Table of contents

A summary is given of the experimental evidence for octupole shapes in nuclei, with emphasis on rotational spectra and dipole transition moments.

The applications of the extensions of relativistic mean field (RMF) theory to the rotating frame, such as cranked relativistic mean field (CRMF) theory and cranked relativistic Hartree-Bogoliubov (CRHB) theory, for the description of superdeformed bands in the A ∼ 60, 140 – 150 and 190 mass regions are overviewed and compared briefly with the results obtained in non-relativistic mean field theories.

The N = Z+2 nucleus ⁷⁴Kr has been investigated by in-beam conversion electron (CE) and γ ray spectroscopy. The electric-monopole (E0) decay was examined in order to confirm the evidence for a low-lying isomeric 0⁺₂ state and to give insight into the mixing between the predicted coexisting prolate and oblate shapes.

Well deformed and superdeformed rotational structures in the second well of nuclei near doubly-magic ⁵⁶Ni were recently identified by means of heavy-ion fusion-evaporation reactions. Most interestingly, some of these bands were found to decay by prompt particle emission in competition to the expected γ decay-out. Subsequently, dedicated experiments were performed to investigate this exotic decay mode in more detail. First results from these studies are reported.

I'll start off by reminding you of one of the most striking properties of superdeformed states, namely the way they decay to states of smaller deformation. I'll then try and convince you that the decay can be described using the same terminology in all the different mass regions. In such an approach, the general trends of the decay-out process and the general features of the decay-out spectrum can be explained satisfactorily. However, not everything is understood. This aspect will be the subject of the last part of my talk, where I'll present some recent work concerning the nature of the decay mechanism.

We study the phenomenon of shape coexistence at or near single-closed shells. For that purpose, we describe multi-particle-hole intruder excitations on equal footing with regular excitations in the interacting boson model, by introducing the particle-hole degree of freedom, through a new quantum number, called I(ntruder)-spin. The resulting horizontal classification scheme of multi-particle-hole intruder excitations in terms of I-spin multiplets is useful to interpret data and to describe global properties of intruder excitations throughout a mass region. On the other hand, the creation and annihilation of particle-hole pairs, using a non-compact algebraic structure U(6,6), allows to account for local properties associated with mixing between regular and intruder excitations. We will illustrate the model by discussing a particular series of isotopes where shape coexistence may be present, ^192–210Po.

High-spin states in N ≈ Z nuclei in the A ∼ 60 region have been studied in a series of experiments with Gammasphere and the Microball charged-particle detector array. These experiments have led to the identification of deformed and superdeformed rotational bands in more than a dozen proton-rich Ni, Cu, and Zn isotopes. Because of the limited spin content of the single-particle configurations in these relatively light nuclei, many of these bands are observed close to their terminating states. For two sets of strongly-coupled bands in ⁶²Zn, lifetime measurements have been possible all the way to the terminating states and these measurements have confirmed the predicted loss of collectivity associated with the smooth termination of rotational bands. These investigations have also firmly established an island of superdeformation around particle numbers N, Z ≈ 30 and have led to a number of interesting observations. These include the influence of limited single-particle spin content on the high-spin properties of superdeformed bands in this region, rotational alignments in N ≈ Z superdeformed nuclei, and relatively unhindered linking transitions connecting superdeformed and near-spherical states.

High-spin states in ^113–116Cd have been investigated with the heavy-ion induced fission reaction ²⁸Si + ¹⁷⁶Yb at 165 MeV. The experiment was performed with the Eurogam II array. New rotational bands based on two quasi-particle states have been observed for even-even cadmium isotopes. A new level scheme based on the 11/2^– isomeric state is proposed for ¹¹⁵Cd and the one of ¹¹³Cd has been extended to spin (31/2^–). Hartree–Fock calculations for even-even isotopes show a prolate deformation in this mass region. The decoupled bands identified in both odd nuclei are interpreted as being built upon a low-Ω_11/2 quasi-neutron configuration.

