J. Bang

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.

A realistic three-body model of 6Li with local interactions

Abstract The ground state energy and wave functions are found for 6 Li, treated as an inert α-particle, a proton and a neutron, interacting with each other by local, realistic forces, taking the Pauli principle into account. The Faddeev equations in space are solved, and values for theenergy and charge radius are obtained which are in agreement with experimental values.

Stripping reactions leading to decaying states

Abstract Cross sections for stripping reactions leading to states in the continuum, described as single-particle resonances, are given, using Gamows decaying state function as form factors in DWBA calculations. The results are compared to measured differential cross sections and estimates of spectroscopic factors for the cases Zr(d, n) and Pb(d, p).

One-particle transfer reactions to highly excited states in deformed nuclei

Abstract A method for calculation of single-particle wave functions in a deformed Woods-Saxon potential is developed. The wave functions are used as form factors in stripping and pick-up calculations, and the resulting cross sections are compared to experimental data.

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.

Model calculations with pairing forces

Abstract Energies and occupation numbers for a symmetric 32-level model with pairing interaction are investigated. Exact calculations are compared with the approximations BCS and BCS+ RPA+projection. The numbers calculated with the last method are shown to be in good agreement with the exact values for the present model.

Expansion of continuum functions on resonance wave functions and amplitudes

Abstract The pole expansion (Mittag-Leffler expansion) of wave functions, scattering amplitudes, and Green functions at positive energies are discussed in a mathematically rigorous way. The general proofs of convergence are supplemented by numerical calculations, which, for a simple example, show the convergence to be fast. Applications of the method to nuclear structure calculations are discussed.

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.

Differential cross sections for (d, p) reactions from the WBP model

Abstract A detailed study is made of the weakly bound projectile (WBP) model for (d, p) reactions. Differential cross sections calculated from an approximate form of the model are reported for six reactions on closed-shell, spin-zero targets ranging from 16 O to 88 Sr. Good fits have been found for the six angular distributions with the spectroscopic factor S = 1 and one fixed set of nucleon-nucleus parameters. It is shown how the WBP model gives insight into the stripping mechanism. Certain features of the cross sections can be attributed to the transferred neutron; others arise mainly from the scattered proton. The results support the basic picture of WBP. A more refined version of the WBP model should thus be useful for extracting accurate spectroscopic factors from stripping measurements.