J. S. Vaagen

Bound state properties of Borromean halo nuclei: 6He and 11Li

Abstract The nuclei 6 He and 11 Li which exhibit pronounced halo-structures with two loosely bound valence neutrons, are currently being explored as secondary-beam projectiles. These nuclei are Borromean, i.e. while they are bound (only one bound state) they have, considered as three-body systems, no bound states in the binary subsystems. We argue that a three-body description is the natural one for central properties of such exotic loosely bound nuclei, and give the state of the art by comparing fully blown three-body calculations for 6 He (and neighboring A =6 nuclei) with a range of measured observables. We restrict this review to bound state properties, with emphasis on genuine three-body features. The bound state is the initial stage of the various reaction scenarios that now are being studied experimentally and a main objective of these studies. Currently used procedures for solving the three-body bound state problem are outlined, with emphasis on expansions on hyperspherical harmonics and also the coordinate space Faddeev approach. Although strict calculations can also be carried out for 11 Li, they are inconclusive concerning the details of the structure since the available information on the binary neutron- 9 Li(core) channel is insufficient. Calculations for a number of plausible model interactions, including treatments of the Pauli principle, are presented. They all reproduce the binding energy and halo characteristics such as valence one-particle density and give about the same internal r.m.s. geometry for 11 Li. In spite of this, the wave functions have pronounced differences in their spatial correlations. The same ambiguity is also present in other inclusive observables, such as momentum distributions. We also demonstrate that candidates for the nuclear structure can be explored within an approximate scheme COSMA. Predictions of exclusive observables are discussed, and quantities such as momentum correlations in complete measurements are found to be more sensitive to the detailed features of the nuclear structure of the bound state.

THREE-BODY CONTINUUM STRUCTURE AND RESPONSE FUNCTIONS OF HALO NUCLEI (I) :6HE

Abstract Three-body scattering states of the Borromean two-neutron halo nuclei are explored in a core + n + n model using the method of hyperspherical harmonics. We analyse the continuum structure (the properties of the continuum wave functions) separately from the continuum response (the magnitudes of one-step transitions from the ground state to the continuum). Predictions are made for the positions and strengths of the isoscalar monopole, electric dipole and quadrupole excitations, as well as for nuclear inelastic and charge-exchange response functions, for the 6 He nucleus. The known 2 + resonance in 6 He is reproduced. We find 1 − strength concentrations at lower energies in the proximity of the three-body threshold, and predict new 2 + , 1 + (and possibly 0 + ) resonances at slightly higher energies in 6 He.

Exploratory coupled channels calculations for loosely bound carbon isotopes

Abstract We have investigated the loosely bound halo candidates 17 C and 19 C in a neutron+core coupling model. A deformed Woods-Saxon potential is used for the neutron-core interaction and the coupled channels equations are solved with Sturmian expansions of the relative motion wave functions for experimental one-neutron separation energies. The r.m.s. matter radii, longitudinal momentum distributions, E1 strength functions, neutron stripping cross sections and electromagnetic dissociation cross sections are calculated. Their sensitivity to the structural assumptions is explored. Available data does not allow final conclusions to be drawn for 19 C but an assessment of the possible character of 17 C and 19 C is made, and in particular, of the role of s -orbital motion between halo-neutron and core.

Calculation of 11Li in the framework of a three-body model with simple central potentials

Abstract The ground state of the 11Li nucleus is investigated by means of the hyperspherical harmonics method. The binding energy, RMS distances between constituents and inclusive momentum distributions are calculated together with 9Li-n and n-n momentum correlations.

Strength functions for 6He excitations

Abstract Wave functions for the ground and scattering states of the halo nucleus 6 He are calculated in an α + n + n three-body model and used to predict the strengths of nuclear monopole and electric dipole excitations. Strength concentrations at lower energies are found, but no narrow resonances.

Rainbows in Nuclear Reactions and the Optical Potential

Nucleus-nucleus scattering and charge-exchange reactions are studied in a region where rainbow-like phenomena are seen. Optical potentials are found which give fits to the cross sections, but in spite of the rainbow-like phenomena and contrary to apparently accepted expectations, not determined unambiguously. Other possibilities of resolving the ambiguities are discussed.

Direct Experimental Evidence for a Soft-Dipole Response in 6He

The differential cross-sections of the charge exchange reaction 6Li(7Li, 7Be) 6He were measured at beam energies 78 and 82 MeV. In addition to the 0+ bound state and sharp 2+ resonance, three wide bumps were identified in the experimental continuum spectrum of 7Be at small angles. The maximum at excitation energy of ~ 6 MeV (Γ ~ 5 MeV FWHM) is consistent with a soft-dipole response, expected in nuclei with neutron halo.

Three-body structure of 8Li and the 7Li(n,γ)8Li reaction

Abstract A three-body cluster 4He+t+n model is developed for 8Li using the method of hyperspherical harmonics with realistic cluster-cluster interactions fitted to experimental data. The model is used to calculate wave functions, spatial and matter densities of the ground state and the low lying excited state of 8Li. The model reproduces experimentally known properties of 8Li. Contrary to two-body models, our prediction for the radiative neutron capture on 7Li at low energies supports a lower cross section value.

Scattering of 3He on 12C and the inelastic form factor

Abstract Measurements of inelastic scattering of 3He on 12C at EHe = 72 MeV with excitation of low lying 2+, 3−, 0+ states of the target are reported. The data were analyzed both by DWBA and coupled-channels approximation, the latter leading to only minor changes, and we argue that nuclear rainbow effects are present. It is possible to reproduce the main features of the 2+ and 3− inelastic angular distributions by means of the optical model potential previously selected for the reaction (3He, t) on 13,14C targets, only if the derivative excitation form factors are modified in the vicinity of the strong absorption radius. The fit is improved in detail and can be made nearly perfect if more flexible model-independent form factors are employed. An alternative potential is also discussed.

Effective interaction techniques for the Gamow shell model

We apply a contour deformation technique in momentum space to the newly developed Gamow shell model, using the drip-line nuclei