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International audience; A systematics of over 300 complete and incomplete fusion cross section data points covering energies beyond the barrier for fusion is presented. Owing to a usual reduction of the fusion cross sections by the total reaction cross sections and an original scaling of energy, a fusion excitation function common to all the data points is established. A universal description of the fusion exci-tation function relying on basic nuclear concepts is proposed and its dependence on the reaction cross section used for the cross section normalization is discussed. The pioneering empirical model proposed by Bass in 1974 to describe the complete fusion cross sections is rather successful for the incomplete fusion too and provides cross section predictions in satisfactory agreement with the observed universality of the fusion excitation function. The sophisticated microscopic transport DYWAN model not only reproduces the data but also predicts that fusion reaction mechanism disappears due to weakened nuclear stopping power around the Fermi energy.

Peculiar nuclear structures of two colliding nuclei such has clustering, neutron halo/skin or very low breakup thresholds can affect the reaction dynamics below the Coulomb barrier and this may also have astrophysical consequences. In order to have a better understanding of this topic, in the last decade, several experiments were performed. A typical experimental challenge of such studies is the need to measure excitation functions below the Coulomb barrier, having a strong energy dependence, with rather large beam energy dispersions inside the target. This may easily lead to ambiguities in associating the measured cross section with a proper beam energy. In this paper a discussion on this topic is reported and a new technique to deal with the above problem will be proposed.

The fusion excitation function of 48 Ti + 58 Fe has been measured in a wide energy range around the Coulomb barrier, covering 6 orders of magnitude of the cross sections. We present here the preliminary re- sults of this experiment, and a full comparison with the near-by system 58 Ni + 54 Fe where evidence of fusion hindrance shows up at relatively high cross sections. The sub-barrier cross sections of 48 Ti + 58 Fe are much larger than those of 58 Ni + 54 Fe. Significant differences are also observed in the logarithmic derivatives, astro- physical S-factors and fusion barrier distributions. The influence of low-energy nuclear structure on all these trends is pointed out and commented. Coupled-channels calculations using a Woods-Saxon potential are able to reproduce the experimental results for 48 Ti + 58 Fe. The logarithmic derivative of the excitation function is very nicely fit, and no evidence of hindrance is observed down to around 1 μb. The fusion barrier distribution is rather wide, flat and structureless. It is only in qualitative agreement with the calculated distribution.

The sub-barrier fusion excitation function of Ca-40 + Zr-96 has been measured down to cross sections similar or equal to 2.4 mu b, i.e. two orders of magnitude smaller than obtained in the previous experiment, where the sub-barrier fusion of this system was found to be greatly enhanced with respect to Ca-40 + Zr-90, and the need of coupling to transfer channels was suggested. The purpose of this work was to investigate the behavior of Ca-40 + Zr-96 fusion far below the barrier. The smooth trend of the excitation function has been found to continue, and the logarithmic slope increases very slowly. No indication of hindrance shows up, and a comparison with Ca-48 + Zr-96 is very useful in this respect. A new CC analysis of the complete excitation function has been performed, including explicitly one- and two-nucleon Q > 0 transfer channels. Such transfer couplings bring significant cross section enhancements, even at the level of a few mu b. Locating the hindrance threshold, if any, in Ca-40 + Zr-96 would require challenging measurements of cross sections in the sub-mu b range.

International audience; We report on the comprehensive systematics of nearly 400 fusion-evaporation and/or fusion-fission cross-section data for a very large variety of systems over an energy range ∼3A to 155A MeV. Scaled by the reaction cross section and expressed as a function of the center-of-mass energy per nucleon, the fusion cross section displays a universal behavior. Within experimental errors, this behavior does not depend on system mass, mass asymmetry, or system isospin. The deduced homographic functional dependence for complete and summed complete and incomplete fusion excitation functions is derived from basic strong absorption model formulas for reaction cross sections and allows us to draw the main properties of these functions. The limiting energy for the complete fusion and the main characteristics (onset, maximum, and extinction) of the incomplete fusion excitation functions are determined. The complete fusion reaction process disappears around 6.5 MeV/nucleon and the incomplete one disappears at about 13 MeV/nucleon in the center-of-mass frame. The regularity in fusion data is particularly obvious for the evaporation-residue subset of the data ensemble. Adding the fusion-fission data component does not alter the general data trend but somewhat obscures it owing to the larger uncertainty and/or possible normalization problems.

We report on a systematics of fusion cross section data at energies above the reaction threshold to those of disappearance of fusion process. By an appropriate scaling of both cross sections and energy, a fusion excitation function common to all the data points is established. A universal description of the fusion excitation function relying on basic nuclear concepts is proposed and its dependence on the reaction cross section used for the cross section normalization is discussed.

