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The spectra of rapidly rotating nuclei reveal two distinct components in the build up of the total angular momentum, corresponding to collective rotation and alignment of orbital angular momentum of individual particles. Various aspects of the interplay of these two mechanisms are discussed. The pattern of collective excitations built upon an yrast state of aligned particle motion is analyzed on the basis of a simple model. For the strongly deformed nuclei, the relative contribution of alignment and collective rotation is characterized by two different moments of inertia referring to the yrast envelope and the collective bands. The behaviour of these moments in the transition region from superfluid to normal phase is considered. Finally, some of the consequences of the build up of angular momentum by alignment and collective rotation are considered for the region of the highest spins, where pair correlations are expected to play a minor role.

Cranked HFB calculations are shown for simple models of several particles in a single j shell and compared with exact results. It is shown that there are interesting differences between the results for pairing forces and delta forces. However, it is also demonstrated that the HFB approximation is in general not adequate to display those differences.

The study of γ-rays following heavy-ion induced reactions has provided most of our information regarding nuclear properties at very high angular momentum. The limits set at high angular momentum to the observation of the γ-rays and an alternative possibility for extending our knowledge to still higher angular momenta are considered in this review. A short discussion is given of the limits set by the entrance channel and to the existence of an equilibrated nucleus by the Rotating Liquid Drop Model. Competition between the particle, fission and γ-ray decay modes is described in the framework of the statistical model of the nucleus. Attention is drawn to some of the uncertainties in such analyses and, in particular, to our lack of knowledge of the average squared matrix elements for statistical γ-decay. The necessity to include the important effect of the collective E2 transitions in bands roughly parallel to the yrast line is stressed; this has not normally been done. The limits imposed by α-decay in competition with γ-emission and by higher chance fission are considered. The effect of shell structure and shape changes on decay probabilities and on the recently proposed possibility of observing α-decay from super-deformed nuclei is discussed. It is pointed out that the many open questions can only be solved by very complete and systematic measurements, which hardly exist to date.

The importance of considering the deformation of nuclei at high angular momenta in computing transmission coefficients for their decay is the major topic of this work. Deformations based on the rotating liquid drop model were used to generate transmission coefficients versus compound nucleus angular momentum. The results were then used in a Hauser-Feshbach code which included fission competition to assess the ultimate importance of deformation modified transmission coefficients. It was found that for a broad range of prolate nuclei (superdeformed) the course of deexcitation predicted changes totally from predominant fission to predominant α decay because of a new mechanism called cluster-decay amplification. The phase space relationships responsible for this new mechanism are presented. It is shown that this predicted new decay mode of superdeformed nuclei is consistent with a large body of existing experimental results, though more explicit experiments must be completed to confirm the new mechanism.

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Experimental data are summarized for massive transfer, a type of heavy-ion reaction in which a massive portion of the projectile is transferred to the target nucleus and a light fragment is observed as a forward-peaked, energetic spectator particle. The γ-ray spectra obtained in coincidence with the light fragment indicate that low-L partial waves do not participate in the reaction. γ-ray multiplicities are consistent with the massive fragment being absorbed at a distance corresponding to the critical distance for fusion. Channel-selected energy spectra and angular distributions are presented for alpha particles and Z = 1 particles associated with massive transfer. A recent model by Udagawa and Tamura that is based on their multi-step direct reaction theory accounts well for these experimental data. Possible applications of massive transfer in high-spin spectroscopy, in the sysnthesis of cold nuclei near the yrast line, and in the study of neutron-rich nuclei are discussed.

