Si ternary structures. This work involves fundamental investigation into development of a scalable synthesis process involving binary and ternary transitional metal silicide thin films and Nano-structures using low energy ion beams. Binary structures were synthesized by implanting Fe- at 50 keV energy. Since ion implantation is a dynamic process, Dynamic simulation techniques were used in these studies to determine saturation fluences for ion implantation. Also, static and dynamic simulation results were compared with experimental results. The outcome of simulations and experimental results indicate, dynamic simulation codes are more suitable than static version of the TRIM to simulate high fluence, low energy and, heavy ion implantation processes. Furthermore, binary Fe-Si phase distribution was determined at different implantation fluences and annealing temperatures. A higher fluence implantation at 2.16×1017 atoms/cm2 and annealing at 500 oC showed three different Fe-Si phase formations (β-FeSi2, FeSi and Fe3Si) in substrate. Further, annealing the samples at 800 oC for 60 minutes converted the Fe3Si phase into FeSi2 and FeSi phases. As an extension, a second set of Fe- ion implantations was carried with the same parameters while the substrate was placed under an external magnetic field. External magnetic fields stimulate the formation of magnetic phase centers in the ...
Date: December 2016
Creator: Lakshantha, Wickramaarachchige Jayampath

Local Phase Manipulation for Multi-Beam Interference Lithography for the Fabrication of Two and Three Dimensional Photonic Crystal Templates

Description: In this work, we study the use of a spatial light modulator (SLM) for local manipulation of phase in interfering laser beams to fabricate photonic crystal templates with embedded, engineered defects. A SLM displaying geometric phase patterns was used as a digitally programmable phase mask to fabricate 4-fold and 6-fold symmetric photonic crystal templates. Through pixel-by-pixel phase engineering, digital control of the phases of one or more of the interfering beams was demonstrated, thus allowing change in the interference pattern. The phases of the generated beams were programmed at specific locations, resulting in defect structures in the fabricated photonic lattices such as missing lattice line defects, and single-motif lattice defects in dual-motif lattice background. The diffraction efficiency from the phase pattern was used to locally modify the filling fraction in holographically fabricated structures, resulting in defects with a different fill fraction than the bulk lattice. Through two steps of phase engineering, a spatially variant lattice defect with a 90° bend in a periodic bulk lattice was fabricated. Finally, by reducing the relative phase shift of the defect line and utilizing the different diffraction efficiency between the defect line and the background phase pattern, desired and functional defect lattices can be registered into the background lattice through direct imaging of the designed phase patterns.
Date: December 2016
Creator: Lutkenhaus, Jeffrey Ryan

Low-Energy Electron Irradiation of Preheated and Gas-Exposed Single-Wall Carbon Nanotubes

Description: We investigate the conditions under which electron irradiation of single-walled carbon nanotube (SWCNT) bundles with 2 keV electrons produces an increase in the Raman D peak. We find that an increase in the D peak does not occur when SWCNTs are preheated in situ at 600 C for 1 h in ultrahigh vacuum (UHV) before irradiation is performed. Exposing SWCNTs to air or other gases after preheating in UHV and before irradiation results in an increase in the D peak. Small diameter SWCNTs that are not preheated or preheated and exposed to air show a significant increase in the D and G bands after irradiation. X-ray photoelectron spectroscopy shows no chemical shifts in the C1s peak of SWCNTs that have been irradiated versus SWCNTs that have not been irradiated, suggesting that the increase in the D peak is not due to chemisorption of adsorbates on the nanotubes.
Date: December 2016
Creator: Ecton, Philip

A Theoretical Investigation of Bound Roton Pairs in Superfluid Helium-4

Description: 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.
Date: August 1974
Creator: Cheng, Shih-ta

A Calculation of the Excitation Spectrum of Superfluid Helium-4

Description: The Hartree-Fock-Bogoliubov theory of homogeneous boson systems at finite temperatures is rederived using, a free energy variational principle. It is shown that a t-matrix naturally emerges in the theory. Phenomenological modifications are made (1) to remove the energy gap at zero momentum, and (2) to eliminate the Hartree-Fock-like terms, which dress the kinetic energy of the particle. A numerical calculation of the energy spectrum is made over a temperature range of 0.00 to 3.14 K using the Morse dipole-dipole-2 potential and the Frost-Musulin potential. The energy spectrum of the elementary excitations is calculated self-consistently. It has a phonon behavior at low momentum and a roton behavior at higher momentum, so it is in qualitative agreement with the observed energy spectrum of liquid He II. However, the temperature dependence of the spectrum is incorrectly given. At the observed density of 0.0219 atoms A-3, the depletion of the zero-momentum state at zero temperature is 40.5% for the Morse dipole-dipole-2potential, and 43.2% for the Frost- Musulin potential. The depletion increases gradually until at 3.14 K the zero momentum density becomes zero discontinuously, which indicates a transition to the ideal Bose gas.
Date: May 1974
Creator: Goble, Gerald W.