Table of contents

Shapes and current distributions of nuclei and alkali clusters are discussed in terms of the single particle motion of fermions in the average potential. For small particle number, an interpretation in terms of the lowest spherical harmonics is presented. For large particle number, an interpretation in terms of classical periodic orbits is presented.

A short survey of the semi-classical periodic orbit theory, initiated by Gutzwiller and generalized by many other authors, is given. Via so-called semi-classical trace formulae, gross-shell effects in bound fermion systems can be interpreted in terms of a few periodic orbits of the corresponding classical systems. In integrable systems, these are usually the shortest members of the most degenerate families or orbits, but in some systems also less degenerate orbits can determine the gross-shell structure. Applications to nuclei, metal clusters, semiconductor nanostructures and trapped dilute atom gases are discussed.

Semi-classical analysis of shell structures in realistic nuclear potentials are presented using periodic-orbit theory. We adopted an r^α potential model and examined classical-quantum correspondence using Fourier transformation technique. Spin–orbit coupling is also taken into account in the model Hamiltonian. Gross shell structure for a certain combination of surface diffuseness and spin–orbit parameters is investigated and its relation to pseudospin symmetry is discussed. An analysis of superdeformed shell structure in a realistic model is also presented.

Nuclear chirality is a novel manifestation of spontaneous symmetry breaking resulting from an orthogonal coupling of angular momentum vectors. In triaxial nuclei with an odd number of protons and neutrons three perpendicular angular momenta provided by the valence particles and collective rotation can form two systems of opposite handedness. The electromagnetic properties of the resulting doublet bands offer the opportunity to probe formation of chiral geometry according to the model predictions. The status of current theoretical and experimental investigation of electromagnetic properties of the doublet bands is discussed.

The Strutinsky shell correction method is modified. The smooth part of the energy has been evaluated by performing the Gauss–Hermite folding in the particle-number () space, i.e. not over the single-particle energies as was done in the original prescription. Similar folding in the -space applied to the BCS energy leads to a stable and simple method to evaluate the total microscopic correction which consists of the shell and pairing energies.

Nuclear physics plays an essential role in the dynamics of a type II supernova (a collapsing star). Recent advances in nuclear many-body theory now allow us to calculate the stellar weak-interaction processes involving nuclei. The most important process is electron capture on finite nuclei with mass numbers A>55. It is found that the respective capture rates, derived from modern many-body models, differ noticeably from previous, more phenomenological estimates. This leads to significant changes in the stellar trajectory during the supernova explosion, as has been found in state-of-the-art supernova simulations.

We use the configuration interaction technique to study vortex formation in rotating systems of interacting spinless fermions and bosons trapped in a two-dimensional harmonic potential. In the fermionic case, the vortices appear as holes in the Fermi sea and localize in rings. The yrast spectrum is dominated by rigid rotation of the vortex ring, showing periodic oscillations. The Bose system shows a similar yrast spectrum and vortex formation. This can be explained by a one-to-one correspondence of the fermion and boson many-particle configurations. A simple mean-field model can reproduce the oscillations in the yrast spectrum, but fails to explain the localization of vortices.

It was recently shown in self-consistent Hartree–Fock calculations that a harmonically trapped dilute gas of fermionic atoms with a repulsive two-body interaction exhibits a pronounced super-shell structure: the shell fillings due to the spherical harmonic trapping potential are modulated by a beat mode. This changes the 'magic numbers' occurring between the beat nodes by half a period. The length and amplitude of the beating mode depends on the strength of the interaction. We give a qualitative interpretation of the beat structure in terms of a semi-classical trace formula that uniformly describes the symmetry breaking U(3) → SO(3) in a three-dimensional harmonic oscillator potential perturbed by an anharmonic term ∝r⁴ with arbitrary strength. We show that at low Fermi energies (or particle numbers), the beating gross-shell structure of this system is dominated solely by the twofold degenerate circular and (diametrically) pendulating orbits.

At the RIKEN Accelerator Research Facility, various spectroscopic studies have been made using fast exotic beams. Most of the studies are performed in the reversed-kinematics by measuring de-excitation γ rays or particle decays from excited levels of unstable nuclei. Several examples of spectroscopic studies of unstable nuclei are presented. The RIKEN RI Beam Factory, which will have the first beam at the end of 2006, will greatly extend the region of study to more exotic and heavier nuclei.