A qualitative theory of the macroscopic dynamics of nucleus-nucleus collisions is presented. Attention is focused on three degrees of freedom: asymmetry, fragment separation, and neck size. The physical ingredients are a macroscopic (liquid-drop) potential energy [1], a macroscopic dissipation (in the form of the Wall- and Wall-plus-Window formulae [2, 3]) and a simplified treatment of the inertial force. These ingredients are distilled into algebraic equations of motion that can often be solved in closed form. The applications include the calculation of the normal modes of motion around the saddle-point shapes, and the division of nuclear reactions into: (a) dinucleus (deep-inelastic) reactions, (b) mononucleus or composite nucleus (quasi-fission) reactions, and (c) compound-nucleus reactions. Static and dynamic scaling rules are deduced for comparing different dinuclear reactions in a systematic way. Estimates are given for the critical curve in the space of target and projectile mass above which deep-inelastic reactions ought to make their appearance. The extra push over the interaction barrier needed to make two nuclei form a composite nucleus or else to fuse into a compound nucleus is also estimated.

Proton spectra have been measured for individual channels of the ²⁰⁹Bi (α, pxn) reaction at beam energies of 45 and 75 MeV using p-γ coincidence techniques. Each reaction channel is characterized by a pronounced and well separated proton peak. For the (α, p) channel, e.g., the peak energies are 26.5 and 55.4 MeV for beam energies of 45 and 75 MeV, respectively. At a beam energy of 75 MeV the proton spectra have additional low-energy tails for the (α, p2n) and (α, p3n) channels. The angular distributions of the protons for the different channels as measured at a beam energy of 45 MeV are strongly forward peaked. For the peak regions the protons carry away almost all available excitation energy and the neutrons are evaporated. The energies of the protons can be understood in the framework of the yrast picture, as discussed in the paper, considering that they populate the entry line. Protons of the observed high energies may be produced by the coupling of the relative motion with the Fermi motion. A comparison with the PEP model is given.

Non statistical processes of γ and neutron deexcitations following (particle, xnypγ) reactions were studied, The deexcitation process of unresolved γ-rays in the highly excited region of 5-15 MeV excitation energy and 10-30 ℏ angular momentum was discussed on the experimental basis of the yrast level population, the spin alignment, the K-isomer ratio, the conversion electrons of unresolved transitions, and the unresolved γ-ray multiplicity. The observed quantities support the K-band deexcitation model which takes explicitly into account the E2 enhancement, the K-selection rule and some band structures for highly excited states. Neutrons following (particle, xn) reactions induced by energetic projectiles beyond the Fermi velocity were found to be emitted at the pre-equilibrium phase. The pre-equilibrium neutrons remove some angular mementum, still keeping the initial spin alignment. These stretched neutrons reflect the exciton dynamics in the highly excited (10-100 MeV) high spin region.

Though nuclei with a neutron number N > 90 in the rare earth region exhibit a rotational behaviour up to spin ∼ 60 ℏ, a different trend is observed for the neutron deficient erbium isotopes. In the spin window 30 ℏ < I < 65 ℏ, the associated continuum γ spectra exhibit two bumps of constant energy (∼ 650 keV and ∼ 1400 keV respectively) for these very high spin values. These results are discussed in the framework of current models.

Intensities and energy dependent multiplicity distributions of γ-rays have been measured for ¹⁵²Dy and ¹⁵⁶Dy nuclei populated in (¹²C, xn) and (¹²C, αxn) reactions at E = 70-101 MeV. The relative population of the yrast states in ¹⁵⁶Dy is found to be almost independent of the input angular momentum, which is not the case for ¹⁵²Dy. In the latter nucleus the yrast states up to spin values close to the maximum input angular momentum are strongly populated whereas in the former the transition intensities decrease very rapidly with increasing level spin. Quasi-continuum feeding cascades in ¹⁵⁶Dy are found to have considerably higher multiplicity than those in ¹⁵²Dy at comparable input angular momentum. These features can be understood in ¹⁵⁶Dy by assuming the existence of a number of collective bands which funnel the γ-ray deexcitation below the entry region away from the high spin yrast states whereas in ¹⁵²Dy short γ-ray cascades feed directly the yrast states. The entry regions in ¹⁵⁶Dy have been determined as a function of bombarding energy for the (¹²C, 6n) reaction. A decrease of the entry angular momentum above 90 MeV beam energy is found and explained by the existence of strong competing (¹²C, αxn) incomplete fusion reaction channels. Similar γ-ray sidefeeding patterns and multiplicity distributions for yrast states are observed in ¹²C induced complete (CF) and incomplete fusion (ICF) reactions leading to ¹⁵⁶Dy. However, the data for quasi-continuum feeding multiplicites indicate a more narrow initial angular momentum distribution for ICF than for CF reactions. The mean initial angular momentum for ICF is found to be about 10 h higher than the one for CF and it is close to the critical angular momentum for CF as deduced from a simple reaction model.

