Onset of Chaos in  The Nuclear Response to  The Nuclear Response to

Probing the nucleus at the limits of angular momentum and at extreme shapes

Rapidly rotating, highly excited nuclei are produced in nuclear reactions using beams of accelerated heavy ions. The response of the nucleus to the rotational stress gives rise to a wide variety of nuclear structure phenomena. Information on the properties and the behaviour of the nucleus is contained in a cascade of about thirty gamma-rays emitted as it deexcites from the highly excited state in which it was produced to the ground state. Improvements in high-resolution detector systems have steadily expanded the limits of what can be observed and new phenomena have been discovered leading to unexpected insights into the nature of the nucleus. The European Ge-detectors arrays NORDBALL, EUROGAM and GASP have significantly contributed in recent years to such progress and some of the challenging new ideas in this field await exploitation with EUROBALL. One new phenomenon, recently discovered in spherical nuclei, takes the form of regular sequences of very enhanced magnetic dipole transitions. They were first observed in light-mass Pb and Bi isotopes, and then in nuclei in the mass 110 and 140 regions. This observation contradicts the familiar, intuitive idea that nuclei only show rotational bands if their mass distribution is deformed. In these cases it turns out to be a large magnetic dipole moment which breaks the symmetry and fixes a rotation angle. This moment rotates about the angular momentum axis and generates the strong magnetic radiation. Thus, ``magnetic rotation'' is, in addition to the familiar ``electric rotation'', a new manifestation of quantal rotation New types of rotational bands should also exist in nuclei with stable triaxial shapes, which are only just beginning to be explored. In the Lu isotopes large-deformation bands with sizeable triaxiality have been found. These nuclei are good candidates in which to search for the theoretically predicted ``chiral-twin bands'', where the triaxiality defines the direction of rotation. Isomeric states have long been a prolific source of information about nuclear structure. For deformed nuclei the approximate conservation of the angular-momentum projection, K, on the symmetry axis leads to high-K isomers in regions where the Fermi surfaces lie high in the subshells. Recent research on K-isomers has provided new insight into shape tunnelling with a single-step decay from very large-K to low-K states, tilted rotation and the quenching of pairing correlations. The availability of radioactive beams will greatly extend the range of K-isomers that are accessible to study and promises to reveal examples of states with extreme numbers of quasi-particles. They will open up areas that are of interest to $\gamma$-ray lasers and to stellar nucleosynthesis. The interplay between collective and single-particle motion may very well be demonstrated at the extreme high-spin end of rotational bands. When the angular momentum reaches that of the sum of the valence nucleons outside a closed shell or subshell, the nucleons align their spins and the mass distribution changes from prolate to oblate. This change may be sudden, leading to an abrupt band termination, or it may be smoother, resulting in a soft termination with a gradual change in the moments-of-inertia. Determining the expected decrease in collectivity in the spin 50 to 60 $\hbar$ region is a challenging task even for the largest Ge-detector arrays such as EUROBALL. Reproducing the existence of superdeformed nuclei at high spins has been one great success of the predictive power of nuclear mean field calculations. In the last five years the nucleus in its second (superdeformed) minimum has constituted a unique laboratory where we were able to test our ideas of the nuclear many-body problem. Indeed, a large body of detailed experimental information, including quadrupole moments, explicit single-particle configurations and moments-of-inertia, could be explained by mean field calculations based on the cranking formalism. On the other hand, superdeformed nuclei show some surprising and unexpected properties. The most challenging observation, not predicted by theory, has been the observation that rotational bands in neighbouring nuclei are almost identical in many cases, see figure . At present, a global and consistent theory of identical bands is still lacking and the origin of the unexpected stability of moments-of-inertia remains the primary question to be investigated. A satisfactory solution to this problem could potentially lead to new insights into the structure of nuclei, to a better understanding of effective interactions, or even point to the exciting possibility that a hitherto unnoticed symmetry is realised in nuclei. New types of symmetry have been invoked to explain another surprising discovery made in superdeformed nuclei, namely the oscillations of the moments-of-inertia of certain bands. The microscopic origin of the staggering in the $\gamma$-ray energies, see figure , is not yet understood. A possible explanation of the phenomenon involves the C₄ point-group symmetry. The existence of other symmetries is still to be investigated. One other recent major achievement in this field, made possible by the increased sensitivity of modern Ge-detector arrays, has been the finding, in a few cases in the mass A=190 region, of the transitions linking the SD minimum to the normal deformed states. This fixes the excitation energy and the angular momentum of the bands. Despite rapid progress in our studies of superdeformed states, many questions remain unresolved and new questions have been posed. One major challenge is to determine the excitation energies and spins of the superdeformed levels since, for example, there is not a single superdeformed band in the A=150 region for which these properties are known. Indeed, in this mass region the decay is so fragmented that even more powerful instruments than EUROBALL will be needed. Another major deficiency is that we have no detailed spectroscopy in the superdeformed potential well. The known excited SD bands are believed to correspond to particle or quasi-particle excitations, but the collective modes associated with states at large deformation are yet to be found. To shed more light on the cause of identical bands, it will be necessary to perform precise lifetime and g-factor measurements for such bands in various mass regions. The results forthcoming from powerful arrays such as EUROBALL will bring positive answers to some of these open questions.   

