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.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc500722 |
| Date | 05 1900 |
| Creators | Harper, John Howard |
| Contributors | Kobe, Donald Holm, Gray, Thomas James, 1917-, Deering, William D., McIntyre, Bernard, Krishnan, Raj Muthu |
| Publisher | North Texas State University |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | viii, 174 leaves : ill., Text |
| Rights | Public, Harper, John Howard, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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