Hindrance of heavy-ion fusion due to nuclear incompressibility

Colliding heavy nuclei take multiple identities on the path to fusion

The properties of superheavy elements probe extremes of physics and chemistry. They are synthesised at accelerator laboratories using nuclear fusion, where two atomic nuclei collide, stick together (capture), then with low probability evolve to a compact superheavy nucleus. The fundamental microscopic mechanisms controlling fusion are not fully understood, limiting predictive capability. Even capture, considered to be the simplest stage of fusion, is not matched by models. Here we show that collisions of 40Ca with 208Pb, experience an 'explosion' of mass and charge transfers between the nuclei before capture, with unexpectedly high probability and complexity. Ninety different partitions of the protons and neutrons between the projectile-like and target-like nuclei are observed. Since each is expected to have a different probability of fusion, the early stages of collisions may be crucial in superheavy element synthesis. Our interpretation challenges the current view of fusion, explains both the successes and failures of current capture models, and provides a framework for improved models.

Fusion Hindrance and Pauli Blocking in 58Ni + 64Ni

58Ni +64Ni is the first case where the influence of positive Q-value transfer channels on sub-barrier fusion was evidenced, in a very well known experiment by Beckerman et al., by comparing with the two systems 58Ni + 58Ni and 64Ni+64Ni. Subsequent measurements on 64Ni + 64Ni showed that fusion hindrance is clearly present in this case. On the other hand, no indication of hindrance can be observed for 58Ni + 64Ni down to the measured level of 0.1 mb. In the present experiment the excitation function has been extended by two orders of magnitude downward. The cross sections for 58Ni + 64Ni continue decreasing very smoothly below the barrier, down to '1 µb. The logarithmic slope of the excitation function increases slowly, showing a tendency to saturate at the lowest energies. No maximum of the astrophysical S -factor is observed. Coupled-channels (CC) calculations using a Woods-Saxon potential and includinginelastic excitations only, underestimate the sub-barrier cross sections by a large amount. Good agreement is found by adding two-neutron transfer couplings to a schematical level. This behaviour is quite different from what already observed for 64Ni+ 64Ni (no positive Q-value transfer channels available), where a clear low-energy maximum of the S -factorappears, and whose excitation function is overestimated by a standard Woods-Saxon CC calculation. No hindrance effect is observed in 58Ni+ 64Ni in the measured energy range. This trend at deep sub-barrier energies reinforces the recent suggestion that the availability of several states following transfer with Q>0, effectively counterbalances the Pauli repulsion that, in general, is predicted to reduce tunneling probability inside the Coulomb barrier.

Fusion hindrance for a positive-q-value system (24)Mg+(30)Si

Measurements of the excitation function for the fusion of (24)Mg+(30)Si (Q=17.89  MeV)have been extended toward lower energies with respect to previous experimental data. The S-factor maximum observed in this large, positive-Q-value system is the most pronounced among such systems studied thus far. The significance and the systematics of an S-factor maximum in systems with positive fusion Q values are discussed. This result would strongly impact the extrapolated cross sections and reaction rates in the carbon and oxygen burnings and, thus, the study of the history of stellar evolution.

Origin and consequences of 12C+12C fusion resonances at deep sub-barrier energies

Previous explanations for the resonance behavior of (12)C+(12)C fusion at low energies were based on a nonresonant compound-nucleus background and an additional contribution from a series of resonances. This separation into "resonance" and "background" contributions of the cross section is artificial. We propose to explain this phenomenon through the impact on the cross section of the relatively large spacings and the narrow widths of (24)Mg compound levels in the corresponding excitation-energy region.

Exploring fusion at extreme sub-barrier energies with weakly bound nuclei

Results of measurement of residues formed in fusion of (6)Li with (198)Pt in the energy range of 0.68 < E/V(b) < 1.3 using a new sensitive off-beam technique are reported. The fusion excitation function and the derived average angular momenta do not indicate a change of slope at deep sub-barrier energies, contrary to recent observations. The present results for a system with weakly bound projectile confront the current understanding of the fusion hindrance at these low energies, underlying the role of internal reorganization on the dynamical path towards fusion.

Signature of smooth transition from sudden to adiabatic states in heavy-ion fusion reactions at deep sub-barrier energies

We propose a novel extension of the standard coupled-channels framework for heavy-ion reactions in order to analyze fusion reactions at deep-sub-barrier incident energies. This extension simulates a smooth transition between the two-body and the adiabatic one-body states. To this end, we damp gradually the off-diagonal part of the coupling potential, for which the position of the onset of the damping varies for each eigenchannel. We show that this model accounts well for the steep falloff of the fusion cross sections for the (16)O + (208)Pb, (64)Ni + (64)Ni, and (58)Ni + (58)Ni reactions.

Beyond the coherent coupled channels description of nuclear fusion

New measurements of fusion cross sections at deep sub-barrier energies for the reactions 16O+{204,208}Pb show a steep but almost saturated logarithmic slope, unlike 64Ni-induced reactions. Coupled channels calculations cannot simultaneously reproduce these new data and above-barrier cross-sections with the same Woods-Saxon nuclear potential. It is argued that this highlights an inadequacy of the coherent coupled channels approach. It is proposed that a new approach explicitly including gradual decoherence is needed to allow a consistent description of nuclear fusion.