Gamma-transition-energy correlations are studied at high spins. Although the particular system ⁴⁰Ar + ¹³⁰Te is mainly considered, the observed features are believed to be fairly general. In constrast to other measurements, this method gives access to the collective moment of inertia of the successive bands through which a nucleus decays. Both the decrease of this moment of inertia and the less regular structure at high frequencies suggest that many band crossings occur at high spins. It is shown how one might be able to identify those crossings at specific frequencies within a cascade.

Several models for nuclear structure are explored with respect to their implications for quasi-continuum gamma-ray spectra. Gamma transition-energy correlations are considered as a means of studying collective bands. The intensity of correlated events at very high spins is found to be high even in nuclei with relatively low collectivity. Calculations are made which have bearing on the available experimental data in the rare-earth region and possible extensions of these measurements. Shape changes as well as band crossings are shown to have major effects.

A two-dimensional γ-ray coincidence spectrum is recorded using several NaI (T1) detectors during the bombardment of a ¹²⁴Sn target with 118 MeV ¹²C ions. Essentially four residual nuclei are produced, namely ^128,129,139Ba and ¹²⁶Xe. After subtraction of an uncorrelated background from the coincidence matrix, a correlated spectrum is obtained. This spectrum exhibits a valley along the 45° diagonal from about E_γ ≃ 0.5 MeV to E_γ ≃ 1.35 MeV, reflecting the rotational properties of the residual nuclei. The width of the valley decreases up to a transition energy E_γ ≃ 0.8 MeV. This width is directly related to the moment of inertia _band⁽²⁾ = dI/dω and is found to be in good agreement with the deduced values from known ground-band energies, although the nucleus probably decays through many different paths in this energy region. For the regions 800 < E_γ < 1050 keV and 1200 keV < E_γ < 1300 keV, the width of the valley remains nearly constant and the moment of inertia (2_band⁽²⁾/ℏ² = 80 and 95 MeV^-1, respectively) is close to the rigid-body value. A "bridge" across the valley at E_γ = 1.12 MeV is interpreted as being due to band crossing. Cranked shell model calculations indicate that the aligned angular momentum at this rotational frequency may result from the occupation of the highest aligned h_9/2 or i_13/2 neutron orbitals.

General properties of the shell structure in superdeformed nuclei at high rotational frequencies are studied in simple models. Special emphasis is laid on shell effects for various reflection asymmetric and strongly elongated nuclear shapes formed in peripheral collisions of heavy ions. A detailed discussion of the shell energy in (Z, ω) space is presented for symmetric 2:1 and 3:1 configurations in light nuclei (10 < Z < 34). In the realistic calculations, we use the cranking Strutinsky (CS) approach and the Saxon-Woods (SW) potential. Our aim here is to discuss the nuclear stability with respect to fission and shape changes at high spins. Moreover, we gave an explanation of the oscillatory behaviour of σ_fus^max (N, Z) observed in 1p, 2s-1d nuclei.

Nuclear superdeformation is studied theoretically using both simple models and more realistic numerical calculations. From the simple models general rules are formulated about the shell structure of the nucleus at large deformation, its affinity for reflection asymmetric or necked-in distortions and its response to rotation. The numerical calculations are based on realistic single-particle schemes and indicate that important trends in superdeformed nuclei may be understood from the simpler considerations. Particular attention is focussed on the 2:1 prolate configuration.

