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.

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 …

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.

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.

This investigation is a theoretical study of the influence of defects of finite volume on the electrical conductivity in the quantum size effect regime. Correction terms to existing equations are derived, and a physical explanation of the results is given. Many macroscopic properties of films exhibit an oscillatory dependence on thickness when the thickness is comparable to the de Broglie wavelength of an electron at the Fermi surface. This behavior is called the quantum size effect. In very thin films, scattering from surfaces, phonons, and crystal defects plays an increasingly important role. In this investigation the influence of scattering centers (defects) in semimetal films on the electrical conductivity is explored by extending existing work to include scattering centers of finite range. The purpose of this study is to determine the overall change in the conductivity and the alteration of the amplitude of the oscillations. The Boltzmann transport equation is the starting point for the calculation. An equation for the vector mean free path is derived, and a solution is obtained by the iterative process. The relaxation approximation need not be made since the vector mean free path is determined. The sample is a thin slab that is infinite in two …

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.

The purpose of this study is to determine the characteristics of the solar cosmic ray flux. This report describes the design and construction of a cosmic ray detector system used in this study and describes the analysis of the data obtained from these systems.

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.

The usual virial theorem, relating kinetic and potential energy, is extended to a molecule by the use of the true wave function. The virial theorem is also obtained for a molecule from a trial wave function which is scaled separately for electronic and nuclear coordinates.