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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.

K-Shell Ionization Cross Sections of Selected Elements from Ag to La for Proton Bombardment from 0.6 to 2.0 MeV

Description: The K-shell x-ray and ionization cross sections are measured for protons on Ag, Cd, Sn, Sb, Te, Ba, and La over the ion energy range of 0.6 to 2.0 MeV. The data are compared to the predictions of the PWBA, the PWBA with corrections for binding energy and/or Coulomb deflection, the BEA, and the constrained BEA predictions. In general, the non-relativistic PWBA with binding energy correction gives the best overall agreement with the measurements of proton-induced x-ray processes for the K-shell of the elements studied in this work. The data further suggest the need for relativistic PWBA treatment of the interactions in the K-shell for the range of binding energies represented by the elements investigated in this work.
Date: May 1974
Creator: Khelil, Najat Arafat

Microwave Line Widths of the Asymmetric Top Formic Acid Molecule

Description: This work consisted of an experimental investigation of the formic acid (HCOOH) molecule's rotational spectrum. Measurements of line widths were obtained for J = 5, 12, 13, 19, and 20 for a pressure range from 1 to 10 microns. A linear behavior between Av and p was observed as predicted by theory. The line width parameter Avp was observed to depend on the quantum number J. Hard sphere collision diameters b1 were calculated using the obtained AvP values. These deduced hard sphere values were found to be larger than the physical size of the molecule. This result was found to be in general agreement with other investigation in which long range forces (dipole-dipole) dominate.
Date: August 1974
Creator: Maynard, Wayne R.

Microwave Properties of Liquids and Solids, Using a Resonant Microwave Cavity as a Probe

Description: The frequency shifts and Q changes of a resonant microwave cavity were utilized as a basis for determining microwave properties of solids and liquids. The method employed consisted of varying the depth of penetration of a cylindrical sample of the material into a cavity operating in the TM0 1 0 Mode. The liquid samples were contained in a thin-walled quartz tube. The perturbation of the cavity was achieved by advancing the sample into the cavity along the symmetry axis by employing a micrometer drive appropriately calibrated for depth of penetration of the sample. A differentiation method was used to obtain the half-power points of the cavity resonance profile at each depth of penetration. The perturbation techniques for resonant cavities were used to reduce the experimental data obtained to physical parameters for the samples. The probing frequency employed was near 9 gHz.
Date: May 1974
Creator: Hong, Ki H.

Proton-Induced L-shell X-Rays of Pr, Sm, Eu, Gd, and Dy

Description: Characteristic L-shell x rays of the five rare earths Pr, Sm, Eu, Gd, and Dy were studied in this work. The x rays were produced by ionization from 0.3 to 2.0 MeV protons from the 2.0 MV Van de Graaff at North Texas State University. Total L-shell ionization and x-ray production cross sections were measured for Sm and compared to the BEA, CBEA and PWBA theories. Total L-shell ionization cross sections were measured for Pr, Eu, Gd, and Dy and compared to the BEA, CBEA, and PWBA. The CBEA and PWBA fit the samarium data well for both ionization and x-ray production cross sections. The BEA was generally 40 per cent lower than the data. The CBEA and the PWBA also fit the ionization cross section data for Pr, Eu, Gd and Dy, while the BEA was generally 40 per cent lower than the data.
Date: August 1974
Creator: Abrath, Frederick G.

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