Heavy-ion fusion reactions at extreme sub-barrier energies

The study of fusion reactions at extreme sub-barrier energies has seen an increased interest in recent years, although difficult to measure due to their very small cross sections. Such reactions are extremely important for our understanding of the production of heavy elements in various environments. In this article, the status of the field is reviewed covering the experimental techniques, the available data, and the theoretical approaches used to describe such reactions. The fusion hindrance effect, first discovered in medium-mass systems, has been found to be relevant also for lighter systems. In some light systems, resonance structures are found to be important, while for heavy systems, the fission process plays an important role. In the near barrier region, couplings to collective excitations in the fusion participants and transfer reactions have been found to give a good description of the measured fusion cross sections and it results in a distribution of fusion barrier heights. New physics ingredients, related to the overlap process of the two projectiles, have to be introduced to describe the hindrance behavior. In addition, it has recently been found that the fusion cross section in both near-barrier and sub-barrier regions can be described very well in many cases using simple, analytical forms of the barrier-height distributions or a modified version of the classic Wong formula.

Influence of halo single-neutron transfer on near barrier $$^{15}$$C + $$^{12}$$C total fusion

A recent comparison of the average fusion cross section, $$\left\langle \sigma _\mathrm {F}\right\rangle $$ σ F , for energies just above the Coulomb barrier for the $$^{12-15}$$ 12 - 15 C + $$^{12}$$ 12 C systems found that the behaviour as a function of projectile neutron excess could not be satisfactorily explained by static barrier penetration model calculations and suggested that the neutron dynamics plays an important rôle. In this work we demonstrate that the ($$^{15}$$ 15 C,$$^{14}$$ 14 C) single neutron transfer has a significant influence on the above barrier $$^{15}$$ 15 C + $$^{12}$$ 12 C total fusion, although not quite in the way expected since it leads to a reduction in the cross section, contrary to the trend in the measured $$\left\langle \sigma _\mathrm {F}\right\rangle $$ σ F . However, this result underlines the danger of ignoring the effect of neutron transfer reactions on fusion in systems involving neutron halo nuclei.

Coupled channels calculations of fusion reactions for 46Ti+64Ni, 40Ca+194Pt and 40Ar+148Sm systems

In this work, the fusion cross section , fusion barrier distribution and the probability of fusion have been investigated by coupled channel method for the systems 46Ti+64Ni, 40Ca+194Pt and 40Ar+148Sm with semi-classical and quantum mechanical approach using SCF and CCFULL Fortran codes respectively. The results for these calculations are compared with available experimental data. The results show that the quantum calculations agree better with experimental data, especially bellow the Coulomb barrier, for the studied systems while above this barrier, the two codes reproduce the data.

Fusion cross-sections for deuterium cycle fusion reactors (D-cycle): an analysis of geometric, Gamow-Sommerfeld and astrophysical S-factors

Fusion reactions in the deuterium cycle (D+D, D+T and D+3He) are the main nucleus-nucleus interactions which occur in tokamaks and stellerators. These reactions are the limiting case between the Woods-Saxon potential field at nuclear distances and the Coulomb electrostatic potential (scattering) at longer distances. In this paper several fusion cross-sections, geometric, Gamow-Sommerfeld and astrophysical S-factors have been reviewed and compared with experimental data from the last ENDF/B-VIII.0 cross-section library. The XDC-fusion code has been developed to calculate fusion cross-sections, geometric, Gamow-Sommerfeld and S-factors of the deuterium-cycle (D-cycle), including resonance parameters (energy and partial width). The software estimates also fusion reaction heat (Q) and Woods-Saxon/Coulomb proximity potentials. Although relative differences between fusion cross-sections are lower than 5 %, S-factors present considerable differences between the energies and partial width (FWHM) of the single-level Breit-Wigner (SLBW) resonances. The energy at which is placed the maximum fusion cross-section is also different between cases. In conclusion, fusion reaction models for light nuclei (deuterium, tritium and helium) should be reviewed in order to apply fusion to energy production in safety conditions.

Investigation of the Calculation of Coupled Channels for Some Halo Systems

The fusion reaction for systems involving halo nuclei are investigated by two- and multicoupled channel calculations for the systems 8B+58Ni, 11Be+209Bi, and 15C+232Th. The effect of coupling between the breakup channel and the elastic channel have been considered using the Continuum Discretized Coupled Channels (CDCC) method in full quantum and semiclassical approaches. The calculation of the fusion cross-section qfus (mb), fusion barrier distribution Dfus (mb/MeV) and fusion probability Pfus reproduces the measured data for the systems under study quite well above and below the Coulomb barrier VB. In the case of two-channel coupling both in semiclassical and quantum mechanical approaches, the measured data above the Coulomb barrier VB are overestimated.