Radioactive Nuclear Beam Theory

(at the dep. of Theoretical Physics.)

``The Borromean Rings''

Russian - Nordic - British - Theory Collaboration

Radioactive nuclear beam theory

Recent developments of radioactive nuclear beam techniques have made it possible to reach the neutron dripline for light nuclei. Striking halo clusterizations of matter into a normal core and a loosely bound low density veil of neutrons seem to be more a rule than an exception. Thus we may study matter with exceptionally low density. The theoretical exploration of bound states of dripline matter within few-body models will be continued, and we are now also investigating what specific features the continuum of a system with a halo ground state may have.

By adding neutrons to light nuclei, surprising dripline structures have been discovered. The Helium chain is an example; adding a neutron to an alpha particle does not produce a bound system, adding one neutron more does; $^6$He a loosely bound halo-like system. The same happens if we continue. While $^7$He and $^9$He are unbound, $^8$He is bound and $^{10}$He nearly bound; 2 protons and 8 neutrons!

Substantial evidence has by now been accumulated for halo like phenomena in nuclear physics: Abnormally large light nuclei at the neutron dripline which exhibit a clear separation between a ``normal'' core nucleus and a loosely bound low-density veil of neutrons. This offers new and very interesting possibilities for studies of neutron matter under extreme conditions in a low-density background and, vice versa, the response of the core nucleus in a cloud of neutrons. If we try to support our thinking by using shell model pictures with a simple local field, the core and halo neutrons have no simple relations to a common field.

The Russian - Nordic - British Theory (RNBT) collaboration for RNB physics has now formally existed since 1991, with main (1994) participants from: R - RRC-Kurchatov(Moscow), JINR(Dubna), N - SENTEF UiB (Bergen), CTU/GU (Göteborg), NBI Univ. Copenhagen, B - CNP Univ. Surrey (Guildford). The collaboration is coordinated from Bergen (J.S. Vaagen). About fifteen theorists, including junior staff, now take part in the work. The collaboration has active contact with leading experimental groups and access to most recent data, also prior to publication.

The RNBT work has so far focused on few-body theory for light halo-like nuclei: Borromean systems. The Borromean rings, heraldic symbol of the princes of Borromeo, are carved in the stone of their castle on an island in Lago Maggiore in Northern Italy. The three rings are interlocked in such a way that if any of them were removed, the other two would also fall apart. The 3-body quantum analog is one where the 3-body system is bound, but where none of the two-body subsystems are bound.

Nature has realised Borromean systems in loosely bound halo-like nuclei such as 11Li, which are now produced as secondary beams. To understand these systems one needs to go beyond the mean field approach, to few-body theoretical procedures such as expansion on hyperspherical harmonics or the coordinate space Faddeev approach. Nuclei like 6He and 11Li can (a realistic starting point!) be modeled as a core surrounded by two loosely bound valence neutrons. Not only the bound state (6He and 11Li both have only one bound state!), but also the structure of the continuum and the details of reaction mechanisms are being studied. The knowledge is important for astrophysics, and the role of halo nuclei in nucleosynthesis in supernovae is currently being investigated.

The physics of the halo phenomena seems to be the homefield for few-body cluster models. To understand why these new clustering features emerge from the nuclear many-body problem is a challenge for the future. RNBT has chosen to develope few-body approaches to increasing sophistication, where the interactions between the constituents are tuned to available experimental data. This approach provides the practitioners with tools for learning how cluster phenomena are interrelated, and is a natural continuation of the way it all started. Our collaboration has, for the 3-body problem, in particular found two procedures for the bound-state problem useful, also in conjunction; expansion on hyperspherical harmonics and the coordinate space Faddeev approach, with slightly different merits.

Few-body systems have had small place in the standard teaching of quantum mechanics as they have been considered prohibitively difficult. With modern computers, the situation has changed in recent years. RNBT has taken the initiative to form training networks such as the NorFA network Subatomex and also within Nordplus.

The most exciting two-nucleon halo nuclei at the driplines are Borromean, i.e. while the three-body-like system is bound (but very loosely) none of the binary subsystems are bound. A theoretical treatment in terms of hyperspherical harmonics (HH) leads to a set of coupled equations in the hyperradius which technically in many ways resembles a binary problem. The Borromean property gives for bound states a unique and simple asymptotic behavior which is exponential (neutrons) in the hyperradius and governed by the two-nucleon separation energy.

We have, using again $^6$He as the benchmark system, extended the HH calculations to the Borromean continuum. Using operators for charge-exchange and inelastic scattering on nucleon targets, we have predicted structures in the $^6$He continuum below 10 MeV where previously only a sharp low-lying 2+ resonance was known. Thus we have predicted a second genuine three-body 2+ resonance, low-lying 1- and 0+ strength accumulations none of which qualify as three-body resonances, and also weaker unnatural parity responses. International laboratories have now set out to search for these structures. An essential part of our work has been to find physical classifications for low-lying responses in halo systems. A simple analytic users formula has been found for the electric dipole (E1) excitation of a two-neutron halo system.

We have also suggested that the halo structure found in a two-neutron halo system such as $^6$He may persist if we change halo neutrons into protons, and coined the word halo analog states. Again the A=6 nuclei have been the test bench, but we have suggested that the concept may also apply to systems like $^{11}$Li where the isospin of the core is different from zero. Again experimentalists have started to look for such states.

We have also by studying 1-neutron halo systems, examined how various halo observables are sensitive to the core region and core degrees of freedom. We have partly used a supersymmetric (SUSY) transform to probe dependence on the nodal structure and partly a coupled channels Sturmian procedure to examine consequences of core excitation. Our findings are that the halo picture is quite robust, but that core degrees of freedom are needed for energy and spectroscopic strength observables. The SUSY analysis gave us confidence in the way we have treated the Pauli principle (core-blocking) in our past HH calculations.

A dream of the 1950s was to be able to study nuclear reactions starting from the nucleon-nucleon operator. The large size (loose binding) of halo nuclei seems now to make this come true. Thus we have formulated a parameter free treatment of charge-exchange on nucleon targets and applied it successfully to 200MeV data for A=6 systems i.e. at sufficiently high energy.

The NORDITA programme for dripline theory where RNBT played an instrumental role, was completed in 1995. RNBT has used Nordic mobility programmes such as Nordplus in its operation. The study weekend HALO'95 was again held in Copenhagen. The EU TMR-network application TRIBE, coordinated from Bergen, will be repeated in 1996. Again RNBT's international participation as invited speakers and on advisory boards has been substantial.

Some of our achievements were mentioned in the Science in Pictures article "Halo Nuclei" by Austin and Bertsch in Scientific American June 1995 and very recently in the feature article "Nuclei on the dripline" by Al-Khalili in Physics World (June 1996). Some of our published papers have already an extraordinary number of citations. Thus our Physics Reports 231 (Zhukov et al., 1993) is one of the most cited theory papers in the field with in 1995 about 10 times the average in nuclear theory.

Department of Physics at the University of Bergen

Last modified: July 4, 1996