Three-body Thomas-Ehrman shifts of analog states of 17^{17}Ne and 17^{17}N

The lowest-lying states of the Borromean nucleus $^{17}$Ne ($^{15}$O+$p$ + $p$) and its mirror nucleus $^{17}$N ($^{15}$N+$n$ + $n$) are compared by using the hyperspheric adiabatic expansion. Three-body resonances are computed by use of the complex scaling method. The measured size of $^{15}$O and the low-lying resonances of $^{16}$F ($^{15}$O+$p$) 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 $0^+$ resonance in a model benchmark system of three identical bosons; the $2^+$ resonance in the $^6$He nucleus within the $\alpha+n+n$ model; and the two $0^+$ resonances in $^{12}$C within the three-$\alpha$ model.Comment: 20 pages, 10 figure