15,486 research outputs found
Origin of three-body resonances
We expose the relation between the properties of the three-body continuum
states and their two-body subsystems. These properties refer to their bound and
virtual states and resonances, all defined as poles of the -matrix. For one
infinitely heavy core and two non-interacting light particles, the complex
energies of the three-body poles are the sum of the two two-body complex
pole-energies. These generic relations are modified by center-of-mass effects
which alone can produce a Borromean system. We show how the three-body states
evolve in He, Li, and Be when the nucleon-nucleon interaction is
continuously switched on. The schematic model is able to reproduce the main
properties in their spectra. Realistic calculations for these nuclei are shown
in detail for comparison. The implications of a core with non-zero spin are
investigated and illustrated for Ne (O+p+p). Dimensionless units
allow predictions for systems of different scales.Comment: 15 pages, 7 figure
Square-well solution to the three-body problem
The angular part of the Faddeev equations is solved analytically for s-states
for two-body square-well potentials. The results are, still analytically,
generalized to arbitrary short-range potentials for both small and large
distances. We consider systems with three identical bosons, three non-identical
particles and two identical spin-1/2 fermions plus a third particle with
arbitrary spin. The angular wave functions are in general linear combinations
of trigonometric and exponential functions. The Efimov conditions are obtained
at large distances. General properties and applications to arbitrary potentials
are discussed. Gaussian potentials are used for illustrations. The results are
useful for numerical calculations, where for example large distances can be
treated analytically and matched to the numerical solutions at smaller
distances. The saving is substantial.Comment: 34 pages, LaTeX file, 9 postscript figures included using epsf.st
Efimov effect in nuclear three-body resonance decays
We investigate the effects of the nearly fulfilled Efimov conditions on the
properties of three-body resonances. Using the hyper-spheric adiabatic
expansion method we compute energy distributions of fragments in a three-body
decay of a nuclear resonance. As a realistic example we investigate the 1-
state in the halo nucleus 11Li within a three-body 9Li+n+n model.
Characteristic features appear as sharp peaks in the energy distributions.
Their origin, as in the Efimov effect, is in the large two-body s-wave
scattering lengths between the pairs of fragments
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