The heaviest stable nucleus is ²⁰⁹Bi. The heaviest naturally occurring isotope with a half life of the order of the age of the solar system is ²³⁸U. A simple calculation using the liquid drop model of the nucleus shows, that if a nucleus contains more than roughly a hundred protons the resulting Coulomb forces are sufficient to tear it apart. But if the quantum nature of the nucleons is taken into account in the shell model, one of the long standing predictions is that the binding energies can be increased enough to yield significant half lives for nuclei containing well over a hundred protons. As yet, the various mean field theories give very different predictions when extrapolated to nuclei beyond ²³⁸U and one goal of current research is to increase our experimental knowledge of very heavy nuclei.

Our group plays a central role in an international research programme studying in-beam and decay spectroscopy on very heavy nuclei such as ²⁵⁴No, with 102 protons, and its neighbours. The small production cross section allows the creation of these nuclei at a rate of several per hour which is enough to establish their structure in in-beam experiments using powerful combination of target spectrometers and recoil separators to filter the compound nucleus from the huge background of fission. Several such experiments have been performed at the Argonne National Laboratory, USA, using the Fragment Mass Analyser, and in Jyväskylä, Finland, using the gas filled separator RITU. So far the nuclides ^252,253,254No, ²⁵⁰Fm and ²⁵⁵Lr have been studied. The cross sections for the reactions ranged from 2 microbarns down to 200 nanobarns. One major result is the confirmation of the expected strong deformation of nuclei in this region with a maximum at the neutron number N=152. The deduced deformation parameters are comparable to those in the well-deformed rare earth region.

The SACRED electron spectrometer designed by the Liverpool group, used in conjunction with the recoil separator RITU in Jyväskylä, will be used to study odd-mass nuclei in-beam. For these nuclei most of the low-lying transitions proceed through highly converted M1 transitions, emitting conversion electrons rather than gamma rays. Another major advance in these studies will come from the use of the GREAT spectrometer, a highly sensitive instrument designed to observe the decay of radioactive products (alpha particles, protons, conversion electrons, X-rays and gamma-rays) at the focal plane of recoil separators such as RITU. The use of this spectrometer will allow measurements be made of low-lying states in even-even and odd mass superheavy nuclei, as well as measurements of long-lived high-K states that hold the key to the structure of superheavy nuclei.

The ground-state mass of a nucleus, and thus its binding energy, is one of the most fundamental nuclear properties since all the information about the strong force acting in such a system of nucleons is contained in this quantity. It is observed that N=Z nuclei are more bound than their neighbours. This empirical fact is known as the Wigner term in mass formulae, and cannot be properly explained by modern theories. The study of the residual interaction between the last proton and the last neutron, which plays a very important role in the structure of nuclei, is directly accessible from masses through double binding-energy differences. Ground state masses of N=Z nuclei are scarcely and poorly known above ⁶²Ga. New precise measurements around the N=Z region with Z~30 would allow the study of the A-dependence of the neutron-proton strength and provide a simple and clear signature of the Wigner spin-isospin symmetry.

A new experimental programme has recently started at GANIL to extend the systematics to N~Z~40-50, up to the doubly-magic ¹⁰⁰Sn region. These very challenging mass-measurement experiments are performed by means of an original direct time-of-flight technique using the CSS2 cyclotron as a high-resolution spectrometer. The exotic nuclei are produced by fusion-evaporation from a heavy-ion primary beam delivered by the first GANIL cyclotron, CSS1, impinging on a target located between the two cyclotrons. A new method for the measurement of the masses of very exotic nuclei with a precision better than 10^-6, using the new CIME cyclotron of SPIRAL, is being developed. Measurements can beforeseen with the CIME and CSS2 cyclotrons, which are complementary to the mass-measurement programmes at ISOLTRAP and MISTRAL at ISOLDE or ESR at GSI. The aim is to perform high-precision mass measurements of some of the most exotic nuclei that are key to our understanding of nuclear structure.

The study of excited states of nuclei near ¹⁰⁰Sn, using gamma-ray spectroscopy, will produce important information on residual interactions and correlations for systems near the doubly closed shell. As nucleons are added to this system, strong octupole correlations should occur for identical proton and neutron states, a hitherto unexplored scenario. The study of neutron deficient nuclei near N = Z in the mass 40-80 region and approaching N = Z in the mass 100-140 region will bring interesting new physics. The number of neutrons and protons is such that the valence nucleons occupy the same orbitals. Information on neutron-proton pairing, single particle orbitals far from stability and new regions of deformation can be obtained.

For the study of these nuclei, beams of post-accelerated radioactive ions are being exploited. At GANIL, these ions are accelerated in SPIRAL and are then used to produce compound nuclei that are studied using EXOGAM, a highly efficient gamma-ray spectrometer, and VAMOS, a versatile recoil spectrometer. Another new technique being developed for experiments at SPIRAL, REX-ISOLDE (CERN) and the FRS at GSI is the Coulomb excitation of the exotic nuclei as they pass through a target foil at both sub-Coulomb and relativistic energies.