A new development within the high spin Nilsson-Strutinsky formalism is presented and applied to certain sd-shell nuclei. The previous method of calculating potential-energy surfaces as a function of angular momentum using interpolated spin values is not satisfactory when studying the individual bands for these light nuclei. In the present research, many-particle many-hole excitations are considered in the rotating system at each deformation in order to calculate the lowest energy at each spin. It is thus possible to calculate not only yrast states but also excited configurations. Potential-energy surfaces in the (, γ)-plane (with each grid point minimized with respect to ₄) are calculated at various values of spin, parity and signature. Special attention is paid to the problem of signature splitting ("decoupled bands") and in some cases the two signatures are found to correspond to different shape changes of the nucleus with increasing spin. Detailed investigations of the nuclei ^20,22Ne, ²⁴Mg, ²⁷Al and ²⁸Si are presented.

Octupole excitations frequently occur in the yrast lines of nuclei above ¹⁴⁶Gd. One-particle phonon exchange coupling identified in the Tb isotopes gives rise to low-lying ΔI = 2 octupole excitations; two-particle phonon exchange coupling in Dy isotopes causes ΔI = 1 octupole excitations in the yrast lines above 3 MeV which deexcite by E1 transitions of ≃ 1 MeV. The predominant octupole nature of the low-lying 13/2⁺ states in the N = 83 nuclei is emphasized, and the two-phonon octupole character of a 19/2^- level in ¹⁴⁷Gd which decays by E3 to the 13/2⁺ (νf_7/2 × 3^-) state is discussed.

Shell structure for protons at Z = 64 near N = 82 is studied in the Woods-Saxon (WS) average field with the extended version of the spin-orbit potential which parametrizes the contribution of the tensor force to the spin-orbit splitting. We find that the energy gap between πd_5/2 and πh_11/2 orbitals at Z = 64 is at most ΔE ∼ 1.65 MeV and is smaller than obtained for other magic proton (neutron) numbers. Properties of nuclei around ¹⁴⁶₆₄Gd₈₂ are determined by both the strong proton pairing correlations and the subshell effects at the πd_5/2 closure. The stability of the ∼ 1.6 MeV energy gap at Z = 64 is broken by the appearance of deformation for N > 86.

The nuclear structure at high spin for nuclei in the mass region around A = 156 was studied via in-beam γ-ray spectroscopy, after high spin states had been identified in heavy-ion induced reactions. For nuclei in the vicinity of the closed N = 82 shell, the levels appear as individual particle states, with large irregularities in the yrast sequence of energies and with the presence of high spin isomers. In heavier nuclei where the yrast levels exhibit a collective behavior, emphasis was put on the study of the second backbending effect.

Few-particle aspects of high-spin excitations are analysed in the mass regions A ≈ 150 and A ≈ 180. High-spin multiplets of nuclei in the vicinity of ¹⁴⁶Gd are interpreted in terms of shell model states on the basis of systematics which suggest, e.g., configuration assignments to 6-particle states in ¹⁵²Dy. Blocking of angular momentum is discussed for the first time in the neutron and proton systems in connection with the same core excitations (¹⁸⁹Ir-¹⁹⁰Pt-¹⁹¹Pt). The 10^- isomers in ^190,192Pt are interpreted as level inversions due to the partial filling of the i_13/2 neutron shell. Connections between few-particle excitations and the onset of deformation or the disappearance of the suprafluid phase are discussed in the A ≈ 150 region.

Selected topics related to the yrast spectroscopy in the ¹⁴⁶Gd region are discussed from the point of view of the deformed independent particle model with empirically based spherical single particle energies, a pairing force treated in the BCS approximation with variation of the gap parameters after particle number projection, and Strutinsky renormalization.

