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.
Abstract 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 $$E\sigma $$ E σ in relation to their first energy derivatives $$d(E\sigma )/dE$$ d ( E σ ) / d E . The relation between $$d(E\sigma )/dE$$ d ( E σ ) / d E and $$E\sigma $$ 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.
Early data of sub-barrier fusion teached us that cross sections may strongly depend on the structure of colliding nuclei and on couplings to transfer channels. The influence of transfer is clearly ...indicated in the excitation functions of different nickel isotopes and various Ca+Zr systems. Fusion barrier distributions often yield the fingerprint of the relevant inelastic and transfer couplings. At lower energies, far below the barrier the slope of the excitation function keeps increasing in many cases, so that the cross sections are strongly over-predicted by standard coupled-channels (CC) calculations; this was named a hindrance effect. Furthermore, light heavy-ion systems show cross section oscillations above the Coulomb barrier. Recent experiments have been performed on the fusion of 28,30Si+28,30Si systems where all phenomena cited above show up. In particular regular oscillations that have been revealed above the barrier for 28Si+28Si and have been interpreted as the consequence of the strong channel couplings and/or the oblate deformation of 28Si.
One and two proton transfer channels have been measured in 116Sn+60Ni with the magnetic spectrometer PRISMA by making an excitation function at several bombarding energies, from above to well below ...the Coulomb barrier. The total kinetic energy loss distributions show the predominance of quasi-elastic processes in the sub-barrier regime. The data have been compared with calculations performed with the GRAZING program, based on semiclassical formalism, and in the Distorted Wave Born Approximation (DWBA), which provided a good theoretical description of the extracted transfer probabilities for the one proton transfers. The much larger values of the experimental two proton transfers compared with those evaluated within an independent particle transfer mechanism, indicate the presence of strong proton-proton correlations. The results complement the ones of the previously analyzed one- and two-neutron transfers, providing significant new information on the subject compared to past works.
This paper is devoted mainly to the fusion hindrance phenomenon, in its various aspects. Recent experimental results on medium-light systems where the fusion Q-value is positive are discussed. The ...application of the coupled-channels model using a shallow ion-ion potential is illustrated for 32,36S + 48Ca. The detailed influence of nuclear structure on the low-energy fusion cross sections is shown for the pair of systems 48Ti + 58Fe and 58Ni + 54Fe, where the low-lying quadrupole modes have a different degree of collectivity. The sub-barrier excitation function of 48Ti + 58Fe is much larger than for 58Ni + 54Fe. The lighter symmetric system 28Si +28Si has been the object of recent experimental investigations. Its fusion cross sections have been measured in a wide energy range down to ≤1µb. Above the barrier, we have a clear indication of oscillations in the excitation function, probably due to the penetration of successive centrifugal barriers, that are in rather good agreement with previous calculations. The CC model using the shallow M3Y+ repulsion potential is able to reproduce also the sub-barrier part of the excitation function of 28Si +28Si.
Lifetimes or lifetime limits of a small number of excited states of the sulfur isotopes with mass numbers A=35, 36, 37, and 38 have been measured using the differential recoil-distance method. The ...isotopes of sulfur were populated in binary grazing reactions initiated by a beam of 36S ions of energy 225 MeV incident on a thin 208Pb target which was mounted in the Cologne plunger apparatus. The combination of the PRISMA magnetic spectrometer and an early implementation of the AGATA γ-ray tracking array was used to detect γ rays in coincidence with projectile-like nuclear species. Lifetime measurements of populated states were measured within the range from about 1 to 100 ps. The number of states for which lifetime measurements or lifetime limits were possible was limited by statistics. For 35S, the lifetime was determined for the first 1/2+ state at 1572 keV; the result is compared with a previous published lifetime value. The lifetime of the 3− state of 36S at 4193 keV was determined and compared with earlier measurements. No previous lifetime information exists for the (6+) state at 6690 keV; a lifetime measurement with large associated error was made in the present work. For 37S, the states for which lifetime limits were established were those at 646 keV with Jπ=3/2− and at 2776 keV with Jπ=11/2−; there are no previously published lifetime values for excited states of 37S. Finally, a lifetime limit was established for the Jπ=(6+) state of 38S at 3675 keV; no lifetime information exists for this state in the literature. Measured lifetime values were compared with the results of state-of-the-art shell-model calculations based on the PSDPF, SDPF-U, and FSU effective interactions. In addition, nuclear magnetic-dipole and electric-quadrupole moments, branching ratios, mixing ratios, and electromagnetic transition rates, where available, have been compared with shell-model values. The current work suffers from poor statistics; nevertheless, lifetime values and limits have been possible, allowing a useful discussion of the ability of state-of-the-art shell-model calculations to reproduce the experimental results.