Low-frequency quadrupole vibrations in deformed ^{36, 38, 40}Mg are studied by means of the deformed quasiparticle-RPA based on the coordinate-space Hartree–Fock–Bogoliubov formalism. Strongly collective K^π=0⁺ and 2⁺ excitation modes (carrying 10–20 W.u.) are obtained at about 3 MeV. It is found that dynamical pairing effects play an essential role in generating these modes. It implies that the lowest K^π=0⁺ excitation modes are particularly sensitive indicators of dynamical pairing correlations in deformed nuclei near the neutron drip line.

The importance of single-particle mean field and Coriolis interaction are discussed in the context of proton radioactivity. The calculation of decay widths from pseudo-spin doublets was found to be dependent on the shape of the nuclear mean field, and on the Coriolis interaction, due to the natural mixing by this coupling between states that differ by one unit of angular momentum. The residual interaction cannot be ignored in these studies for a correct interpretation of data.

The region around the doubly magic ¹³²Sn has been the subject of numerous experimental and theoretical studies in the last few years. The reason is that it is of special importance both for nuclear structure as well as nuclear astrophysics. Since the r-process of nucleosynthesis proceeds along the N=82 shell closure there is a close relation between the N=82 shell gap and the A ≈ 130 peak of the solar r-process abundance distribution. Some years ago it had been demonstrated that the assumption of a spherical quenching of the N = 82 neutron shell close to the neutron dripline allows us to properly reproduce the observed abundances. Recently, the unexpected behaviour of the measured 2⁺ excitation energies in the heavy Cd isotopes ^126,128,130Cd have been interpreted as evidence for a weakening of the N = 82 shell closure already one proton pair 'below' ¹³²Sn. This study motivated us to perform a detailed beyond mean field study of this region in order to investigate the origin of the observed anomaly of the 2⁺ energies in the Cd isotopes.

The formation and decay properties of the heaviest nuclei with Z=112–116 and 118 were studied in the reactions ²³⁸U, ^242,244Pu, ²⁴³Am, ^245,248Cm and ²⁴⁹Cf + ⁴⁸Ca. The new nuclides mainly undergo sequential α-decay, which ends with spontaneous fission. The total time of decay ranges from 0.5 ms to ∼1 day, depending on the proton and neutron numbers in the synthesized nuclei. The atomic number of the new elements 115 and 113 was confirmed also by an independent radiochemical experiment based on the identification of the neutron-rich isotope ²⁶⁸Db (T_SF∼30 h), the final product in the chain of α-decays of the odd–odd parent nucleus ²⁸⁸115. The comparison of the decay properties of 29 new nuclides with Z=104–118 and N=162–177 gives evidence of the decisive influence of the structure of superheavy elements on their stability with respect to different modes of radioactive decay. The investigations connected with the search for superheavy elements in Nature and prospects of superheavy element research are also presented.

The experiments were carried out at the Flerov Laboratory of Nuclear Reactions (JINR, Dubna) in collaboration with the Analytical and Nuclear Chemistry Division of the Lawrence Livermore National Laboratory (USA).

The analysis of quasi-particle spectra in the heaviest A∼250 nuclei with spectroscopic data provides an additional constraint for the choice of effective interaction for the description of superheavy nuclei. It strongly suggests that only the parametrizations which predict Z=120 and N=172 as shell closures are reliable for superheavy nuclei within the relativistic mean field theory. The influence of the central depression in the density distribution of spherical superheavy nuclei on the shell structure is studied. A large central depression produces large shell gaps at Z=120 and N=172. The shell gaps at Z=126 and N=184 are favoured by a flat density distribution in the central part of the nucleus. It is shown that approximate particle number projection (PNP) by means of the Lipkin–Nogami (LN) method removes pairing collapse seen at these gaps in the calculations without PNP.

Recent macroscopic–microscopic studies of the heights of (static) fission barriers B_f^st of the heaviest nuclei are reviewed. The studies are motivated by the importance of this quantity in calculation of cross-sections for synthesis of these nuclei. Large deformation spaces, including as high multipolarities of deformation as λ=8, are used for the analysis of B_f^st. The importance of non-axial shapes in this analysis is shown. They reduce B_f^st by up to about 2 MeV. The origin of this large reduction is explained. This is a large (negative) shell correction to the energy, which overcomes a significant stiffness of the macroscopic part of this energy to non-axial deformations of a nucleus.