Lifetimes have been measured for three M1 bands in light Sn/Cd nuclei using the DSAM technique. B(M1) values deduced from these measurements show a rapid decrease with increasing spin for a given configuration. The results have been compared with both Tilted axis cranking and semi-empirical model calculations. These suggest that the shears mechanism is present in this mass region, and that the band in ¹⁰⁶Sn appears to be the first example of almost pure magnetic rotation.

High-K states played a key part in the discovery and understanding of deformed nuclei. An example is given of the recent use of high-K states as a signature of axially-symmetric prolate deformation in a nucleus which is predicted to show co-existence between spherical, oblate and prolate shapes. When associated bands can be identified, high-K states can also be used as a probe of pairing, and its modifiication of rotational motion. New results in ¹⁷⁸W imply that the underlying rigid moment-of-inertia revealed when orbits are blocked to form multi-quasiparticle high-K states is substantially less than the "classical" rigid-body value. The corollary is that static pairing is quenched when only a few orbits are blocked. Recent measurements of g-factors in related high-K states in ¹⁷⁹W allow the extraction of g_R values whose behaviour as a function of seniority agrees with this suggestion.

We have used a tilted axis cranking model in combination with the random phase approximation and particle number projection to analyze the influence of dynamical pairing correlations in the high-K bands of ¹⁷⁸W and their effect on relative energy and angular momentum. The calculations show the importance of dynamical pairing correlations to describe the experiment as well as advantages and problems with the different models in the superfluid and normal state regions.

Reduced hindrance factors of K-forbidden transitions are compiled for nuclei with A ∼ 180 where γ-vibrational states are observed. Correlations between these reduced hindrance factors and a Coriolis forces, statistical level mixing and γ-softness have been studied. It is demonstrated that the K-forbidden transitions probabilities are related to γ-softness. The decay of the high-K bandheads has been studied by means of the two-state mixing, which would be induced by the γ-softness, with the use of a number of K-forbidden transitions compiled in the present work, where high-K bandheads are depopulated by both E2 and ΔI = 1 transitions. The validity of the two-state mixing scheme has been examined by using the proposed identity of the B(M1)/B(E2) ratios of transitions depopulating high-K bandheads and levels of low-K bands. A break down of the identity might indicate that other levels would mediate transitions between high- and low-K states.

γ-spectroscopy methods have been used to search for microsecond isomers among the fragmentation products of a 1 GeV / nucleon ²⁰⁸Pb beam. In particular the population of the known K^π = 35/2^- isomer in ¹⁷⁹W has been investigated and several new isomeric decays have been found for neutron rich nuclei in the A ≈ 180–200 mass region. The ground state band of the neutron rich N = 116 system of ¹⁹⁰W has been identified for the first time and we discuss its structure in comparison to neighboring systems.

The nuclear many-body system may under rotation develop various exotic shapes. Most appealing is the strongly elongated, axially symmetric hyperdeformed shapes with axis ratio 3:1, which are predicted in certain regions but still not realized experimentally. Nuclei may also develop shapes where the axial symmetry is broken. Results of a search programme for rotational bands built on hyperdeformed as well as triaxial superdeformed shapes are presented and the consequences of triaxiality discussed

Nuclear clustering has been a subject of intense study since the advent of heavy ion accelerators. Looking back more than 30 years, we are able today to see the connection between resonances in heavy ion reactions and extreme states in nuclei. In particular, excited states close to the decay thresholds into substructures show pronounced cluster structures. The ever repeated question about the possibility to describe such cluster phenomena in an extended (to a very large basis) and deformed shell model, has recently been revived in view of improved computational facilities. The new experimental facilities and the powerful new detector arrays for γ-spectroscopy and for charged particles have increased the sensitivity to study clustering phenomena by orders of magnitude. Today we are able to study nuclear structure at the limits of the mean field concept. With the advent of radioactive beams and the study of nuclei, which are weakly bound in their ground states, the question of the limits of mean field concepts has reached the low excitation energy region of nuclei.

