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

Higher-order Brunnian structures and possible physical realizations

We consider few-body bound state systems and provide precise definitions of Borromean and Brunnian systems. The initial concepts are more than a hundred years old and originated in mathematical knot-theory as purely geometric considerations. About thirty years ago they were generalized and applied to the binding of systems in nature. It now appears that recent generalization to higher order Brunnian structures may potentially be realized as laboratory made or naturally occurring systems. With the binding energy as measure, we discuss possibilities of physical realization in nuclei, cold atoms, and condensed matter systems. Appearance is not excluded. However, both the form and the strengths of the interactions must be rather special. The most promising subfields for present searches would be in cold atoms because of external control of effective interactions, or perhaps in condensed-matter systems with non-local interactions. In nuclei, it would only be by sheer luck due to a lack of tunability.Comment: 8 pages, 5 figures, revised versio

Nuclear halo and its scaling laws

We have proposed a procedure to extract the probability for valence particle being out of the binding potential from the measured nuclear asymptotic normalization coefficients. With this procedure, available data regarding the nuclear halo candidates are systematically analyzed and a number of halo nuclei are confirmed. Based on these results we have got a much relaxed condition for nuclear halo occurrence. Furthermore, we have presented the scaling laws for the dimensionless quantity $/R^{2}$ of nuclear halo in terms of the analytical expressions of the expectation value for the operator $r^{2}$ in a finite square-well potential.Comment: 14 pages, 3 figure

Extended sudden approximation model for high-energy nucleon removal reactions

A model based on the sudden approximation has been developed to describe high energy single nucleon removal reactions. Within this approach, which takes as its starting point the formalism of Hansen \cite{Anne2}, the nucleon-removal cross section and the full 3-dimensional momentum distributions of the core fragments including absorption, diffraction, Coulomb and nuclear-Coulomb interference amplitudes, have been calculated. The Coulomb breakup has been treated to all orders for the dipole interaction. The model has been compared to experimental data for a range of light, neutron-rich psd-shell nuclei. Good agreement was found for both the inclusive cross sections and momentum distributions. In the case of $^{17}$C, comparison is also made with the results of calculations using the transfer-to-the-continuum model. The calculated 3-dimensional momentum distributions exhibit longitudinal and transverse momentum components that are strongly coupled by the reaction for s-wave states, whilst no such effect is apparent for d-waves. Incomplete detection of transverse momenta arising fromlimited experimental acceptances thus leads to a narrowing of the longitudinal distributions for nuclei with significant s-wave valence neutron configurations, as confirmed by the data. Asymmetries in the longitudinal momentum distributions attributed to diffractive dissociation are also explored.Comment: 16 figures, submitted to Phys. Rev.