Isomeric states in ²⁵⁴No were investigated using a calorimetric method. Two different isomers were found with half-lives of T_1/2=266±2 ms and T_1/2=184±3 μs, respectively. The dominant decay path of the 184 μs isomer proceeds via states feeding the longer-lived 266 ms isomer. The 266 ms isomer in turn decays via a two-quasi-particle K=3 band to the ground-state band. The full decay path was observed with the GREAT spectrometer located at the focal plane of the gas-filled separator RITU at the Accelerator Laboratory in Jyväskylä. This work sheds light on the two-quasi-particle structure in this transfermium nucleus.

In recent years, we have studied the structure of transcurium nuclei using the best available actinide sources and state-of-the-art instruments. These include the largest amount of high-purity samples produced in the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory and the GAMMASPHERE spectrometer located at Argonne. Proton single-particle states in ²⁴⁹Bk were investigated by measuring the γ-ray spectra of an extremely pure ²⁵³Es sample and reactor-produced ²⁴⁹Cm sources. Neutron single-particle states were identified in ²⁵¹Cf by measuring γ-ray spectra of ²⁵⁵Fm sources and a cyclotron-produced ²⁵¹Es source. By combining the results of these measurements with the results of one-nucleon transfer reactions, we were able to identify almost all the single-particle states up to 1 MeV excitation in ²⁴⁹Bk and ²⁵¹Cf. The level energies in these nuclei are in good agreement with energies calculated with a Woods–Saxon potential and pairing interactions.

Simple generic aspects of nuclear pairing in homogeneous media as well as in finite nuclei are discussed. It is argued that low-energy nuclear structure is not sensitive enough to resolve fine details of nuclear nucleon–nucleon (NN) interaction in general and pairing NN interaction in particular which allows for regularization of the ultraviolet (high-momentum) divergences and a consistent formulation of effective superfluid local theory. Some aspects of (dis)entanglement of pairing with various other effects as well as forefront ideas concerning isoscalar pairing are also briefly discussed.

The particle number projected generator coordinate method is applied to the study of generalized pairing Hamiltonians. The calculations reproduce the exact solution where available in the weak, crossover and strong pairing regimes. The behaviour of the wave functions is analysed showing large mixtures in the weak and smaller ones in the strong pairing regime. The physical insight of the ansatz and its numerical simplicity make this theory an excellent tool to study pairing correlations in complex situations and/or involved Hamiltonians.

We first show that the quantum pairing problem can be mapped exactly on to a classical electrostatic problem in two dimensions and then use this analogy to obtain a pictorial representation of how superconductivity arises in a finite fermionic system. Specific application to the nuclei ^114–116Sn suggests some new insight into the evolution of pairing correlations in a quantum system with few active particles. We also summarize other recent work on exactly solvable pairing models, including their applications in a wide variety of strongly correlated quantum systems.

The bare nucleon–nucleon interaction is essential for the production of pair correlations in nuclei, but the induced interaction due to phonon exchange also contributes. In this paper, we shall present examples of the interplay between these two sources of pairing interaction in the case of finite nuclei and of the inner crust of neutron stars.

Coulomb breakup of the two-neutron halo nucleus ¹¹Li has been investigated in a kinematically complete measurement of three-body breakup of ¹¹Li on a Pb target at approximately 70 MeV/nucleon at RIKEN. Cross-talk events have been excluded without affecting the efficiency very much up to very low relative energy. The resultant preliminary B(E1) spectrum has revealed high (E1) strength at E_rel (three-body relative energy) ∼0.3 MeV, which was missing in the previous measurements. This E1 strength with the help of the E1 cluster sum-rule indicates a significant neutron–neutron correlation in the ground state of ¹¹Li.

The Coulomb breakup and pairing excitation of the two-neutron halo nucleus ¹¹Li with the cluster orbital shell model have been studied. For the excited resonances in ¹¹Li, we use the complex scaling method. We get an excited solution of 3/2⁻ in ¹¹Li.

A newly developed technique for dealing with three-body decays of broad isolated levels is extended to deal with the broad, overlapping levels found at 2–9 MeV excitation energy in ⁹Be. The levels are populated through beta-decay of ⁹Li. The method gives firm evidence for the existence of several levels. Angular correlation studies allow spin values to be assigned.

