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We re-examine the well-known Wong formula for heavy-ion fusion cross sections. Although this celebrated formula yields almost-exact results for single-channel calculations for relatively heavy systems such as $^{16}\mathrm{O}+^{144}\mathrm{Sm}$, it tends to overestimate the cross section for light systems such as $^{12}\mathrm{C}+^{12}\mathrm{C}$. We generalize the formula to take account of the energy dependence of the barrier parameters and show that the energy-dependent version gives results practically indistinguishable from a full quantal calculation. We then examine the deviations arising from the discrete nature of the intervening angular momenta, whose effect can lead to an oscillatory contribution to the excitation function. We recall some compact, analytic expressions for these oscillations and highlight the important physical parameters that give rise to them. Oscillations in symmetric systems are discussed, as are systems where the target and projectile identities can be exchanged via a strong transfer channel.

International audience; The perceptive analysis of Rutherford, celebrated at this conference, turned the experiments of Geiger and Marsden into a measurement of the radius of the object that became known as the atomic "nucleus". We now know that the nucleus can have a range of radii that depend on its static and dynamical deformations. These deformations give rise to the distributions of reaction barriers that have been extensively studied over recent years. While fusion reactions are most often used for such studies, there are cases where, for physical or practical reasons, the scattering channels must be exploited. Despite the major advantages gained from modern experimental techniques, the resulting experiments are in spirit essentially the same as those performed over 100 years ago by Rutherford and his colleagues.

International audience; In the context of the creation of heavy evaporation residues, the interplay between capture, quasifission and true compound-nucleus fission is discussed. An approximate factorisation of the cross section into a compound nucleus term and an entrance-channel term is derived, with each of these terms being clearly defined.

Using the random matrix model, we discuss the effect of couplings to non-collective states on the penetrability of a one dimensional potential barrier. We show that these non-collective excitations hinder the penetrability and thus smear the barrier distribution at energies above the barrier, while they do not affect significantly the penetrability at deep subbarrier energies. The energy dependence of the Q-value distribution obtained with this model is also discussed., 4 pages, 2 figures. A talk given at the 10th international conference on nucleus-nucleus collisions (NN2009), Aug. 16-21, 2009, Beijing, China

Large-angle quasielastic scattering has been studied in a high- Z 1 Z 2 nuclear reaction of the type leading to superheavy-element production by cold fusion. We show that despite the presence of strongly dissipative channels, and the complete absence of fusion, the notion of an external barrier distribution, determined by strong coupling to collective excitations of target and projectile, is still valid. Furthermore, our method allows us to deduce some properties of the deep-inelastic processes in this system.

In view of its large deformation, which should give rise to strong barrier structures, the 20 Ne projectile has been used to study the influence of neutron-transfer channels on the distribution of barrier heights. A previous experiment with a combination of projectiles 20,22 Ne suggested that the role of α-particle transfer channels is small. By an appropriate choice of targets (90 Zr and 92 Zr ), having very similar intrinsic structures (excited states and deformation parameters) but giving rise to different Q-values for neutron transfers, we highlight the role of these channels.

Mass, energy and folding angle distributions of the fission fragments as well as multiplicities of neutron and gamma‐quanta emissions accompanying the fission process were measured for fission of 226Th, 227Pa and 234Pu compound nuclei produced in reactions with 18O and 26Mg projectiles over a wide energy range. Data were analyzed with respect to the presence of fission modes. Asymmetric fission was observed even at very high initial excitation for all the measured systems. The so‐called fission mode S1 (caused by the proton shell Z∼50 and neutron shell N∼82 in heavy fragment) was found to be dominant in asymmetric fission of 234Pu. Reactions with not full linear momentum transfer were observed in the folding spectra for all the measured systems.

With the aid of the Geant4 Monte Carlo simulation package a new detection system has been designed for the focal plane of the recoil separator VASSILISSA situated at the Flerov Laboratory of Nuclear Reactions, JINR, Dubna. GABRIELA (Gamma Alpha Beta Recoil Investigations with the Electromagnetic Analyser VASSILISSA) has been optimised to detect the arrival of reaction products and their subsequent radioactive decays involving the emission of alpha- and beta-particles, fission fragments, gamma- and X-rays, and conversion electrons. The new detector system is described and the results of the first commissioning experiments are presented., 24 pages, Submitted to NIM A

Symmetric heavy-ion collisions are known to display an `extra-push' effect. That is, the energy at which the s-wave transmission is 0.5 lies significantly higher than the nominal Coulomb barrier. Despite this, however, the capture cross section is still greatly enhanced below the uncoupled barrier. It is shown that this phenomenon can be simply explained in terms of entrance-channel effects which account for long-range Coulomb excitations., 9 pages, 4 ps figures, uses elsart.cls

