Radius of curvature of the S factor maximum in sub-barrier fusion hindrance

A maximum of the S(E) factor is evidence for an onset of sub-barrier fusion hindrance and it can be well described by a radius-of-curvature expression near the maximum. The systematics of this radius of curvature has been studied over a wide range of projectile-target combinations. It follows a tentative general trend as a function of the parameter ζ=Z1Z2μ, and is strongly affected by effects associated with the nuclear structure of the nuclei in the entrance channel. It also explains the reason why the S factor maximum is not easily recognized visually for lighter, astrophysically interesting fusion systems

Expectations for C12 and O16 induced fusion cross sections at energies of astrophysical interest

The extrapolations of cross sections for fusion reactions involving C12 and O16 nuclei down to energies relevant for explosive stellar burning have been reexamined. Based on a systematic study of fusion in heavier systems, it is expected that a suppression of the fusion process will also be present in these light heavy-ion systems at extreme sub-barrier energies due to the saturation properties of nuclear matter. Previous phenomenological extrapolations of the S factor for light heavy-ion fusion based on optical model calculations may therefore have overestimated the corresponding reaction rates. A new "recipe" is proposed to extrapolate S factors for light heavy-ion reactions to low energies taking the hindrance behavior into account. It is based on a fit to the logarithmic derivative of the experimental cross section which is much less sensitive to overall normalization discrepancies between different data sets than other approaches. This method, therefore, represents a significant improvement over other extrapolations. The impact on the astrophysical reaction rates is discussed

Survey of heavy-ion fusion hindrance for lighter systems

A survey of heavy-ion fusion cross sections at extreme sub-barrier energies has been carried out for lighter systems with positive Q values. A general parametrization is proposed, which describes excitation functions for a wide range of light systems at low energies. This parametrization is then applied to a calculation of excitation functions and S factors for the system O16+O16, which has recently been investigated with various other theoretical approaches. It is suggested that this parametrization is useful for estimating sub-barrier fusion cross sections with exotic neutron-rich partners which cannot be studied in the laboratory

Systematics of heavy-ion fusion hindrance at extreme sub-barrier energies

The recent discovery of hindrance in heavy-ion induced fusion reactions at extreme sub-barrier energies represents a challenge for theoretical models. Previously, it has been shown that in medium-heavy systems, the onset of fusion hindrance depends strongly on the "stiffness" of the nuclei in the entrance channel. In this work, we explore its dependence on the total mass and the Q-value of the fusing systems and find that the fusion hindrance depends in a systematic way on the entrance channel properties over a wide range of systems

Analysis of heavy-ion fusion reactions at extreme sub-barrier energies

A coupled-channels analysis has been carried out for fusion reactions in the system [Formula Presented]. It demonstrates that conventional coupled-channels calculations are unable to reproduce the unexpected steep falloff of the recently measured cross sections at extreme sub-barrier energies. Heavy-ion fusion excitation functions are also analyzed in terms of the [Formula Presented] factor, as this offers a pragmatic way to study fusion behavior in the energy regime of interest. It is shown that the steep falloff in cross section observed in several heavy-ion systems translates into a maximum of the [Formula Presented] factor. The energies where the maximum occurs can be parametrized with a simple empirical formula. The parametrization, which is derived here for rather stiff heavy-ion systems, provides an upper limit for reactions involving softer nuclei

Recent experimental results in sub- and near-barrier heavy ion fusion reactions

Recent advances obtained in the field of near and sub-barrier heavy-ion fusion reactions are reviewed. Emphasis is given to the results obtained in the last decade, and focus will be mainly on the experimental work performed concerning the influence of transfer channels on fusion cross sections and the hindrance phenomenon far below the barrier. Indeed, early data of sub-barrier fusion taught us that cross sections may strongly depend on the low-energy collective modes of the colliding nuclei, and, possibly, on couplings to transfer channels. The coupled-channels (CC) model has been quite successful in the interpretation of the experimental evidences. Fusion barrier distributions often yield the fingerprint of the relevant coupled channels. Recent results obtained by using radioactive beams are reported. At deep sub-barrier energies, the slope of the excitation function in a semi-logarithmic plot keeps increasing in many cases and standard CC calculations over-predict the cross sections. This was named a hindrance phenomenon, and its physical origin is still a matter of debate. Recent theoretical developments suggest that this effect, at least partially, may be a consequence of the Pauli exclusion principle. The hindrance may have far-reaching consequences in astrophysics where fusion of light systems determines stellar evolution during the carbon and oxygen burning stages, and yields important information for exotic reactions that take place in the inner crust of accreting neutron stars.Comment: 40 pages, 63 figures, review paper accepted for EPJ

Origin and consequences of C12+C12 fusion resonances at deep sub-barrier energies

Previous explanations for the resonance behavior of C12+C12 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 Mg24 compound levels in the corresponding excitation-energy region

Do we understand heavy-ion fusion reactions of importance in stellar evolution?

Since the first observation of hindrance in heavy-ion fusion, many extrapolated cross sections for astrophysically interesting fusion reactions, such as 12C + 12C, 12C + 16O, 16O + 16O, 24O etc. need to be reexamined. In this contribution, the effects of fusion hindrance at extreme low energies are discussed

Influence of heavy-ion transfer on fusion reactions

The influence of inelastic excitations on heavy-ion fusion is well established and can be quantitativly described by coupled-channels calculations. The influence of transfer channels, however, is still under debate. We have analyzed a large set of heavy-ion-induced fusion excitation functions involving nuclei with similar structures and show that there is a universal correlation between the shape (and enhancement) of the excitation function and the strength of the total neutron-transfer cross sections for systems ranging from light to heavy masses

Oscillations above the barrier in the fusion of 28Si + 28Si

Fusion cross sections of 28Si + 28Si have been measured in a range above the barrier with a very small energy step (DeltaElab = 0.5 MeV). Regular oscillations have been observed, best evidenced in the first derivative of the energy-weighted excitation function. For the first time, quite different behaviors (the appearance of oscillations and the trend of sub-barrier cross sections) have been reproduced within the same theoretical frame, i.e., the coupled-channel model using the shallow M3Y+repulsion potential. The calculations suggest that channel couplings play an important role in the appearance of the oscillations, and that the simple relation between a peak in the derivative of the energy-weighted cross section and the height of a centrifugal barrier is lost, and so is the interpretation of the second derivative of the excitation function as a barrier distribution for this system, at energies above the Coulomb barrier.Comment: submitted to Physics Letters