A breakthrough was recently obtained in the analysis of the so-called Hyper-Long-HyperDeformed (HLHD) experiment made at the EUROBALL-IV γ-detector array (EB). The ⁶⁴Ni + ⁶⁴Ni ⇒ ¹²⁸Ba* fusion reaction was studied at E_beam = 255 and 261 MeV, reaching the highest angular momentum that the compound nuclei can accommodate. To date no discrete HD rotational bands have been identified. However, rotational patterns in the form of ridge-structures in three-dimensional (3D) rotational mapped spectra are identified with dynamic moments of inertia J⁽²⁾ ranging from 71 to 111ℏ² MeV⁻¹ in 12 different nuclei selected by charged particle- and/or γ-gating. The four nuclei, ¹¹⁸Te, ¹²⁴Cs, ¹²⁵Cs and ¹²⁴Xe found with moment of inertia J⁽²⁾⩾100 ℏ² MeV⁻¹, are most likely hyperdeformed, the remaining nuclei with smaller values of J⁽²⁾, are considered to be superdeformed, in qualitative agreement with recent theoretical calculations.

The three superdeformed (SD) bands in ¹³²Ce and the two SD bands in ¹³¹Ce have been extended to higher spin following experiments with the EUROBALL IV spectrometer. The two SD bands in ¹³¹Ce have been linked together. However, despite the relatively high population intensity of the bands (up to 5% of the respective channel), it has not been possible to unambiguously link any of the five SD bands into the low-spin, normally deformed structures of ^{131, 132}Ce.

In a recent study of superdeformed (SD) bands in the A≈80 region, three discrete linking transitions to states of normal deformation (ND) were identified in ⁸⁴Zr. The properties of the abrupt decay out of the SD well in ⁸⁴Zr are compared with those in other SD mass regions. Several theoretical calculations suggest that there is extensive mixing of configurations in the SD and ND minima and very little potential barrier between the two wells, leading to a rapid, highly fragmented decay-out process.

High-spin terminating bands in heavy nuclei were first identified in nuclei around ¹⁵⁸Er₉₀. While examples of terminating states have been identified in a number of erbium isotopes, almost nothing is known about the states lying beyond band termination. In the present work, the high-spin structure of ^{156, 157, 158}Er has been studied using the Gammasphere spectrometer. The subject of triaxial superdeformation and 'wobbling' modes in Lu nuclei has rightly attracted a great deal of attention. Very recently four strongly or superdeformed (SD) sequences have been observed in ¹⁷⁴Hf, and cranking calculations using the Ultimate Cranker code predict that such structures may have significant triaxial deformation. We have performed two experiments in an attempt to verify the possible triaxial nature of these bands. A lifetime measurement was performed to confirm the large (and similar) deformation of the bands. In addition, a high-statistics, thin-target experiment took place to search for linking transitions between the SD bands, possible wobbling modes, and new SD band structures.

High-spin states in the N=Z nucleus ⁷²Kr have been populated in the ⁴⁰Ca(⁴⁰Ca, 2α)⁷²Kr fusion–evaporation reaction at a beam energy of 165 MeV and using a thin isotopically enriched ⁴⁰Ca target. The experiment, performed at Argonne National Laboratory close to Chicago, USA, employed the Gammasphere array for γ-ray detection coupled to the Microball array for charged particle detection. The previously observed bands in ⁷²Kr were extended to a higher excitation energy of ∼24 MeV and higher angular momentum of 30ℏ. Using the Doppler-shift attenuation method, the lifetimes of high-spin states were measured for the first time in order to investigate deformation changes associated with the g_9/2 proton and neutron alignments in this N=Z nucleus. An excellent agreement with theoretical calculations including only standard t=1 np pairing was observed.

The macroscopic–microscopic method to calculate nuclear masses is extended into the high-spin regime in order to calculate the nuclear binding energy as a function of proton number, neutron number and angular momentum. We describe the method and exemplify it on recent experimental data.

The precession mode, the rotational excitation built on the high-K isomeric state, in comparison with the recently identified wobbling mode has been studied. The random-phase-approximation (RPA) formalism, which has been developed for the nuclear wobbling motion, is invoked and the precession phonon is obtained by the non-collective axially symmetric limit of the formalism. The excitation energies and the electromagnetic properties of the precession bands in ¹⁷⁸W are calculated, and it is found that the results of RPA calculations well correspond to those of the rotor model; the correspondence can be understood by an adiabatic approximation to the RPA phonon. As a by-product, it is also found that the problem of too small out-of-band B(E2) in our previous RPA wobbling calculations can be solved by a suitable choice of the triaxial deformation which corresponds to the one used in the rotor model.