Density functional theory is used to derive an approximative model which is similar for finite fermion clusters as diverse as nuclei or metal clusters. It naturally results in quantitatively comparable deformations of the mean field for both nuclei and clusters. Linear nuclei, tetrahedral deformation and two-dimensional systems are also discussed.

The 1f_7/2-shell nuclei provide an excellent opportunity to study the interplay between single particle and collective degrees of freedom as a function of both angular momentum and valence particle number. A review of the most important experimental results in even-even N = Z nuclei is presented and compared with theoretical calculations. New results in deformed N = Z nuclei, in which band-terminating bands of positive and negative parity have been found, are presented together with a discussion on pairing correlations as a function of spin in isobaric analogue states.

The spherical-deformed shape coexistence of the doubly-magic ⁵⁶Ni nucleus is studied by the Monte Carlo shell model based on the Quantum Monte Carlo Diagonalization method. The coexistence of spherical yrast, first prolate deformed and second deformed states is described by the full pf- and pfg_9/2-shell calculations. The states of the first prolate deformed band are shown to be comprised primarily of four-particle and four-hole excitations on top of the correlated ground state. The second deformed band has negative parity states and can be described by including the g_9/2 degree of freedom.

The generalized Bohr Hamiltonian was used to describe the low-lying collective excitations in even-even isotopes of Ru, Pd, Te, Ba and Nd. The Strutinsky collective potential and cranking inertial functions were obtained using the Nilsson potential. The effect of coupling with the pairing vibrations is taken into account approximately when determining the inertial functions. The calculation does not contain any free parameters.

A first experiment was performed with the Binary Reaction trigger Spectrometer (BRS) for Euroball, as second last experiment of phase III. The reaction ²⁴Mg(³²S, ⁵⁶Ni*) at E = 163.5 MeV was chosen in order to populate a specific hyperdeformed resonance state in the compound nucleus ⁵⁶Ni* at E* = 84 MeV (J^π = 46⁺) and to investigate the spectroscopy of its binary descendents. The experimental setup combined the γ-detector array Euroball III, without the phase I Ge detectors, the two large-area gas detector telescopes of the BRS at forward angles and 31 of the 40 detectors of the 4π silicon ball EUROSiB (now called ROSiB) at backward angles. We report on results of binary reaction triggers collected with one BRS telescope. Binary events are separated from evaporation residues due to (i) the large laboratory scattering angles of the detected reaction fragments, the opening angle of the BRS telescope being θ = 12 ° – 46 °, and (ii) by means of particle identification in the telescope. In this paper channels with emission of ⁸Be plus two protons and of ¹²C will be discussed.

The structure of neutron-rich light nuclei can be investigated by means of in-beam gamma spectroscopy using both stable and radioactive beams. Two such experiments have recently been performed at GANIL. (i) Secondary beams of neutron-rich Ge, Zn and Ni isotopes around N = 40 were produced from the fragmentation of primary ⁷⁰Zn ⁸⁶Kr beams, and analyzed by means of the LISE3 spectrometer. For the transitions between the 0⁺ ground state and the first 2⁺ state, B(E2) values have been extracted from Coulomb excitation cross-section measurement. Some of the obtained results related to the effectiveness of the N = 40 spherical sub-shell closure are discussed. (ii) In-beam γ-spectroscopy of neutron-rich nuclei around ³²Mg produced by fragmentation of ³⁶S have been performed recently. Gamma decay of relatively high-lying excited states have been measured in a large number of exotic light nuclei. New results obtained in a number of neutron-rich nuclei around N = 20 are presented.

