Stability, effective dimensions, and interactions for bosons in deformed fields

The hyperspherical adiabatic method is used to derive stability criteria for Bose-Einstein condensates in deformed external fields. An analytical approximation is obtained. For constant volume the highest stability is found for spherical traps. Analytical approximations to the stability criterion with and without zero point motion are derived. Extreme geometries of the field effectively confine the system to dimensions lower than three. As a function of deformation we compute the dimension to vary continuously between one and three. We derive a dimension-dependent effective radial Hamiltonian and investigate one choice of an effective interaction in the deformed case.Comment: 7 pages, 5 figures, submitted to Phys. Rev. A. In version 2 figures 2 and 5 are added along with more discussions and explanations. Version 3 contains added comments and reference

Condensates and correlated boson systems

We study two-body correlations in a many-boson system with a hyperspherical approach, where we can use arbitrary scattering length and include two-body bound states. As a special application we look on Bose-Einstein condensation and calculate the stability criterium in a comparison with the experimental criterium and the theoretical criterium from the Gross-Pitaevskii equation.Comment: 6 pages, 4 figures. Contribution to Workshop on Critical Stability III in Trento. Submitted to Few-Body System

Investigation of thermionic energy conversion final report, 9 jul. - 9 sep. 1962

Refractory ceramic oxide for thermionic diode

Scattering into Cones and Flux across Surfaces in Quantum Mechanics: a Pathwise Probabilistic Approach

We show how the scattering-into-cones and flux-across-surfaces theorems in Quantum Mechanics have very intuitive pathwise probabilistic versions based on some results by Carlen about large time behaviour of paths of Nelson diffusions. The quantum mechanical results can be then recovered by taking expectations in our pathwise statements.Comment: To appear in Journal of Mathematical Physic

Stability and structure of two coupled boson systems in an external field

The lowest adiabatic potential expressed in hyperspherical coordinates is estimated for two boson systems in an external harmonic trap. Corresponding conditions for stability are investigated and the related structures are extracted for zero-range interactions. Strong repulsion between non-identical particles leads to two new features, respectively when identical particles attract or repel each other. For repulsion new stable structures arise with displaced center of masses. For attraction the mean-field stability region is restricted due to motion of the center of masses

3P_2-3F_2 pairing in neutron matter with modern nucleon-nucleon potentials

We present results for the $^3P_2 - ^3F_2$ pairing gap in neutron matter with several realistic nucleon-nucleon potentials, in particular with recent, phase-shift equivalent potentials. We find that their predictions for the gap cannot be trusted at densities above $\rho\approx 1.7\rho_0$, where $\rho_0$ is the saturation density for symmetric nuclear matter. In order to make predictions above that density, potential models which fit the nucleon-nucleon phase shifts up to about 1 GeV are required.Comment: Revtex style, 19 pages, 6 figures inlude

Anatomy of three-body decay II. Decay mechanism and resonance structure

We use the hyperspherical adiabatic expansion method to discuss the the two mechanisms of sequential and direct three-body decay. Both short-range and Coulomb interactions are included. Resonances are assumed initially populated by a process independent of the subsequent decay. The lowest adiabatic potentials describe the resonances rather accurately at distances smaller than the outer turning point of the confining barrier. We illustrate with realistic examples of nuclei from neutron ($^{6}$He) and proton ($^{17}$Ne) driplines as well as excited states of beta-stable nuclei ($^{12}$C).Comment: To be published in Nuclear Physics