Using a microscopic self-consistent model, we analyse the excitation built upon the rotational band in ¹⁶³Lu, which has been identified as a wobbling excitation on top of the rotation of a triaxial, strongly deformed shape. We find that the presence of pairing correlations substantially affects the energy of the excitation. Our calculations predict the onset of tilted rotation at a critical rotational frequency where the energy of the excitation approaches zero.

We have developed a new method to study the order-to-chaos transition in rotational nuclei. Energy correlations between successive γ-rays are used to determine the average complexity of the levels and thereby the ratio of the interaction between levels to the level spacing. γ-Rays from fusion reactions, leading to ^168,169,170Yb nuclei, were measured with Gammasphere, and the measured ratios span the range from nearly fully ordered to nearly fully chaotic.

Many-body quantum chaos results from interparticle interactions in mesoscopic systems at sufficiently high level density. A short review shows that, going beyond generic properties of local spectral statistics, the ideas of many-body quantum chaos serve as a rich source of new theoretical approaches, computational and experimental tools. Chosen examples include the enhancement of weak perturbations, thermalization in finite systems, exponential convergence of large Hamiltonian matrices and correlations between the states of different symmetry.

Here, the problem of the classical chaos effect on dissipation in nuclear many-body systems is addressed. To investigate this problem, the energy response on parametric driving of external confinement of the simplest interacting many-body system is studied: two identical like-charged particles moving on the plane in the field of a deformed harmonic oscillator, which shows a rich structure of the classical phase space. The parametric driving is represented by the slow periodic modulation of the deformation of confinement. Here, the focus is on how the driven dynamics of particles is defined by the structure of the unperturbed phase space of the system. It has been found that the rate at which the energy of the external driving is pumped into the energy of the interacting two-body system strongly depends on the driven dynamics of the regular orbits. A role of interaction for the energy absorption rate is also discussed.

Shell model calculations are employed to estimate an upper limit of statistical fluctuations in the nuclear ground-state energies. In order to mimic the presence of quantum chaos associated with neutron resonances at energies between 6 and 10 MeV, calculations include random interactions in the upper shells. The upper bound for the energy fluctuations at mid-shell is shown to have the form σ(A)≈20 A^−1.34 MeV. This estimate is consistent with the mass errors found in large-shell model calculations along the N=126 line, and with local mass error estimated using the Garvey–Kelson relations, all being smaller than 100 keV. It agrees in both size and functional form with the fluctuations deduced independently from second-order perturbation theory.

Correlations of the difference between the measured and calculated mass of neighbouring nuclei obtained from different nuclear compilations are studied. The autocorrelation function is found to be, to a good approximation, model independent. The result is well described by a semiclassical theory that assumes the existence of a contribution to the nuclear mass associated with a chaotic motion of the nucleons (Olofsson et al 2006 Phys. Rev. Lett.96 042502). Recent developments in this direction are reviewed and some complementary aspects are studied.

Generic and non-generic features of billiards and nuclei which show up in certain spectral properties are discussed by way of selected examples. Firstly, the short- and long-range correlations of levels belonging to the magnetic dipole Scissors Mode in heavy deformed nuclei at an excitation energy of about 3 MeV prove that this mode is indeed caused by an ordered or regular collective motion. Secondly, the fine structure distribution of the so-called electric Pygmy Dipole Resonance around 6–7 MeV excitation energy seems to indicate a situation where the spectral properties are governed by mixed dynamics, i.e. by regular and chaotic features. However, in nuclei quantitative conclusions are always severely hampered by missing levels due to limited experimental resolution and detector efficiency. Thirdly, it is shown that this situation can be largely overcome by studying spectral properties in superconducting microwave billiards considered as nuclear analogues. As an example resonance strength distributions in billiards of mixed and fully chaotic dynamics are considered. Finally, it is demonstrated how symmetry breaking effects in nuclei—e.g. isospin symmetry breaking—can be studied through those resonance strength distributions by modelling the nuclear problem with coupled billiards.