This article has no abstract

High-spin states of several isotopes in the mass A ≈ 100 region have been investigated following the fission of compound nuclei formed in three heavy-ion fusion-evaporation reactions. New sequences have been assigned to ⁹¹Sr, ¹⁰⁷Ru, and ^{113, 115, 117, 119}Cd isotopes using the complementary fission fragment technique. The ground-state bands have been extended to higher spins in ^{114, 116, 118, 120}Cd. The level schemes of ^88, 90, 92Sr and ¹⁰¹Tc have been considerably enriched. The plethora of results demonstrates the efficiency in which spectroscopic information can be collected on nuclei near the line of stability or slightly neutron-rich from studies of fission fragments following fusion-evaporation reactions. The prompt γ-ray intensity distributions of the fragments following the fission of the ¹⁹⁷Pb compound nucleus are reported. The empirical distributions as a function of Z and A are not reproduced by expected yields of symmetric fission. Rather these distributions reflect the selectivity of Gammasphere to detect collective nuclei and to study high-spin excitations in fission fragments.

The ⁷Li + ¹¹B reaction has been studied in the energy range from 3.1 to 11.5 MeV in the c.m. system by measuring the cross section of the γ-ray transitions in the residual nuclei produced. Statistical compound nucleus calculations have been performed in order to extract cross sections of the individual exit channels and eventually the fusion cross section. The hindrance of the fusion cross section at energies above the interaction barrier has been investigated in terms of macroscopic models.

We report here on a new method, the Recoil Shadow Anisotropy Method (RSAM), which can be used for identifying isomers in the nanosecond range and measuring their half-lives. This method can be applied to in-beam experiments using thin targets and multidetector arrays which include collimated composite detectors. The RSAM was first developed for data obtained with Eurogam II. A number of previously known isomers with half-lives ranging from 0.5 to 17 ns have been re-measured and several new isomeric states have been discovered.

Temperature and heat capacity for the rare earth nuclei ¹⁶²Dy, ¹⁶⁶Er and ¹⁷²Yb have been extracted from experimental data at the Oslo Cyclotron Laboratory (OCL). The starting point to determine thermodynamical quantities is the density of levels as a function of excitation energy. The density of accessible levels in the (³He, α γ)-reaction has been extracted from measured γ-spectra.

The ¹⁷⁴Yb(²⁵Mg, 5n)¹⁹⁴Pb and ¹⁷³Yb(²⁴Mg, 5n)¹⁹²Pb reactions were used to probe the decay of superdeformed (SD) bands. The total γ-ray spectra associated with the SD bands in ^192,194Pb have been studied to determine the energy and angular momenta associated with each step of the cascade, from entry population to decay to the ground state. In particular, the γ-ray spectra associated with the quasicontinuous, non-discrete decay of their respective yrast SD bands has been extracted. Using various model assumptions, the quasicontinuous decay spectrum is expected to have a rapid rise in intensity at an energy associated with the gap, or backshift parameter, in level density; such a rise is observed in the quasicontinuous decay of the SD bands in ^194,192Pb. Values of E_gap ≈ 0.9(1) MeV for ¹⁹⁴Pb at ≈ 6ℏ and E_gap ≈ 0.4^+0.3_-0.1 MeV for ¹⁹²Pb at ≈ 10ℏ have been deduced.

We present a new method to extract level density and γ-strength function from primary γ-spectra. We will focus on the ¹⁶²Dy(³He, ³He')¹⁶²Dy reaction, deduce temperature and heat capacity within the microcanonical and canonical ensemble theory and investigate the γ-strength function properties as function of temperature.

The time evolution of single proton quasi-stationary states emitted from axially deformed nuclei is studied by solving numerically the two-dimensional time dependent Schrödinger equation. Angular distributions of emission with respect to the nuclear axis of symmetry are obtained. It is shown that the main escape paths are determined by the quantum numbers of the metastable state, rather than by the deformation of the potential. Combinations of such numerical studies of multidimensional quantum tunneling and angular distribution measurements from oriented deformed nuclei could provide invaluable nuclear structure information and imaging of Nilsson orbitals.

The possibility of generating and studying new proton-emitting nuclei using projectile fragmentation of very-heavy beams is investigated in this work. The charge, mass and velocity distributions of heavy residues from the interaction of 30 MeV / nucleon ¹⁹⁷Au projectiles with ⁹⁰Zr have been measured with high-resolution using the MSU A1200 fragment separator. A broad range of proton-rich nuclei are produced in this reaction. A number of new p-rich nuclei (14, of which 6 are expected to be proton emitters) are observed in the region Z = 60 - l73. The opportunity of studying proton rich nuclei produced by this approach is discussed.