In intermediate-mass systems, collective excitations of the target and projectile can greatly enhance the subbarrier capture cross section σ cap by giving rise to a distribution of Coulomb barriers. For such systems, capture essentially leads directly to fusion [formation of a compound nucleus (CN)], which then decays through the emission of light particles (neutrons, protons, and alpha particles). Thus, the evaporation-residue (ER) cross section is essentially equal to σ cap. For heavier systems, the experimental situation is significantly more complicated owing to the presence of quasifission (QF) (rapid separation into two fragments before the CN is formed) and by fusion-fission (FF) of the CN itself. Thus, three cross sections need to be measured in order to evaluate σ cap. Although the ER essentially recoil along the beam direction, QF and FF fragments are scattered to all angles and require the measurement of angular distributions in order to obtain the excitation function and barrier distribution for capture. Two other approaches to this problem exist. If QF is not important, one can still measure just the ER cross section and try to reconstruct the corresponding σ cap through use of an evaporation-model code that takes account of the FF degree of freedom. Some earlier results on σ cap obtained in this way will be reanalyzed with detailed coupled-channels calculations, and the “extra-push” phenomenon discussed. One may also try to obtain σ cap by exploiting unitarity, that is, by measuring instead the flux of particles corresponding to quasielastic (QE) scattering from the Coulomb barrier. Some new QE results obtained for the 86Kr + 208Pb system at iThemba LABS in South Africa will be presented.

International audience; 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 Ebeam = 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 1112 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 2 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.

Motivated by the extreme deformation parameters of the projectile, we have measured quasi-elastic scattering for 20 Ne + 118 Sn. In contrast to calculations based on known collective states, the experimental barrier distribution is structureless. A comparison with the system 22 Ne + 118 Sn shows that this smoothing is unlikely to be due to nucleon- or α -transfer channels, and is more likely to be due to coupling to many other weak channels.

Results of the experiments aimed at the study of fission and quasi-fission processes in the reactions ^12C+^204Pb, ^48Ca-^144Sm, ^154Sm, ^168Er, ^208Pb, ^238U, ^244Pu, ^248Cm ; ^58Fe+^208Pb, ^244Pu, ^248Cm, and ^64Ni+^186W, ^242Pu are presented in the work. The choice of the above mentioned reactions was inspired by recent experiments on the production of the isotopes (283)112, (289)114 and (283)116 at Dubna [1], [2] using the same reactions. The Fe-58 and ^64Ni projectiles were chosen since the corresponding projectile-target combinations lead to the synthesis of even heavier elements. The experiments were carried out at the ^400U accelerator of the Flerov Laboratory of Nuclear Reactions (JINR, Russia), the XTU Tandem accelerator of the National Laboratory of Legnaro (LNL, Italy) and the Accelerator of the Laboratory of University of Jyvaskyla (JYFL, Finland) using the time-of-flight spectrometer of fission fragments CORSET[3] and the neutron multi-detector DEMON[4], [5]. The role of shell effects and the influence of the entrance channel on the mechanism of the compound nucleus fusion-fission and the competitive process of quasi-fission are discussed.

Fusion-evaporation and fusion-fission cross sections have been measured in the reaction 48 Ca+ 154 Sm from well below to well above the Coulomb barrier. The comparison of fusion cross sections for this reaction with previous data corresponding to 16 O+ 186 W, leading to the same compound nucleus 202 Pb * , puts in evidence an interesting competition between sub-barrier enhancement, due to the strong couplings related to the 154 Sm deformation, and above barrier suppression for the 48 Ca induced reaction. The fusion hindrance mechanism has been attributed to the strong quasi-fission component observed in the mass-energy distributions of fission fragments.

A recent publication reports that heavy-ion fusion cross sections at extreme subbarrier energies show a continuous change of their logarithmic slope with decreasing energy, resulting in a much steeper excitation function compared with theoretical predictions. We show that the energy dependence of this slope is partly due to the asymmetric shape of the Coulomb barrier, that is its deviation from a harmonic shape. We also point out that the large low-energy slope is consistent with the surprisingly large surface diffusenesses required to fit recent high-precision fusion data., 9 pages, 3 eps figures

Near-barrier excitation functions have been measured for evaporation-residue production and fission in the 12C + 204,206,208Pb and 48Ca + 168,170Er systems that lead to the compound nuclei 216,218,220Ra*. A Pronounced suppression of evaporation-residue production is observed for the more symmetric combinations, 48Ca + 168,170Er. We relate this to the significant quasifission components already observed for these systems.