The sub-barrier fusion excitation function of 40 Ca + 96 Zr has been measured down to cross sections ≃2.4 μb, i.e. two orders of magnitude smaller than obtained in a previous experiment, where the sub-barrier fusion of this system was found to be greatly enhanced with respect to 40 Ca + 90 Zr, and the need of coupling to transfer channels was suggested relying on coupled-channels calculations. The purpose of this work has been to investigate the behavior of 40 Ca + 96 Zr fusion far below the barrier, thereby disentangling the elusive interplay of effects due to inelastic couplings, transfer couplings and, possibly, the appearance of the fusion hindrance. The smooth trend of the excitation function has been found to continue, and the logarithmic slope increases very slowly. No indication of hindrance shows up, and a comparison with 48 Ca + 96 Zr is illuminating in this respect. A new CC analysis of the complete excitation function has been performed, including explicitly one- and two-nucleon Q>0 transfer channels. Such transfer couplings bring significant cross section enhancements, even at the level of a few μb. Locating the hindrance threshold, if any, in 40 Ca + 96 Zr would require challenging measurements of cross sections in the sub-μb range.

The fusion excitation function of the system 28Si + 28Si at energies near and below the Coulomb barrier is known only down to ~15 mb. This precludes any information on both coupling effects on sub-barrier cross sections and the possible appearance of hindrance. The sub-barrier cross sections for 28Si + 28Si are overestimated by coupled-channels calculations based on a standard Woods-Saxon potential, except for the lowest energies. Calculations using the M3Y+repulsion potential are adjusted to fit the 28Si + 28Si and the existing 30Si + 30Si data. An additional weak imaginary potential is required to fit the low-energy trend of 28Si + 28Si.

The fusion excitation function of 32S + 48Ca has been experimentally studied in a wide energy range, from above the Coulomb barrier down to cross sections in the sub-μb region. The measurements were done at INFN–Laboratori Nazionali di Legnaro, using the 32S beam from the XTU Tandem accelerator. The excitation function has a smooth behavior below the barrier, and no evident hindrance character shows up in the measured energy region. The fusion barrier distribution has a peculiar shape with two distinct peaks of similar height, lower and higher than the Akyüz-Winther barrier. Coupled-channels calculations using the M3Y + repulsion potential are presented for this system and for 36S + 48Ca. The results of these calculations give a good account of the data, and indicate the influence of one- and two-nucleon transfer channels with positive Q values, which are only open for 32S + 48Ca.

The fusion excitation function of 40Ca+40Ca has been measured from well above the Coulomb barrier, down to low energies where the cross section is as small as ≃20 μb, and the astrophysical S factor possibly reaches a maximum vs energy. The results of coupled-channels calculations using the M3Y+repulsion potential are presented. A detailed comparison is made with recently published data on the fusion of 40Ca+48Ca and of 48Ca+48Ca, including the excitation functions, their low- energy slopes and the barrier distributions. The presence of the fusion hindrance phenomenon in all cases is pointed out, as well as the influence of the strong octupole excitation in 40Ca and of nucleon transfer channels with positive Q values in 40Ca+48Ca.

Fusion and transfer + breakup channels have been studied in the collision induced by the two-neutron-halo 6He on a 64Zn target at energies from below to above the Coulomb barrier. For comparison, the reaction induced by the stable isotope 4He on the same target has been studied. The fusion cross section has been measured by using an activation technique, detecting off-line the delayed x-ray activity following the electron capture decay of the evaporation residues. New measurements of the 4He + 64Zn fusion cross section at sub-barrier energies have been performed in order to cover the same energy range of the 6He + 64Zn fusion cross section and to compare the excitation functions for the two systems down to the lowest energy data point measured for 6He. From the new comparison a sub-barrier fusion enhancement has been observed in the 6He case with respect to the 4He one whereas no effect on the 6He fusion cross section has been seen at energies above the barrier. It has been concluded that such enhancement seems to be due to the diffuse halo structure properties of the 6He nucleus. Moreover, the reactions induced by 6He have shown a strong yield of α particles coming from direct processes.

The fusion excitation functions of 48 Ca + 48 Ca and 36 S + 64 Ni have been measured down to very low energies, where the phenomenon known as fusion “hindrance” should show up, extending previous measurements which were limited to rather large near-barrier cross sections. Both systems show a steady decrease of the sub-barrier fusion cross sections with no pronounced change of slope. The logarithmic slopes of the two fusion excitation functions have a steep rise in the barrier region with decreasing energy and then level off in both cases. A close analogy with the case of 36 S + 48 Ca, a system with a positive Q-value for fusion ( Q f u s ), that was measured recently, is pointed out.