The three main contributions to the nuclear Hamiltonian–monopole, quadrupole and pairing–are analyzed in a shell model context. The first has to be treated phenomenologically, while the other two can be reliably extracted from the realistic interactions. Due to simple scaling properties, the realistic quadrupole and pairing interactions eliminate the tendency to collapse of their conventional counterparts, while retaining their basic simplicity.

The symmetries of the t = 1 and t = 0 pair-fields are different. The consequences for rotational spectra are discussed. For t = 1, the concept of spontaneous breaking and subsequent restoration of the isospin symmetry turns out to be important. It permits us to describe the proton-neutron pair-correlation within the conventional frame of pairing between like particles. The experimental data are consistent with the presence of a t = 1 field at low spin in N ≈ Z nuclei. For a substantial t = 0 field, the spectra of even-even and odd-odd N ≈ Z nuclei become similar. The possibility of a rotationally induced J = 1 pair-field at high spin is considered.

Isospin generalized pairing is considered for the ground states of even N = Z nuclei with A = 76 - 96. There is a transition from T = 1 pairing at the beginning of this isotope sequence to T = 0 pairing at the end of the sequence. Near the middle of the isotope sequence, there is coexistence of a T = 0 pair superfluid and a T = 1 pair superfluid in the same wave function. The fluctuation in the isospin is eliminated and isospin is conserved if the wave function contains only T = 0 pairing. The fluctuation in the particle number is reduced if the wave function contains np pairing.

The role the exchange of phonons between pairs of fermions moving in time reversal states lying close to the Fermi energy on the superfluidity and on the superconductivity of atomic nuclei and fullerenes respectively is discussed in terms of mean field theory and of ab-initio calculations.

An experiment aiming at finding evidence for γ-decay of the giant dipole resonance built on superdeformed nuclear states has been made using the EUROBALL γ-detector array coupled to the large BaF₂ detectors of the HECTOR system. The reaction ¹¹⁰Pd(³⁷Cl, 4n)¹⁴³Eu at beam energies of 165 MeV and 170 MeV has been employed. A report of the analysis of a part of the data at E_beam = 165 MeV is given here. Results based on more inclusive and on very exclusive high-energy γ-ray spectra are presented. In particular, the spectrum of high-energy γ-rays gated by low-energy transitions between states fed by the superdeformed states are found to show some excess of yield in the 9–11 MeV region with respect to the spectrum gated by transitions not fed by the superdeformed states. This is the γ-ray energy region where one expects to find the γ-decay of the giant dipole oscillation along the long axis of a superdeformed axially symmetric nucleus. The measured excess is found to be of the same order as that predicted by schematic statistical model calculations assuming that the excitation of the GDR built on excited states is restricted to a region of the phase space a few MeV above the yrast line at very high spins.

A systematic description of the evolution of the giant dipole resonance (GDR) at non-zero temperature T is presented within the Phonon Damping Model (PDM). The damping of the GDR is caused by coupling to all ph, pp and hh configurations at T ≠ 0, where the coupling to pp and hh configurations is responsible for the increase and saturation of the GDR width as a function of T. The results of numerical calculations for the GDR width, the strength function and the integrated yield of γ rays in ¹²⁰Sn and ²⁰⁸Pb at 0 ≤ T ≤ 6 MeV are obtained in a reasonable agreement with the most recent experimental data.

The transfer reaction p(⁸He, d)⁷He with the exotic ⁸He-beam has been studied by correlational measurements, and an excited state of ⁷He was observed. Most likely, it has a structure with a neutron in an excited state coupled to the ⁶He-core which itself is in the excited 2⁺-state. The transfer reaction p(⁸He, ²He)⁷H was also studied, and manifestation on the possible existence of the resonance ⁷H was obtained.