The ground states of lead nuclei are spherical because they contain 82 protons, which is `magic number' analogous to the closed electron shells of noble gases. However, in very proton-rich lead nuclei, pairs of protons can be more easily excited into levels above the shell gap to produce oblate and prolate configurations that coexist at low excitation energies close to the spherical ground states. Liverpool is leading experiments to identify and study the interplay between these coexisting structures in lead isotopes, as well as in neighbouring elements from osmium to polonium where two of the shapes (oblate and prolate) are found. One of the most spectacular cases is the triple shape coexistence in the neutron-deficient even-mass Pb isotopes. One of the best studied cases to date is ¹⁸⁶Pb, where three differently shaped 0⁺ states have been observed in our recent alpha-decay study of ¹⁹⁰Po at the velocity filter SHIP, carried out at GSI Darmstadt. The Liverpol group is spearheading programmes of in-beam and decay measurements at Jyväskylä using target arrays such as SACRED and JUROSPHERE used in conjunction with RITU. These measurements will shortly employ the focal plane spectrometer GREAT being designed and constructed by a Liverpool-led collaboration. The group is also pioneering the isomer decay spectroscopy of nuclear fragments separated using the FRS at GSI in a campaign that is preparing the ground for the RISING project. Another new programme of research exploits the radioactive beams from ISOLDE at CERN.

When nuclei are studied at the extreme of very high angular momentum, approaching the fission limit, interesting new properties can be studied. At low spin near their ground states all nucleons are paired. As the nucleus takes up more energy and angular momentum the pairing force is overcome and nuclei behave singly. Studies in nuclei near mass 160 are just reaching the point where evidence is seen that the pairing force no longer has an important influence on the nuclear properties. In nuclei such as ¹⁵⁸Er and ¹⁶⁰Yb this occurs at a spin around 50. The evidence is becoming clear that neutron pairing has broken down as the properties of the nucleus correspond to those expected when the single particles move around without the pairing force. The experimental evidence is less clear for the protons. It is planned to carry out experiments at EUROBALL and GAMMASPHERE to study the properties of an odd proton nucleus (¹⁵⁹Tm) to investigate whether pairing is important at a spin near 50.

Many nuclei take up extremely deformed shapes at high angular momentum. Superdeformed shapes have been studied for many years and a lot of their properties can be explained using a simple collective rotational model. Many recent experiments have shown evidence that the detailed behaviour of these deformed structures can only be understood if the properties of the valence particles are understood and included in any model calculations. In ¹³²Ce a deformed band is known with a deformation of ₂ ~ 0.4. This band is known experimentally to a spin close to 70 and has properties consistent with those expected of a rotational band. The microscopic structure is however increasingly important as the spin is increased. The spin must come from individual nucleons. In ¹³²Ce if all particles outside a ¹⁰⁰Sn core are considered then there is a limit to the spin that can be produced. For a structure including two g_9/2 protons then this limit is 78. An experiment will be carried out at EUROBALL to investigate whether this state can be reached and to determine whether the rotational properties of the nuclei are replaced by single particle features.  Superdeformation in heavier, neutron deficient nuclei between polonium and thorium can be investigated using SACRED, which has a high sensitivity to weak decay sequences, such as those within superdeformed bands.

Nuclear models that have been successful in predicting the properties of `superdeformed' nuclei also predict `hyperdeformed' shapes, i.e. sausage-like nuclei. These shapes are expected to occur when the nucleus is rotating at high speeds. The unrivalled sensitivity of new arrays of gamma-ray spectrometers such as AGATA will be important in searching for them. The study of such states will allow the interplay between collective and single particle motion to be studied at the extremes of the stress caused by rapid rotation. It is expected that the hyperdeformed states be populated at spins where the nucleus would normally be expected to fission. The study of such states is one of the few possible probes of individual states at extreme angular momentum.

The Liverpool group is actively involved in an experimental programme studying the radioactivity of neutron rich light nuclei using the LISE3 spectrometer at GANIL These measurements are designed to reveal details of the underlying microscopic structures which are essential for understanding the properties of halo nuclei, where the wavefunction of the valence neutrons extends to large distances from the core of the nucleus. In one experiment, the gamma rays and neutrons emitted following beta decay were studied for a range of neutron rich nuclei below N=20 for the first time. This region is of particular interest because the `magic number' N=20 fails for these neutron rich nuclei. These new results will provide the basis for further studies in this region, which will eventually employ radioactive beams from SPIRAL, allowing both neutron-rich and proton-rich nuclei to be accessed.

Far from the valley of stability, mass measurements are of primary importance as they allow the determination of the limits of existence of nuclei. In addition, masses provide essential information about nuclear structure. For example, the study of binding energy differences, i.e. separation energies of the last nucleons of the nucleus, can reveal new regions of deformation or the evolution of shell-closures.

A very fruitful experimental programme at GANIL aims to extend mass measurements to very neutron-rich nuclei close to the drip line to investigate the quenching of shell-gaps and the appearance of new magic numbers around N = 20, 28, 34 and 40. The neutron-rich nuclei are produced by fragmentation of a high-intensity high-energy primary beam onto a production target located between the two superconducting solenoids of the SISSI device. Their masses are determined directly from their time-of-flight to the SPEG spectrometer.

Nuclear physics and astrophysics models, developed mainly from existing data on stable nuclei can be greatly improved by extending mass measurements to very exotic nuclei. Masses indeed play an important role in nuclear astrophysics as they allow for instance to account for the abundances of nuclides or to determine the path of nucleosynthesis processes. The rapid proton-capture (rp-) process proceeds along the N = Z line, therefore close to stability for light nuclei but close to the proton drip-line for heavier nuclei. The rapid neutron-capture (r-) process occurs on the neutron rich side of the nuclear chart. Mass-measurements of key neutron-deficient nuclei along and beyond the N = Z line in the region A~60-80 and of key neutron-rich nuclei above A~60 are performed at GANIL/SPIRAL with the SPEG, CSS2 or CIME techniques, in order to help determine the waiting points of the rp- and r-processes and thus provide input for their accurate modelling.