BOUND STATE PROPERTIES of BORROMEAN HALO NUCLEI: 6He and 11Li
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BOUND STATE PROPERTIES OF BORROMEAN HALO NUCLEI: 6He AND 11Li M.V. ZHUKOV, B.V. DANILIN, DV. FEDOROV The Kurchatov Institute of Atomic Energy, 123182 Moscow, Russian Federation J.M. BANG The Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen 0, Denmark I.J. THOMPSON Department of Physics, University of Surrey, GuildfOrd GU2 5XH, UK and J.S. VAAGEN SENTEF, Institute of Physics, University of Bergen, N-5007 Bergen, Norway NORDITA, DK-2100 Copenhagen 0, Denmark NORTH-HOLLAND PHYSICS REPORTS (Review Section of Physics Letters) 231, No. 4 (1993) 151199. PHYSICS REPORTS North-Holland Bound state properties of Borromean halo nuclei: 6He and ‘1Li M.V. Zhukova, B.V. Danilina, D.V. Fedorova, J.M. Bangb, I.J. Thompsonc and J.S. Vaagen’~ The Kurchatov Institute of Atomic Energy, 123182 Moscow, Russian Federation The Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen 0, Denmark C Department of Physics, University of Surrey, Guildford GU2 5XH, UK SENTEF, Institute of Physics, University of Bergen, N-5007 Bergen, Norway ‘NORDITA, DK-2100 Copenhagen 0, Denmark Received November 1992; editor G. Brown Contents: 1. Introduction 153 4.2. Matter distribution; di-neutron and cigar struc- ii. Excitement on the neutron drip line 153 tures in the wave function 171 1.2. Borromean nuclei ‘‘Li, 6He 154 4.3. High energy 6He fragmentation and transverse 1.3. Scope of the article 155 momentum of constituents 174 2. Characteristics of currently used three-body 4.4. 4He—n and n—n momentum correlations 176 procedures 156 5. COSMA method for rapid assessment of “true” 2.1. Expansion on hyperspherical harmonics (HH) 156 wave functions for Borromean nuclei 177 2.2. Treatment of the Pauli principle and effective 5.1. Motivation for COSMA 177 interactions 158 5.2. The model and test for 6He 177 2.3. Coordinate space Faddeev approach (CSF) 160 5.3. Results of calculations for “Li 182 2.4. The cluster-orbital shell model (COSM) 161 5.4. ‘‘Li wave function structure in the framework of 2.5. Two-particle Green’s function method (GFM) 161 COSMA: spatial densities and 9Li—n and n—n 2.6. Variational approaches (VA) and method of correlated momentum distributions 184 integral equations (IE) 162 6. Strict three-body calculations for ‘‘Li 186 3. Tests against the “well known” non-Borromean 6.1. Effective interactions 186 nucleus 6Li 163 6.2. Faddeev (CSF) and HH calculations 187 3.1. Ground and excited states of 5Li 163 6.3. Matter and momentum distributions in the ‘‘Li 3.2. Electromagnetic and weak observables 165 g.s. 191 3.3. Quasielastic scattering of nucleons on 6Li 167 6.4. Predictions for momentum correlations 193 3.4. Conclusion 168 6.5. Summary 194 4. Strict three-body calculations of 6He 168 7. Conclusions and outlook 195 4.1. Energy and geometry of the ground state; wave References 196 function structure 169 Abstract: The nuclei 6He and “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 6He (and neighboring A = 6 nuclei) with a range of measured observables. We restrict this review to bound state properties, with emphasis on genuine three-bodyfeatures. The bound state is the initial stage ofthe 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 ‘‘Li, they are inconclusive concerning the details of the structure since the available information on the binary neutron-9Li(core) channel is insufficient. Calculations for a number of plausible model interactions, including treatments ofthe 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 ‘‘Li. In spite ofthis, 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. 0370-1573/93/$24.00 © 1993 Elsevier Science Publishers By. All rights reserved. 