Two-proton radioactivity in extremely proton-rich fp shell nuclei at high spins is investigated in a theoretical framework. Separation energy and entropy fluctuate with spin and hence affect the location of the proton drip line.

The low-energy structure of ²³¹Ac has been investigated by means of γ, conversion electrons, γ–γ and γ–e⁻ spectroscopy following the β⁻-decay of ²³¹Ra. Here, we report on the precise determination of the ²³¹Ra β-decay half-life.

Fragment production during the nuclear liquid gas phase transition is studied on the basis of the Statistical Multifragmentation Model (SMM) (Bondorf et al 1995 Phys. Rep.257 133). By selecting partitions according to the maximum fragment charge we demonstrate 'bimodality' as an essential feature of the phase transition in finite nuclear systems. We show that the variation of entropies of these two events with excitation energy exhibits a bimodality behaviour as well.

The use of sum energy and multiplicity as obtained with the multidetector array GASP is investigated. The analysis focuses on the identification of the spin-energy region from which a given set of γ-cascades originates in a typical fusion–evaporation reaction.

A formulation of a three-quasiparticle plus rotor model is presented, which is currently applicable to axially symmetric deformed nuclei.

The response of the nuclear energy with respect to relative changes of proton versus neutron distributions is investigated. Contrary to most macroscopic–microscopic approaches, different multipole deformations of both distributions are admitted. The average part of the total energy is evaluated using the Yukawa-folded model, while microscopic energy corrections are obtained within the Strutinsky and BCS methods.

In this paper, we report the preliminary result from the first Coulomb excitation experiment at REX-ISOLDE (Habs et al 1998 Nucl. Instrum. Methods B 139 128) using neutron-deficient Sn-beams. The motivation of the experiment is to deduce the reduced transition probability, B(E2; 2⁺→0⁺), for the sequence of neutron deficient, unstable, even–even Sn-isotopes from ¹¹⁰Sn to ultimately ¹¹⁰Sn. Safe Coulomb excitation using a radioactive beam opens up a new path to study the lifetime of the first excited 2⁺ state in these isotopes. The de-excitation path following fusion–evaporation reactions will for the even–even Sn isotopes pass via an isomeric 6⁺ state, located at higher energy, which thus hampers measurements of the lifetime of the first excited state using, e.g., recoil-distance methods. For this reason the reduced transition probability of the first excited 2⁺ state has remained unknown in this chain of isotopes although the B(E2) value of the stable isotope ¹¹²Sn was measured approximately 30 years ago (see, e.g., Stelson et al 1970 Phys. Rev. C 2 2015). Our experiment is thus the first to accomplish a measurement of this quantity in ¹¹⁰Sn. It is believed that the determination of the B(E2) value in ¹¹⁰Sn will indicate the turnover point from a trend of increasing B(E2) values for the heavier isotopes to a trend characterized by less collectivity. Our first preliminary result indicates that this assumption may well be correct.

A lifetime analysis using the Doppler-shift attenuation method has been performed on the Tellurium isotopes ^{110, 112}Te. The experiment was performed using the Gammasphere array in conjunction with the MICROBALL charged-particle detector. Three strongly coupled bands were previously established in ^{110, 112}Te which were observed up to unusually high spins. In the current experiment, it has been possible to extract lifetime measurements using a Doppler broadened lineshape analysis on one of the ΔI=1 band structures in ¹¹⁰Te. In contrast to similar ΔI=1 structures in other nuclei in this mass region, the extracted B(M1) values did not rapidly decrease with increasing angular momentum. Instead, the strongly coupled band in ¹¹⁰Te represents a deformed 1p-1h structure, rather than a weakly deformed structure showing the shears mechanism.

Fifty years after its prediction, the highest-lying [2 0 2]3/2 orbit among the six Nilsson single-particle orbits originating from the sd shell in prolately deformed nuclei and the rotational band on this orbit were identified. The band members were observed in ²⁵Al at excitation energies of 6–7.5 MeV in a high-resolution ²⁵Mg(³He, t) charge-exchange reaction at 0° having a strong selectivity for Gamow–Teller transitions. In comparison with the analogous M1 transitions in ²⁵Mg, the J^π=3/2⁺ band-head state and the excited 5/2⁺ and 7/2⁺ members were clearly assigned.

Low-lying negative-parity excitations on superdeformed states in the ⁴⁰Ca and neutron-rich sulfur regions were calculated using fully self-consistent random phase approximation calculations with Skyrme interaction.

