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

Assessing the accuracy of Hartree-Fock-Bogoliubov calculations by use of mass relations

The accuracy of three different sets of Hartree-Fock-Bogoliubov calculations of nuclear binding energies is systematically evaluated. To emphasize minor fluctuations, a second order, four-point mass relation, which almost completely eliminates smooth aspects of the binding energy, is introduced. Applying this mass relation yields more scattered results for the calculated binding energies. By examining the Gaussian distributions of the non-smooth aspects which remain, structural differences can be detected between measured and calculated binding energies. Substructures in regions of rapidly changing deformation, specifically around $(N,Z)=(60,40)$ and $(90,60)$, are clearly seen for the measured values, but are missing from the calculations. A similar three-point mass relation is used to emphasize odd-even effects. A clear decrease with neutron excess is seen continuing outside the experimentally known region for the calculations.Comment: 13 pages, 9 figures, published versio

The size of two-body weakly bound objects : short versus long range potentials

The variation of the size of two-body objects is investigated, as the separation energy approaches zero, with both long range potentials and short range potentials having a repulsive core. It is shown that long range potentials can also give rise to very extended systems. The asymptotic laws derived for states with angular momentum l=1,2 differ from the ones obtained with short range potentials. The sensitivity of the asymptotic laws on the shape and length of short range potentials defined by two and three parameters is studied. These ideas as well as the transition from the short to the long range regime for the l=0 case are illustrated using the Kratzer potential.Comment: 5 pages, 3 figures, submitted to Physical Review Letter

Halos and related structures

The halo structure originated in nuclear physics but is now encountered more widely. It appears in loosely bound, clustered systems where the spatial extension of the system is significantly larger than that of the binding potentials. A review is given on our current understanding of these structures, with an emphasis on how the structures evolve as more cluster components are added, and on the experimental situation concerning halo states in light nuclei.Comment: 27 pages, 3 figures, Contribution to Nobel Symposium 152 "Physics With Radioactive Beams