3,269 research outputs found
Three-body Thomas-Ehrman shifts of analog states of Ne and N
The lowest-lying states of the Borromean nucleus Ne (O+ +
) and its mirror nucleus N (N+ + ) are compared by using
the hyperspheric adiabatic expansion. Three-body resonances are computed by use
of the complex scaling method. The measured size of O and the low-lying
resonances of F (O+) are first used as constraints to
determine both central and spin-dependent two-body interactions. The
interaction obtained reproduces relatively accurately both experimental
three-body spectra. The Thomas-Ehrman shifts, involving excitation energy
differences, are computed and found to be less than 3% of the total Coulomb
energy shift for all states.Comment: 9 pages, 3 postscript figures, revtex style. To be published in Phys.
Rev.
Classification of three-body quantum halos
The different kinds of behaviour of three-body systems in the weak binding
limit are classified with specific attention to the transition from a true
three-body system to an effective two-body system. For weakly bound Borromean
systems approaching the limit of binding we show that the size-binding energy
relation is an almost universal function of the three s-wave scattering lengths
measured in units of a hyperradial scaling parameter defined as a mass weighted
average of two-body equivalent square well radii. We explain why three-body
halos follow this curve and why systems appearing above reveal two-body
substructures. Three-body quantum halos 2-3 times larger than the limit set by
zero hypermoment are possible
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
Complex scaling of the hyper-spheric coordinates and Faddeev equations
We implement complex scaling of Faddeev equations using hyper-spheric
coordinates and adiabatic expansion. Complex scaling of coordinates allows
convenient calculations of three-body resonances. We derive the necessary
equations and investigate the adiabatic spectrum at large distances. We
illustrate the viability of the implementation by calculations of several
three-body resonances: a resonance in a model benchmark system of three
identical bosons; the resonance in the He nucleus within the
model; and the two resonances in C within the
three- model.Comment: 20 pages, 10 figure
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