The process of fusion-fission of heavy and superheavy nuclei (SHE) with Z = 82-122 formed in the reactions with Ca-48 and Fe-58 ions at energies near and below the Coulomb barrier has been studied. The experiments were carried out at the U-400 accelerator of the Flerov Laboratory of Nuclear Reactions (JINR) and at the XTU Tandem accelerator of the National Laboratory of Legnaro (LNL) using the time-of-flight spectrometer of fission fragments CORSET and the neutron multidetector DEMON. As a result of the experiments, mass and energy distributions (MED) of fission fragments ; fission, quasifission, and evaporation residue cross sections ; and multiplicities of neutrons and gamma-quanta and their dependences on the mechanism of formation and decay of compound systems have been studied.

Heavy-ion fusion barrier distributions are now routinely obtained directly from experimental data. Measurements of the total γ-ray multiplicity for the fusion channels of the 58 Ni + 60 Ni system, which has striking yet well understood barrier structures, confirm the theoretical predictions that very high spins can be populated at energies close to (and even below) the nominal Coulomb barrier. The mapping from multiplicities to spin populations shows that structures in the barrier distribution are still evident in the γ-ray results.

Through precision measurements of fusion cross sections at energies close to the Coulomb barrier and through the application of the method of “experimental barrier distributions” which these permit, many recent advances have been made in our understanding of the dynamical processes occurring during a heavy-ion collision. It is now clear that the target and projectile reach one another in superpositions of states which correspond to different orientations for rotational nuclei or to different induced deformations for vibrational nuclei. The creation of a neck of neutron matter has also long been postulated and by studying the isotopic dependence of the fusion reaction, some recent results in the 10Ca+90,96Zr systems appear to confirm this result. For large Z1Z2 a type of extra-push effect can arise from the same inelastic entrance-channel effects which enhance the fusion of lighter systems, though this will be absent in cases where the enhancement arises from neutron transfers.

A fascinating challenge in nuclear structure physics is to find the maximum atomic numberZ— the number of protons — for which a relatively stable nucleus can exist. The question is, just how many stable elements is it possible to make?

High precision fusion excitation functions have been measured for the 16 O+ 58 Ni and 16 O+ 62 Ni systems from which fusion barrier distributions have been evaluated. Coupled-reaction-channels (CRC) calculations, which describe elastic and quasi-elastic scattering, also satisfactorily reproduce the fusion cross sections and barrier distributions. The small value of Z 1 Z 2 in this case leads to barrier distributions with relatively little structure. However, in conjunction with the detailed elastic scattering data for these systems, this allows us to elucidate the role of previously ignored states in 16 O in pushing the entire distribution to lower energies. These shifts are consistent with derived magnitudes of polarization potentials for both systems.

Exact many-body calculations have been performed in a large Nilsson-model basis using a two-body monopole-pairing force. The diagonalisations are reduced to a manageable size by exploiting the symmetry of the general pairing Hamiltonian and time-reversal invariance. The results have been successfully applied to a study of multi-quasiparticle states in the Hf-W region. An extension of this work, calculating nuclear masses, allows a comparison with the experimental neutron-pairing energiesP N. These have been studied in detail for the Kr isotopes. Two important conclusions emerge (i) the monopole-pairing term must be generalized to a state-dependent interaction; good results being obtained for a delta-function force (ii) the small nuclear deformations relevant to this mass region appear to vary smoothly, as given by laser spectroscopy experiments, rather than showing the fluctuations of microscopic-macroscopic calculations.

The extraction of representations of the fusion barrier distribution from backward-angle, quasi-elastic, elastic and transfer excitation functions is discussed. Such excitation functions have been measured for , and projectiles incident on a variety of targets. The results are compared with representations obtained from fusion excitation functions. Varying in their sensitivity, all representations show evidence of the barrier structure. Differences between the scattering and the fusion representations can be related to the effects of coupling to residual, weak reaction channels.

We study in detail the barrier distributions extracted from large-angle quasi-elastic scattering of heavy ions at energies near the Coulomb barrier. Using a closed-form expression for scattering from a single barrier, we compare the quasi-elastic barrier distribution with the corresponding test function for fusion. We examine the isocentrifugal approximation in coupled-channels calculations of quasi-elastic scattering and find that for backward angles, it works well, justifying the concept of a barrier distribution for scattering processes. This method offers an interesting tool for investigating unstable nuclei. We illustrate this for the $^{32}$Mg + $^{208}$Pb reaction, where the quadrupole collectivity of the neutron-rich $^{32}$Mg remains to be clarified experimentally., Comment: 26 pages, 10 eps figures