In the present work the fusion cross section of the 12C+24Mg system has been measured down to energies far below the coulomb barrier around 4μb. This system is slightly heavier than those of ...astrophysical interest, like 12C+12C and 16O+16O. The data points highlight the presence of hindrance in 12C+24Mg because the excitation function is over-estimated by standard Coupled-Channels calculations, and a clear maximum of the S factor has been observed. The cross section at hindrance threshold is found to be remarkably large (σ ≈0.75mb). The S-factor maximum is nicely fitted using both an empirical interpolation in the spirit of the adiabatic model, and the hindrance parametrisation. The data far below the barrier may suggest that the coupling strengths gradually decrease and vanish, so that the excitation function seems to be well reproduced by a simple one-dimensional tunnelling through the potential barrier in that energy range. On the other hand, the equally good fit obtained with the hindrance model, indicates that discriminating between the two approaches would require further precise measurements at slightly lower energies.
Lifetimes of excited states of the phosphorus isotopes 33 , 34 , 35 , 36 15 P have been measured by using the differential recoil-distance method. The isotopes of phosphorus were populated in binary ...grazing reactions initiated by a beam of 36 S ions of energy 225 MeV incident on a thin 208 Pb target mounted in the Cologne plunger apparatus. The combination of the PRISMA magnetic spectrometer and an early implementation of the AGATA γ -ray tracking array was used to detect γ rays in coincidence with projectile-like nuclear species. Lifetime measurements of populated states were made within the range from about 1 to 100 ps. The number of states for which lifetime measurements were possible was limited by statistics. For 33 P , lifetime limits were determined for the first 3/2+ and 5/2+ states at 1431 and 1848 keV, respectively; the results are compared with previous published lifetime values. The lifetime of the first 2+ state of 34 P at 429 keV was determined and compared with earlier measurements. For 35 P , the states for which lifetimes, or lifetime limits, were determined were those at 2386, 3860, 4101, and 4493 keV, with Jπ values of 3/2+, 5/2+, 7/2− 1 , and 7/2− 2 , respectively. There have been no previous published lifetimes for states in this nucleus. A lifetime was measured for the stretched π ( 1 f 7 / 2 ) ⊗ ν ( 1 f 7 / 2 ) J π = ( 7 + ) state of 36 P at 5212 keV and a lifetime limit was established for the stretched π ( 1 d 3 / 2 ) ⊗ ν ( 1 f 7 / 2 ) J π = ( 5 − ) state at 2030 keV. There are no previously published lifetimes for states of 36 P . Measured lifetime values were compared with the results of state-of-the-art shell-model calculations based on the PSDPF effective interaction. In addition, measured branching ratios, published mixing ratios, and electromagnetic transition rates, where available, have been compared with shell-model values. In general, there is good agreement between experiment and the shell model; however there is evidence that the shell-model values of the M1 transition rates for the 3/2+1→ 1 / 2 + (ground state) and 5/2+1→ 3 / 2 + 1 transitions in 33 P underestimate the experimental values by a factor between 5 and 10. In 35 P there are some disagreements between experimental and shell-model values of branching ratios for the first and second excited 7/2− states. In particular, there is a serious disagreement for the decay characteristics of the second 7/2− state at 4493 keV, for which the shell-model counterpart lies at 4754 keV. In this case, the shell-model competing electromagnetic decay branches are dominated by E1 and M1 transitions.
We present some of the recent experimental results in heavy-ion transfer reactions obtained with the large solid angle magnetic spectrometer PRISMA at energies close to the Coulomb barrier. We focus ...on a series of experiments that have been carried out to study the nucleon-nucleon correlations for closed shell and superfluid systems. They are discussed together with the newest results concerning the proton transfer channels above and below the Coulomb barrier. The second set of the experiments was performed to study the production mechanism of heavy neutron-rich nuclei and the related effects of secondary processes.
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