A comparative study of light pf shell nuclei using cranked Nilsson–Strutinsky model and the spherical shell model indicates that some of the signature splitting between the partner bands in odd-A nuclei originates from a gradual decrease in the contents of the pairing energy as spin increases.

We describe several quantum and thermodynamical characteristics of different nuclear fission stages based on the generalized model of the nucleus.

A two-dimensional mean-field Hamiltonian is constructed in analogy with the three-dimensional Nilsson model and applied to a quantum dot.

Lifetimes have been measured for four quadrupole bands in ¹⁴²Gd with EUROBALL using the Doppler-shift attenuation method. The deduced B(E2) values have been compared with results of Interacting Boson Model calculations.

A short survey of α-cluster data, and level densities of mass A∼20–50 nuclei are given. It is shown that α-particle clusters persist to high excitation, ⩾\!\!30 MeV, and that level densities at these excitations are not as high as usually presumed.

The DIAMANT light charged-particle detector will be coupled with the AFRODITE γ-ray spectrometer at iThemba LABS under a bilateral agreement between South Africa and Hungary. As a first step, the standalone 'Chessboard' section of DIAMANT has been integrated with AFRODITE in order to study incomplete fusion reactions instigated by beams of ¹³C ions incident on targets of ¹⁷⁰Er and ¹⁷⁶Yb. A fuller implementation of DIAMANT with AFRODITE will take place in due course.

We have performed self-consistent calculations of the binding energies of 171 spherical even–even nuclei within the relativistic mean field theory with NL3 and the Gogny model with the D1S parameter set. The results are presented for two types of shell correction methods: the traditional Strutinsky one by smoothing in the single-particle energy space (e-smoothing) and a new one, by smoothing in the nucleon-number space (-smoothing). The macroscopic energies obtained in these four cases are fitted by the Myers–Świaţecki type liquid drop formula and compared to the phenomenological values fitted to experimental masses.

The level structure of ¹⁴⁰₆₀Nd₈₀ has been established up to spin 48 by in-beam γ-ray spectroscopy using the ⁹⁶Zr(⁴⁸Ca, 4n) reaction. High-fold γ-ray coincidences were measured with the EUROBALL spectrometer. Twelve new rotational bands have been discovered at high spins, showing the change from a spherical single-particle behaviour at low spins to a deformed regime with stable triaxiality at high spins. Possible configurations are assigned to the observed bands on the basis of configuration-dependent cranked Nilsson–Strutinsky calculations.

The neutron deficient rare-earth nuclei of the A∼130 region are of particular interest since highly deformed prolate ground states are expected. Indeed these nuclei are predicted to show maximal ground-state deformations of β₂ ∼ 0.40 (axis ratio of 3:2), comparable to the deformation deduced for superdeformed cerium isotopes at high spin. A fusion–evaporation experiment was performed with radioactive ion beams at GANIL in October 2004 which had the goal to reach very proton-rich exotic nuclei located near the proton drip-line. A radioactive ⁷⁶Kr beam, delivered by the SPIRAL facility, was used to bombard a thin ⁵⁸Ni target. Emitted γ-rays were detected by the EXOGAM γ-ray spectrometer which was, for the first time, coupled with both the DIAMANT charged-particle array and the VAMOS spectrometer.

We have obtained very close approximations to the projection before the variation solutions with a restricted variation after projection method in a multilevel pairing Hamiltonian and particle number projection. The study of the projected potential energy surfaces defined along the direction of (ΔN)² and (ΔN)⁴ allows the enlargement of the variational space in order to take into account more correlations within the projection after variation framework. The results show the equivalence of the full variational projected solution to a restricted one, the latter obtained with a more feasible method from a computational point of view than the former.

Large-scale macroscopic–microscopic calculations taking into account thermal effects are performed in the mass A∼130 nuclei to search for hyper-deformation (HD). An emphasis is set on the role of the Jacobi shape transition for the population of hyper-deformed states. The hyper-deformed configurations are predicted to exist at the very high spins only, in contrast to the super-deformed ones. Moments of inertia are calculated and compared with experiment, showing good agreement.