1. Introduction 1.1. Excitement on the neutron drip line The recent development of sufficiently intense secondary radioactive nuclear beams (RNB), produced through high-energy fragmentation of nuclei, has opened up new and exciting possibili- ties in the nuclear physics of light radioactive nuclei, in particular of nuclei near the neutron drip line. It bears promises for many applications in different fields of nuclear science, but especially for nuclear structure and reaction studies. The first experiments measured interaction cross-sections or reaction cross-sections at high and low energies for light radioactive neutron drip line nuclei [1—4] revealing abnormally large cross-sections for neutron rich nuclei such as “Li, “Be, ‘4Be, 17B These data provided important information on the nuclear sizes, and put on the agenda the question about existence of large neutron halos or dilute neutron skins (with long neutron tails extending well outside the nucleus) in loosely bound nuclei near the neutron drip line, in particular for the “Li nucleus. It should be noted that extended neutron halos had not been seen before in nuclei. Subsequent experiments with break-up of loosely bound neutron-rich projectiles on light targets [5—7]supported the existence of neutron halos in these systems. In particular, a very narrow °Li transverse momentum distribution (as compared to stable nuclei) was found from “Li fragmenta- tion at high energy [5]. Extremely narrow neutron angular distributions were also found from ~1~i break-up at low energy [6]. A very recent measurement of the 9Li longitudinal momentum distribution [8] shows an even narrower 9Li momentum distribution than that found in [5]. These experiments give substance to the idea of a neutron halo, and questions about the detailed structure of the neutron halos should now be asked. Based on the neutron halo hypothesis, existence of a new low-lying giant dipole resonance mode, the so-called soft dipole mode, has been suggested [9] for such systems. Its appearance is connected with suggested low-frequency oscillations of the halo neutrons against the core, giving rise to low-lying dipole excitations. Assuming that “Li is composed of a 9Li core and a dineutron, large electromagnetic dissociation (EMD) cross-sections for ~ incident on heavy targets were predicted [10, 11]. The large cross-sections expected for Coulomb dissociation of ~ have been confirmed experimentally(at least qualitatively) at high [12], intermediate [13] and low [6] energies. It is very important that the EMD cross sections of “Li on a lead target (at high energy [12]) are approximately 80 times larger than those of the nearby normally bound projectile nucleus ‘2C after appropriate scaling of the cross section by Z2 of the projectile. Similarly large EMD cross sections were also obtained at high energy on heavy targets for two other neutron-rich nuclei, 6He and 8He [14]. The current rapid development of radioactive nuclear beam techniques at many nuclear facilities in the world [15] promises good progress in the near future. Some of the recent experiments with RNB and some of the experiments in progress or being planned are: (a) experiments with high intensity polarized beams and their applications to studying nuclei far from the stability line (the first results of measurements of g-factors of exotic nuclei were reported in [16]), 153 6He and ‘‘Li 154 MV. Zhukor eta!., The Borromean halo nuclei (b) reactions of astrophysical interest are studied at many laboratories, and many new results were reported at the Second International Conference on Radioactive Nuclear Beams (Louvain- la-Neuve, Belgium, 1991), (c) elastic scattering of exotic nuclei (low energy 6He scattering on light and heavy targets was measured in [17, 18] as well as low energy 13N + ‘2’13C elastic scattering [19], and the first results for intermediate energy “Li + p elastic scattering were reported in [16]), (d) inelastic scattering and transfer reactions with RNB, (e) measurements of EMD cross sections at different energies, (f) measurements of pion charge-exchange and double charge-exchange reactions (the first results on the “B (~—, ~ ~ ~ reaction have been published [20]), (g) beta-decay studies may also provide very important information about neutron halos in drip-line nuclei. First found was the beta-delayed deuteron emission from the decay of 6He [21], and subsequently the beta-decay of the neutron-rich nuclei 6’8He and 9”Lj was measured [22]. In all cases strong transitions were observed to states that lie close in energy to the initial state. More experiments concerning beta-decay studies ~ofneutron halo nuclei are planned for the near future. (h) Correlation studies of RNB fragmentation. The first results on neutron-neutron coincidence for (‘‘Li, 9Li) fragmentation on different targets at low energy were reported in [23]. Measure- ments of correlations between neutron and core-fragment have recently been carried out for 1’Li at low and high energies [24—26].They are in progress for the 6He case.