Unexpected behavior of heavy-ion fusion cross sections at extreme sub-barrier energies

The slopes of sub-barrier heavy-ion fusion excitation functions shed light on the dynamics of quantum tunnelling

Quantum tunnelling plays a crucial role in heavy-ion fusion reactions at sub-barrier energies, especially in the context of nuclear physics and astrophysics. The nuclear structure of the colliding nuclei and nucleon transfer processes represent intrinsic degrees of freedom. They are coupled to the relative ion motion and, in general, increase the probability of tunnelling. The influence of couplings to nucleon transfer channels relatively to inelastic excitations, on heavy-ion fusion cross sections, is one of the still open problems in this field. We present a new analysis of several systems, based on the combined observation of the energy-weighted excitation functions E σ in relation to their first energy derivatives d ( E σ ) / d E . The relation between d ( E σ ) / d E and E σ removes the basic differences due to the varying Coulomb barrier when comparing different systems. We show that, depending on the nuclear structure and/or the presence of strong transfer channels, this representation reveals characteristic features below the barrier. The possible presence of cross section oscillations makes this analysis less clear for light- or medium-light systems.

Direct Measurement of Carbon Fusion at Astrophysical Energies with Gamma-Particle Coincidences

We present 12C+12C direct fusion measurements with STELLA UKFATIMA, that reach into the region of astrophysics interest relevant to massive stars (M⊙ ≈ 25) using self-supporting thin rotating carbon foils [1]. We demonstrate that detecting gammas and light charged particles in coincidence with nanosecond timing is key for effective background reduction achieving reliable measurements in the sub-nanobarn range. We give details about core developments of the detection apparatus as well as the coincidence-analysis procedure of low count statistics. The present data largely follows the phenomenological hindrance interpolation and shows indication for resonant behaviour at the lowest energy explored.

Searching for treasures at sub-barrier energies: the case of 8B and 7Be

Unexpected and challenging experimental results, at below barrier energies for weakly bound nuclei, are briefly reviewed in this article. The emphasis will be on our recent breakup results for 8B+208Pb at deep sub-barrier energies, indicating a dominance of direct mechanisms at this low energy regime. We will also present, a preliminary analysis of the 4He and 3He - particle production events for the 7Be + 208Pb reaction. These data were collected at the same experiment and at similar deep sub-barrier energies, exhibiting large yields compatible with cluster transfer processes. To confirm these results a new experiment to be performed at TriSol is planned, as soon as the upgrading of this facility will be completed.

Advances in the Direct Study of Carbon Burning in Massive Stars

The ^{12}C+^{12}C fusion reaction plays a critical role in the evolution of massive stars and also strongly impacts various explosive astrophysical scenarios. The presence of resonances in this reaction at energies around and below the Coulomb barrier makes it impossible to carry out a simple extrapolation down to the Gamow window-the energy regime relevant to carbon burning in massive stars. The ^{12}C+^{12}C system forms a unique laboratory for challenging the contemporary picture of deep sub-barrier fusion (possible sub-barrier hindrance) and its interplay with nuclear structure (sub-barrier resonances). Here, we show that direct measurements of the ^{12}C+^{12}C fusion cross section may be made into the Gamow window using an advanced particle-gamma coincidence technique. The sensitivity of this technique effectively removes ambiguities in existing measurements made with gamma ray or charged-particle detection alone. The present cross-section data span over 8 orders of magnitude and support the fusion-hindrance model at deep sub-barrier energies.

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.

Hindrance of heavy-ion fusion due to nuclear incompressibility

We propose a new mechanism to explain the unexpected steep falloff of fusion cross sections at energies far below the Coulomb barrier. The saturation properties of nuclear matter are causing a hindrance to large overlap of the reacting nuclei and consequently a sensitive change of the nuclear potential inside the barrier. We report in this Letter a good agreement with the data of coupled-channels calculation for the 64Ni + 64Ni combination using the double-folding potential with Michigan-3-Yukawa-Reid effective N - N forces supplemented with a repulsive core that reproduces the nuclear incompressibility for total overlap.