PRAMANA ­c Indian Academy of Sciences Vol. 53, No. 3 — journal of September 1999 physics pp. 365–380 Nuclear structure studies on halo nuclei by direct reactions with radioactive beams PETER EGELHOF Gesellschaft f¨ur Schwerionenforschung (GSI), D-64291 Darmstadt, Germany Abstract. The investigation of direct reactions with exotic beams in inverse kinematics gives access to a wide field of nuclear structure studies in the region far off stability. The basic concept and the methods involved are briefly discussed. The present contribution will focus on the investigation of light neutron-rich halo nuclei. Such nuclei reveal a new type of nuclear structure, namely an extended neutron distribution surrounding a nuclear core. An overview on this phenomenon, and on the various methods which gave first evidence and qualitative confirmation of our present picture of halo nuclei, is given. To obtain more quantitative information on the radial shape of halo nuclei, elastic proton scattering on neutron-rich light nuclei at intermediate energies was recently investigated for the first time. This method is demonstrated to be an effective means for studying the nuclear matter distributions of 8 such nuclei. The results on the nuclear matter radii of 6 He and He, the deduced nuclear matter density distributions, and the significance of the data on the halo structure is discussed. The present data allow also a sensitive test of theoretical model calculations on the structure of neutron-rich helium isotopes. A few examples are presented. The investigation of few-nucleon transfer reactions in inverse kinematics may provide new and complementary information on nuclear structure, as well as astrophysical questions. The physics motivation and the experimental concept for such experiments, to be performed due to momentum matching reasons at low incident energies around 5 – 20 MeV/u at the new generation low energy radioactive beam facilities SPIRAL, PIAFE, etc., is briefly discussed. Keywords. Halo nuclei; direct reactions with radioactive beams; nuclear matter radii. PACS Nos 21.10.Gv; 25.40.Cm; 25.60.-t; 25.60.Dz; 25.60.Gc; 27.20.+n 1. Introduction One of the most powerful classical methods for obtaining spectroscopic information on the structure of nuclei is the investigation of light-ion induced direct reactions, i.e. elastic or inelastic scattering, or one- and few-nucleon transfer reactions. A lot of what we know about the structure of stable nuclei was obtained from such investigations. Of course, before the availability of radioactive ion beams, this method was limited to stable or very long-lived nuclei for which targets could be prepared. The use of good-quality secondary exotic beams now enables to study such reactions on exotic nuclei using the method of d; Ôµ inverse kinematics, which is sketched in figure 1 for the example of a ´ reaction. In principle, a large variety of light-ion induced reactions with various physics motiva- d; Ôµ ´Ô; dµ tions may be investigated. One- and few-nucleon transfer reactions, such as ´ , , 365 Peter Egelhof d; Ôµ Figure 1. The method of inverse kinematics is sketched for the example of a ´ - reaction on the nucleus A X. Figure 2. Schematic view of the accelerator facilities at GSI, Darmstadt. Heavy-ion ¾¿8 ¾¼ beams of all ion species up to U from the linear accelerator UNILAC ( E MeV/u) ¾ are post-accelerated by the heavy-ion synchrotron SIS (E GeV/u), and may be in- jected into the fragment separator FRS and (or) into the experimental storage ring ESR. ¿ ¿ d; ص ´d; µ ´ «µ ´ , He , He, , etc., allow to populate single-particle (hole) states or two- ¼ ¼ Ô; Ô µ ´«; « µ particle (two-hole) states, whereas inelastic ´ , , etc. scattering leads to the Ô; Ôµ ´«; «µ population of collective states, and ´ , , etc. elastic scattering allows to deduce information on the nuclear matter distribution of nuclei. Of particular physics interest are, for example, the nuclear shell model in the region far off stability, the two-body residual in- teraction in nuclei, as well as astrophysical questions, transition densities and deformation parameters, the radial shape of nuclei, etc. The new heavy-ion accelerator facilities at GSI Darmstadt (see figure 2), which came into operation in 1990, opened new opportunities for a variety of nuclear physics studies. With respect to exotic nuclei the combination of the heavy-ion synchrotron SIS, the frag- ment separator FRS and, for selected cases, the experimental storage ring ESR provides good-quality beams of relatively short-lived nuclei, extending to isotopes far off stability, in the energy range from the Coulomb barrier up to intermediate energies around 1 GeV/u. 366 Pramana – J. Phys., Vol. 53, No. 3, September 1999 Direct reactions with radioactive beams The present contribution will focus on nuclear structure studies on light neutron-rich 8 halo nuclei. Such nuclei, located near or at the