Figure: Spectrum of $\gamma$-rays de-exciting superdeformed yrast states in ¹⁴⁹Gd (top panel) and an excited superdeformed band in ¹⁴⁸Gd (lower panel) which exhibit identical moments of inertia. Insert: difference in energy (compared to a smooth reference) between adjacent $\gamma$-ray lines as a function of their energy. The same ``zig-zag'' pattern is present in both bands.

 

At even higher spins, nuclear states with hyperdeformed shapes are predicted by improved mean field calculations. Here we are still in the situation with regard to superdeformation before 1986, i.e. there are signs of its presence from some ridge structure but no discrete rotational bands have been identified. Of course, the first step is to find such discrete bands and then establish their hyperdeformed character from lifetime measurements. We expect that they will be populated with an intensity at least one order-of-magnitude smaller than that of superdeformed bands, which means that they lie at the limits of sensitivity of the coming generation of large spectrometers. EUROBALL may provide an answer to the question of the existence of states with this exotic shape at high spins. Detailed studies of the properties of such exotic shapes will demand more sophisticated spectrometers of even greater sensitivity. Very elongated shapes are also predicted in light nuclei. The most exotic examples involve chains of several $\alpha$ particles. To date their existence is deduced only from the observation of resonances in light symmetric systems in binary reaction channels. On the theoretical side, there are efforts to find more adequate microscopic descriptions of nuclear rotation including three-dimensional cranking models, generator co-ordinate projection methods, and large scale spherical shell model calculations. It will also be of primary importance to establish the role of time-odd components in the effective Hamiltonian/Lagrangian. At lower angular momentum Coulomb excitation has been the main tool to probe the collective properties of stable nuclei. A recent example is the long sought observation of multi-phonon surface vibrations in strongly deformed nuclei; future investigations will have to concentrate on the elusiveness of two and higher phonon states and on the question of the fragmentation of the vibrational strength. Multi-nucleon transfer reactions with the multiple Coulomb excitation process provide the only promising tool for populating collective states in heavy transactinide nuclei and studying their behaviour at high angular momentum, which is important for our understanding of the shell structure of the heaviest elements. With the advent of radioactive beams we will also be able to investigate in detail the collectivity of nuclei with exotic proton/neutron ratios. First Coulomb excitation studies confirmed definitely the sudden shape change in n-rich S isotopes and the fact that the semi-magic nucleus ³²Mg is superdeformed. These findings encourage further investigations of the structure of these nuclei as well as of heavier isotopic chains to study the effect of the neutron excess on their shell structure (e.g. vanishing shell gaps). To gain access to higher spin states up to almost 20 $\hbar$, peripheral nuclear fragmentation reactions can be employed. Relativistic Coulomb excitation also leads to the population of the E1 giant dipole resonance, thus providing an unorthodox approach to the ground state quadrupole deformation of exotic nuclei via the splitting of the resonance. Alternatively, Coulomb excitation with low energy radioactive beams may be used to determine E3 octupole matrix elements of nuclei predicted to exhibit reflection asymmetry. In addition, one should note that much of the information on the structure of very neutron-rich nuclei at higher excitations with spins up to 14 $\hbar$ have come from the studies, which employ spontaneous fission sources and large Ge-detector arrays. Most of the examples discussed in this section are associated with rather low production rates or can only be studied in reactions with low intensity radioactive projectiles. To overcome these difficulties, it is clear that a major effort has to be started right now to develop more sophisticated arrays if we are to make a significant advance both in efficiency and sensitivity.