Collective properties at low and high spin for nuclei with Z ≳ 64 and N ≳ 82 are calculated on the basis of deformed single-particle potentials. The calculations are confronted with the available experimental data like low-lying octupole bands, rotational bands of transitional nuclei with N ≳ 90 and evidence for collectivity in high-spin single-particle spectra. In the latter collective triaxiality and collective rotation perpendicular to the aligned spin are investigated by cranking and RPA. Predicted regimes of different shapes and shape transitions at high spins are presented. In a gamma cascade calculation, it is shown how the calculated regimes for ¹⁵²Dy are consistent with the measured inclusive spectrum.

The population of the yrast states of ¹⁵²Dy has been measured as a function of the angular momentum input, l_max, in the ¹²²Sn (³⁴S, 4n)¹⁵²Dy reaction. For l_max ≳ 57ℏ, states with spins of up to 29 receive ∼ 90% of the channel cross-section, indicating little or no side-feeding below this spin, and the population of states with higher spin does not increase with l_max. The increased angular momentum input is reflected in the continuum γ spectrum, which show an enhanced yield around 1.3 MeV of stretched quadrupole character and around 0.6 MeV of stretched dipole character. These observations imply that the deexcitation of high-l events (l≳ 30ℏ) is not feeding the yrast line directly via statistical transitions, but is diverted by continuum cascades and only reaches the yrast line in the spin interval between 30 and 38. Several possible reasons for this behavior are suggested.

The decay and feeding of two yrast isomer (I ∼ 26ℏ and I ∼ 36ℏ respectively) in ¹⁵²Er is measured. The isomeric delays are used to separate the spectrum of γ-rays from the highest angular momentum states from the spectrum due to the decay of low spin states. Strong dipole as well as quadrupole radiation dominates the yrast cascades which feed into the I ∼ 36ℏ isomer, and the correlation spectrum for the feeding transitions does not indicate any collective structure for spins below 50ℏ. It is tentatively concluded that the near magic nucleus ¹⁵²Er remains spherical or oblate up to this high spin value.

The experimental values of E2 transition probabilities in nuclei with N ⩽ 90, and in particular in ^155,154Er, are examined. Some collectivity is definitely present in ¹⁵⁵Er, indicating that this nucleus is a moderately deformed rotor. In the nucleus ¹⁵⁴Er, whose level scheme is compatible with a description using the oblate coupling scheme, experimental ambiguities do not allow a definite conclusion on the presence of collective E2 transitions.

States of the N = 86 isotones ¹⁵⁶Yb and ¹⁵⁰Gd have been studied by means of the ¹⁴⁴Sm(¹⁶O, 4n)¹⁵⁶Yb, ¹¹³In(⁴⁶Ti, p2n)¹⁵⁶Yb and the ¹²⁴Sn(³⁰Si, 4n)¹⁵⁰Gd reactions. Levels have been established to spin 36ℏ and over 12.5 MeV in excitation in ¹⁵⁰Gd and to beyond spin 25ℏ in ¹⁵⁶Yb. The systematics of levels in the N = 86 isotones from ¹⁵⁰Gd to ¹⁵⁶Yb are described, and the near-spherical shell model description for states in this region to near spin 30ℏ is discussed. A T_1/2 = 6 ns, 72 keV isomeric transition in ¹⁵⁶Yb has been discovered, and an E1 multipolarity is assigned to this transition. The spin-parity of the isomeric state is established as 11^-.

Backbending due to the rotational alignment of two i_13/2 neutrons oscillates as a function of the neutron number. This is explained in a particle number and angular momentum conserving model. The neutrons in the i_13/2-shell are described by shell model wave functions and are weakly coupled to the rotation of the core. It is shown that the alignment is arranged by the nucleus by scattering two i_13/2 neutrons mainly from the Ω = 1/2 and Ω = 3/2 i_13/2 orbits into the core. The aligned band has therefore in average two neutrons less in the i_13/2-shell. Interaction between the valence nucleon and the core is due to the pairing force. It is shown that this interaction has j -3/2 zeros. No interaction between the ground band and the aligned band means strong backbending while a strong interaction means no backbending. In the second part of this contribution we explain the behaviour of the second anomaly of the moment of inertia by the alignment of two h_11/2 protons corresponding to the same oscillating behaviour as discussed before. In this way we can explain that for the N = 90 isotones ₆₆¹⁵⁶Dy shows no backbending, ₆₈¹⁵⁸Er shows upbending and ₇₀¹⁶⁰Yb shows a strong second anomaly of the moment of inertia.

