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A variational energy calculation for an N-particle boson system has been performed. A two-body Hamiltonian, containing the phenomenological Lennard-Jones 6-10 potential, has been assumed, and the parameters of the Lennard-Jones potential have been chosen appropriate for liquid helium II. The trial wave function was assumed to be of the Jastrow type with two parameters. The value of one of the parameters was chosen to satisfy a liquid-structure-factor consistency condition. The expectation value for the ground state energy is expressed in terms of a generalized normalization integral. To evaluate the 3-N fold integrals, the normalization integral is approximated by truncating its expansion. After performing the variation, the ground-state energy is expressed as a function of the reduced particle number density. The cluster approximations used were found insufficient to effect saturation. / M.S.

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.

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We were unable to verify the existence of ion mobility discontinuities in either superfluid helium at 1 K or liquid nitrogen. The velocity-field dependence in helium was described by an increased interaction with the normal fluid, due to an increase in the roton number density close to the ion surface. The mobility results in nitrogen were interpreted as being due to liquid motion, following a theory by Kopylov. The D.C. results showed that the effect of a grid on the transmission of an ion beam could be described by a field dependent grid transmission coefficient, independent of the ion velocity. The vortex ring transmission through a grid was a complex function of vorticity being captured by the grid, the capture and escape probabilities of the bare ions by vorticity, and the onset for vorticity propagating throughout the ion cell.

published_or_final_version / Physics / Doctoral / Doctor of Philosophy

R.D. Maurer [and] Melvin A. Herlin. / "June 13, 1949." / Bibliography: p. 5. / Army Signal Corps Contract No. W36-039-sc-32037 Project No. 102B. Dept. of the Army Project No. 3-99-10-022.

J.R. Pellam. / "November 25, 1948." / Bibliography: p. 22. / Army Signal Corps Contract No. W36-039-sc-32037 Project No. 102B. Dept. of the Army Project No. 3-99-10-022.