neutron drip line, in particular 6 He, He, ½4 ½½ Li, Be, etc., have attracted much attention in the recent years since there is clear ex- perimental evidence that these nuclei reveal a qualitatively new type of nuclear structure, namely an extended neutron distribution surrounding a nuclear core. A brief overview on this phenomenon and on some of the experimental methods which gave first evidence, and which were used for further experimental access to the halo struc- ture of nuclei, is given in the following section. The third section is dedicated to the investigation of nuclear matter distributions of halo nuclei by intermediate-energy elastic proton scattering, a method which was applied on exotic nuclei for the first time in recent experiments at GSI. Finally, the investigation of few-nucleon transfer reactions in inverse kinematics is discussed which may in future provide complementary information on the structure of halo nuclei. 2. Halo nuclei – A new phenomenon of the structure of nuclei The discovery and the interpretation of the phenomenon of halo nuclei was initiated in the mid-eighties by the pioneering work of Tanihata and coworkers [1–3]. In these experiments the total interaction cross section Á was determined for the interaction of light neutron- rich isotopes with various targets. Á was deduced from the change of intensity of a beam of exotic nuclei before and after hitting a target. From the measured interaction cross Ê ´ÔÖÓ j:µ sections the nuclear matter radii Á of the projectile nuclei may be estimated by simple geometrical considerations using the relation ¾ = [Ê ´ÔÖÓ j:µ·Ê ´ØaÖ:µ] ; Á Á Á (1) Ê ´ØaÖ:µ Á being the matter radius of the target nucleus (it should be noted that for a quan- titative determination of the matter radii a more sophisticated analysis taking into account the reaction dynamics was used). ½½ The surprisingly steep rise of Á for Li in the chain of the Li-isotopes, and less pro- 8 nounced, for 6 He and He for the He-isotopes, was therefore interpreted as due to a pro- nounced increase of the nuclear matter radius. In figure 3 a compilation of such data [3] measured for a larger number of neutron-rich isotopes is displayed. In almost all of the ´½=¿µ isotope chains we observe for the most neutron-rich nuclei a deviation from the A -law (see dotted line in figure 3), which is well established for stable and less exotic nuclei. These findings were at that time interpreted in terms of the following picture (see also figure 4): For the case of ‘normal’ nuclei, which are stable or are situated close to the val- ley of stability, and which therefore possess only a small excess of neutrons, the neutrons and protons are equally distributed (left part of figure 4), and the addition of one neutron will not drastically change the spatial extension of the nucleus. In contrast, a new phe- nomenon of nuclear structure appears for some nuclei which are close to the drip line, and for which the binding energy of additional valence nuclei is consequently very low, usually of the order of a few hundred keV only. Adding one or more neutrons to such an already very neutron-rich nucleus will produce in certain cases a so-called ‘halo’ around a nuclear core, consisting of an extremely spatially extended, low-density aureole in which the ad- ditional neutrons are located (right part of figure 4). Thus, in special cases, a significant Pramana – J. Phys., Vol. 53, No. 3, September 1999 367 Peter Egelhof Ê Figure 3. Nuclear matter radii Á deduced from measured total interaction cross sec- tions for several isotope chains of light neutron-rich nuclei (from ref. [3]. Figure 4. Density distributions of nuclear matter for stable nuclei and extremely neutron-rich nuclei. fraction of more than 90% of the valence neutron wave function can be outside the central part of the nucleus, leading to an extended radius of the nuclear matter distribution. So, ¿¾ for example, the nuclear radius determined for ½½ Li is similar to that of the stable S, which consists of approximately three times the number of nucleons. It turns out that the phenomenon of halo nuclei is always closely connected to a very low binding energy of the valence nucleons. In order to confirm the present picture of halo nuclei, and to get a deeper insight into the structure of such nuclei, halo nuclei were subjected to numerous studies during the last decade, using various methods. For a detailed overview over this field the reader may be referred to recent review articles [4–7]. Experiments performed at the on-line mass separator ISOLDE at CERN focused on the electric and magnetic moments of halo nuclei 368 Pramana – J. Phys., Vol. 53, No. 3, September 1999 Direct reactions with radioactive beams [8,9]. Beta-decay measurements following in-beam polarization by optical pumping on 9 Li and ½½ Li showed that the electric and magnetic properties of both nuclei are very similar.