The fusion excitation function of 58Ni + 54Fe has been measured in a cross sections range from ~1 microbarn up to around 450 milibarn. Coupled-channels calculations, using a standard Woods-Saxon ionion potential, reproduce the excitation function down to about 180 microbarn. At lower energies, fusion cross sections drop faster than calculations, with a steep slope. The astrophysical S factor shows a maximum at the lowest energies. These results are compared with various evidences coming from recent experiments on other systems with projectile and target in the mass range A~30-60.

The fusion excitation function for 36S+48Ca with positive Q-value for the compound nucleus formation, has been measured from near the barrier down to very low energies, where “ fusion hindrance” may be expected. No evidence of hindrance shows up in the measured energy range. Coupled-channels calculations have been performed with a large diffuseness parameter of the Wood-Saxon potential, reproducing the data above and below the barrier.

A precise fusion excitation function has been measured for $^{40}$Ca+$^{94}$Zr at near- and sub-barrier energies, and the fusion barrier distribution has been extracted. Comparing with the existing data for $^{40,48}$Ca+$^{90,96}$Zr shows that couplings to inelastic excitations determine the fusion cross sections and the shape of the barrier distributions near the barrier. At lower energies, the two systems possessing neutron-transfer channels with large positive Q-values ($^{40}$Ca+$^{94,96}$Zr) have remarkably similar cross sections, and both show a large enhancement with respect to the other systems and to coupled-channels calculations including up to three quadrupole and octupole phonons in the Zr targets.

Fusion cross sections have been measured in the 40 Ca + 58 Ni and 40 Ca + 64 Ni systems at beam energies ranging from Elab = 104.75 MeV to 153.5 MeV using the Laboratori Nazionali di Legnaro electrostatic deflector. Distributions of barriers have been extracted from the experimental data. Preliminary coupled channel calculations were performed and hints of effects of neutron transfers on the fusion below the barrier in the 40 Ca + 64 Ni are discussed.

Excitation functions have been measured for the fusion of the weakly bound nuclei 6Li and 7Li respectively with 120Sn and 119Sn at energies around the Coulomb barrier by using an activation technique. With such a study we aim to investigate the role played by direct processes as neutron transfer and breakup on fusion. At energies above the barrier, the complete fusion cross section are lower than those predicted by fusion models. This suppression is independent of beam energy and is in agreement with the values reported in literature for heavier systems. At energies below the barrier, no significant enhancement due to the positive Q-value for one and two neutron transfer for the 7Li+119Sn system is observed as compared with the 6Li+120Sn.

Fusion excitation functions have been measured for the 6 Li+120 Sn and 7 Li+119 Sn systems at energies around the Coulomb barrier, to investigate the effects of neutron transfer and breakup on the fusion process. At energies above the barrier, a suppression of the complete fusion excitation function with respect to the prediction of the 1D - Barrier Penetration Model has been observed, in both cases. At energies below the Coulomb barrier, no significant difference between the two excitation function, imputable to the different neutron transfer Q-values of the two systems has been observed.

A new measurement of fusion cross-section for the system 4 He+64 Zn was performed at sub-barrier energy in order to cover the same energy region of previous measurements of 6 He+64 Zn. The fusion cross-section was obtained using an activation technique. From the comparison of the two excitation functions an enhancement of the fusion cross section was observed, at energy below the Coulomb barrier, in the reaction induced by 6 He in respect to the one induced by 4 He.

Trabajo presentado a la "5th International Conference FUSION11" celebrada del 2 al 6 de mayo del 2011 en Francia.-- This is an Open Access article distributed under the terms of the Creative Commons Attribution-Noncommercial License 3.0.-- et al., The collision induced by the three Beryllium isotopes, Be-9,Be-10,Be-11, on a Zn-64 target were investigated at E-c.m. approximate to 1.4 the Coulomb barrier. The experiments with the radioactive Be-10,Be-11 beams were performed at the Rex-Isolde facility at CERN. In the case of 9'1 Be, elastic scattering angular distributions were measured whereas, in the Be-11 case, the quasielastic scattering angular distribution was obtained. A strong damping of the quasielastic cross-section was observed in the Be-11 case, in the angular range around the Coulomb-nuclear interference peak. In this latter case a large totalreaction cross-section is found. Such a cross-section is more than a factor of two larger than the ones extracted in the reactions induced by the non-halo Beryllium isotopes. A large contribution to the total-reaction cross-section in the Be-11 case could be attributed to transfer and/or break-up events.