We discuss experimental and theoretical achievements and problems connected with studies of light halo nuclei during the last few years. In this talk the discussion is limited to the case of one-nucleon halo systems: ⁸B, ¹¹Be and ¹⁹C. Each of these nuclei has its own peculiarities and we consider examples of recent experiments with radioactive beams of these nuclei at intermediate and high energies. We discuss some of the developments of the theoretical understanding of one-nucleon halo nuclei. Special attention is paid to the problems which should be solved in the future.

Recent studies of lighter dripline nuclei have revealed dramatic deviations from the matter distribution of ordinary stable nuclei and shell model ordering. New stability patterns such as halo nuclei with co-existence of normal and low-density nucleonic matter have been discovered, the Borromean nuclei being the most outstanding. Lessons of the last decade which have led to enrichment of the nuclear paradigm are discussed.

The perspectives in nuclear structure physics opened by the impressive technical developments of accelerator facilities for both stable and radioactive beams, and of the new concept in segmented multi-detector arrays are reviewed, with focus on the advances in Europe, explicitly. The new development of γ-ray tracking techniques makes it possible to built arrays with efficiencies as high as ≈ 30%, pointing to average γ-coincidence fold measurements of 10 out of high spin γ-cascades. This will increase the selectivity in γ-ray spectroscopy several orders of magnitude, and thereby open a bank of new possibilities, both for stable- and radioactive beam experiments. A few examples of the possibilities with stable beams are discussed. Special emphasis is made to stress the need for new developments in analysis of high fold data.

At the International Conference on Achievements and Perspectives in Nuclear Structure, held at Aghia Palaghia in Crete, Greece between 11-17 July 1999, several currently burning questions in nuclear structure physics were addressed in 25 invited talks and 20 oral contributions. This volume of Physica Scripta contains the manuscripts from most of these talks.

Nuclear structure physics is today in an exciting and fascinating phase with many new results and several planned future experimental projects. A central theme in contemporary nuclear structure research is to extrapolate the nuclear parameters (such as temperature, angular momentum, isospin and mass) to unknown areas. By this we will achieve an improved understanding of the complicated nuclear many-body problem and most probably discover new nuclear phenomena. Several of these questions were addressed during the conference.

The new generation of high resolution, full solid angle gamma-ray detectors have recently produced most interesting results on warm and cold rapidly rotating nuclei. Nuclei with different kinds of exotic shapes have been found, such as superdeformations, triaxial shapes and octupole shapes, and given new insights into nuclear structure. Several sessions at the conference were consequently devoted to a variety of more or less exotic Nuclear Shapes, and particular phenomena in Warm Nuclei were discussed in one session. New phenomena occurring in rapidly rotating nuclei, such as magnetic rotation, braking of the K-quantum number, etc, were discussed on sessions on High-Spin Physics. Through different kinds of nuclear reactions, nuclei have been produced far away from the valley of stability, and particular nuclear phenomena occurring Far from Stability, such as nuclear halos, proton radioactivity, etc, were reported on in sessions dealing with this topic. Different kinds of pairing, in particular the special role of the neutron-proton pairing interaction in nuclei with N = Z, were discussed in a session on Pairing Modes. In a session on Phonon Excitations new results were presented, especially on the giant dipole resonance in warm and rotating nuclei. The conference was concluded by a round table discussion on Experimental Perspectives, where prospects of new experimental facilities, in particular the use of radioactive nuclear beams, were discussed.

The conference programme was set up guided by an international advisory committee, to whom we are most grateful. The members of the committee were:

A short time after the conference ended we were reached by a sad message: our dear friend, Dr Jerry D. Garrett, had passed away. The Crete conference was the last physics meeting Jerry attended and he was, as usual, a key participant. He worried about a coming operation, but nobody could expect this to be so devastating. Jerry was a very close personal friend and an outstanding nuclear physicist. His impact on nuclear structure research was indeed large, and by his death the whole nuclear physics community has lost an important researcher. We shall particularly remember him for his exceptional kindness, always prepared to help in an unselfish way. We dedicate this volume to the memory of Jerry Garrett.