In this paper, isovector and isoscalar pairing correlations were investigated using generalized Bardeen–Cooper–Shrieffer theory and a Skyrme force-like form of the residual interaction. The calculations are done for even–even N∼Z germanium nuclei in an axially symmetric Skyrme–Hartree–Fock + BCS scheme with SIII force and time-reversal invariance. A coexistence of T=0 and T=1 superfluid phases is observed.

Using a ⁵⁸Ni(⁴⁶Ti, α2n) reaction, a total of 24 different residual nuclei were identified. Among them were ⁹⁸Cd and ⁹⁷Ag. The level scheme of ⁹⁸Cd was extended to J^π=(15⁺). An isomeric state at 6634 keV excitation energy was confirmed. This state decays by a 4207 keV transition feeding the known 8⁺ state. The level scheme of ⁹⁷Ag was also extended to J^π=(33/2⁺) and the half-lives of two isomeric states were measured. Experimental energies of the excited states were compared with the results of ab initio shell-model calculations based on a realistic two-nucleon interaction. The Gammasphere Ge array, coupled with the Microball and the Neutron Shell ancillary particle detectors, was used at the 88 inch cyclotron at Lawrence Berkeley National Laboratory, USA.

We discuss features of the giant resonance embedded in the continuum.

The multi-dimensional potential energy surface has been calculated for Fm isotopes with A=240–266 in the HFB framework. The spontaneous fission half-lives have been compared with the experimental data.

Continuum effects for pairing correlations and low-frequency vibrational excitations in nuclei close to the neutron drip line are investigated within the framework of quasiparticle random phase approximation (QRPA) based on the coordinate space Hartree–Fock–Bogoliubov (HFB) method. Quasiparticle states with small orbital angular momentum ℓ, that suffer a significant change of the spatial structure by pairing correlations, bring about the spatially extended structure of the pairing density that leads to the enhancement of the pairing energy. The similar mechanism in two-quasiparticle states also causes the strong transition strength of low-frequency vibrational excitations.

The cranked Nilsson–Strutinsky formalism is developed to include the perpendicular spin component of specific orbitals. The formalism is applied to the 'magnetic bands' in ¹⁹⁹Pb.

In 1955 Sven Gösta Nilsson published the paper `Binding States of Individual Nucleons in Strongly Deformed Nuclei'. This eminent work has been crucial for the understanding of the structure of deformed atomic nuclei. Moreover, the so-called Nilsson model has been widely used for the description of other types of finite systems of fermions such as quantum dots and cold fermionic atoms. During one week in June 2005 we celebrated in Lund the 50th anniversary of the Nilsson model with the International Conference on Finite Fermionic Systems – Nilsson Model 50 Years. With the historical view in mind, the conference focused on present and future problems in nuclear structure physics as well as on the physics of other types of finite Fermi systems. As a background to the recent developments Nobel Laureate Ben Mottelson presented a recollection of early applications and achievements of the Nilsson model in the first talk of the conference, including a personal view of Sven Gösta Nilsson. We are particularly pleased that this contribution could be included in these proceedings. The scientific programme was structured according to the following subjects:

• Shell structure and deformations

• The heaviest elements and beyond

• Nuclei far from stability

• Pairing correlations

• Nuclear spectroscopy: large deformations

• Nuclear spectroscopy: rotational states

• Order and chaos

• Cold fermionic atoms

• Quantum dots

Many new and interesting results were presented in the 15 invited talks, 30 oral contributions, and in the 33 papers of the poster sessions. The present volume of Physica Scripta contains most of the talks, as well as the short contributions of the posters.

We thank the speakers and all participants who actively contributed to give this memorable conference a very high scientific level in the presented contributions, as well as in numerous discussions inside and outside the sessions. We also thank the international advisory committee for their invaluable work in helping us setting up a high standing scientific programme. Finally, we thank the Royal Swedish Academy of Sciences through its Nobel Committee for Physics, the Royal Physiographical Society in Lund, the Technical Faculty (LTH) at Lund University, and the Swedish Research Council (VR) for financial support.

Sven Aberg, Ragnar Bengtsson, Ingemar Ragnarsson and Stephanie Reimann Department of Mathematical Physics, Lund Institute of Technology, S-22100 Lund, Sweden Joakim Cederkäll, Claes Fahlander and Dirk Rudolph Division of Nuclear Physics, Lund University, S-22100 Lund, Sweden

In this opening address, Professor Ben Mottelson gives an overview of the life and work of Sven Gösta Nilsson.

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