High spin states in ¹⁵⁶Er are studied in terms of the independent quasi-particle approximation in a rotating nuclear potential.

Recent (HI, xn) data on rotational Yb and Hf nuclei are used to describe the motivations and techniques for pushing discrete-line spectroscopy to the realm of the weakly populated yrast and non-yrast states. Three aspects of these studies are discussed: extraction of moments of inertia in different aligned bands, observation and understanding of high-frequency band crossings, and dependence of feeding patterns on nuclear structure.

High-spin states in ¹⁶⁶Yb have been studied via the ¹⁵⁴Sm(¹⁶O, 4n)¹⁶⁶Yb reaction with 80 MeV ¹⁶O ions from the NBI tandem accelerator. γ-γ coincidence data were accumulated with an array of four Ge(Li) and four NaI(Tl) detectors to favour high multiplicity events. Totally about 3 × 10⁸ events were accumulated in the coincidence experiment. Measurements of the angular distribution of the γ-radiation and the conversion coefficients were furthermore performed. Four weakly populated side bands are observed besides the yrast cascade which is followed up to its 24⁺ member. The ground state band has thus been identified to its 18⁺ state, while the crossing Stockholm band becomes the yrast band from its 16⁺ member. The S-band is established from its 12⁺ state. The observed level energies and transition rates are well reproduced in calculations within the particle rotor model.

Magnetic moments for rotational states in heavy nuclei have been calculated in the framework of the cranked Nilsson model. Pairing interactions are included and treated fully selfconsistently, thus taking into account rotational alignment and Coriolis antipairing effects. The calculated g-factors reflect the backbending behavior: nuclei with sharp backbends show strong drops of the g-factors with spin I. Measurements of g-factors would thus constitute the first experimental proof of neutron alignment.

An experimental study of the actinide nucleus ²³⁸U was performed by Coulomb excitation with ²⁰⁸Pb projectiles. The E2-transition matrix elements in the ground state band were measured up to spin 28 by comparing experimental Coulomb excitation yields to semiclassical calculations and by analysing Doppler broadened line shapes measured in coincidence with a gamma-ray sum spectrometer. The E2-metrix elements agree within their errors with the rigid rotor predictions. Neither an increase of the collective transition strength at high spin due to centrifugal stretching as predicted by the Rotation Vibration Model nor a cutoff in collectively as postulated by the Interacting Boson Model is observed. The excitation energies in the ground state band show the presence of an aligned angular momentum of 5ℏ at spin 30 which can be explained by a crossing of an aligned band at ℏ_ω ≈ 250 keV. The octupole band shows a constant angular momentum alignment of 3ℏ (above spin 7) and no indication of a bandcrossing.

The Cranked Shell Model (CSM) interprets the rotational bands of deformed nuclei as configurations of quasiparticles moving in a rotating potential. The most important consequences of this independent particle picture, such as the additivity of the aligned angular momentum, the grouping of band crossings around characteristic frequencies and the oscillating strength of band mixing seem to be born out by the data on i_13/2 neutron aligned bands. The alignment process in the other high spin orbitals, as h_11/2-, h_9/2-, i_13/2-proton and j_15/2-neutron are surveyed. The available data are compatible with the CSM-predictions. At the highest angular momenta high spin orbitals from the adjacent shells (specially i_13/2-protons) enter the yrast region. An analysis of rotational bands in terms of aligned and collective angular momentum indicates a reduced collective part in the presence of aligned quasiparticles. The relation to γ-γ correlation experiments is discussed.