Competition between binary reactions and fusion in heavy-ion collisions at the Coulomb barrier

Mass and charge distributions for binary reaction channels have been measured for the reactions⁸⁶Kr with⁷⁶Ge,¹⁰⁴Ru and¹³⁰Te at the Coulomb barrier using chemical separations and-ray spectroscopy. These systems span the region where dynamical hindrance to complete fusion sets in. The binary reactions can be subdivided into two components associated withi) reflection from the outer potential barrier (quasielastic), andii) reseparation after passing the barrier (complex reactions). The sum of complex-reaction channels and evaporation residues from complete fusion can be reproduced by a barrier passing calculation. The fraction of the barrier passing flux leading to reseparation increases from 26±10% for the lightest system to more than 90% for the heaviest system. The data indicate that fusion hindrance is primarily caused by reseparation shortly after passage of the barrier before Swiatecki's conditional saddlepoint is overcome, resulting in partitions close to the entrance channel configuration. In addition, for the heaviest system, a quasifission component representing somewhat less than 20% of the barrier-passing flux was observed. From the missing masses of fragment pairs we can deduce that the reseparating complex-reaction products have kinetic energies well below the fusion barrier and share the excitation energy in a way similar to the sawtooth-like curve known from low-energy fission. The quasielastic, predominantly one- and two-nucleon transfer channels, have strongly varying cross sections for the three systems despite similar effectiveQ-values. A systematics of one-neutron transfer cross sections at the Coulomb barrier is established and shown to differ considerably from the smooth behaviour observed at energies 20–30% above the barrier. The connection to nuclear polarization phenomena and orbit matching is pointed out.Nuclear reactions:⁷⁶Ge,¹⁰⁴Ru,¹³⁰Te(⁸⁶Kr, X).E=3.22 MeV/u, (3.64) 3.84 MeV/u, 3.96 MeV/u; enriched targets; catcher foil technique, chemical separations,-ray spectroscopy; deduced mass and charge distributions for binary reactions; competition with complete fusion     

Competition of fusion and quasifission in reactions leading to production of superheavy elements

The mechanism of fusion hindrance, an effect observed in the reactions of cold, warm, and hot fusion leading to production of superheavy elements, is investigated. A systematics of transfermium production cross sections is used to determine fusion probabilities. The mechanism of fusion hindrance is described as a competition of fusion and quasifission. Available evaporation residue cross sections in the superheavy region are reproduced satisfactorily. Analysis of the measured capture cross sections is performed and a sudden disappearance of the capture cross sections is observed at low fusion probabilities. A dependence of the fusion hindrance on the asymmetry of the projectile-target system is investigated using the available data. The most promising pathways for further experiments are suggested.     

Polarization in heavy-ion reactions

A series of experiments is described in which beta-ray asymmetry has been used to determine polarization of heavy-ion reaction products¹²B and the present status of the studies of polarization phenomena in heavy-ion reactions is reviewed. A large amount of angular momentum sustained by the two colliding nuclei gives rise to polarization phenomena of reaction products. Coupling between the degrees of freedom accompanying the intrinsic and the relative motions is investigated from the systematic behaviour of polarization of reaction products disclosed by the experiments.     

Catalytic reactions in heavy-ion collisions

We discuss a new type of reactions of a ?-meson production on hyperons, ??Y ?? ?Y and antikaons -KN ?? ?Y. These reactions are not suppressed according to Okubo-Zweig-Iizuka rule and can be a new efficient source of ? mesons in a nucleus-nucleus collision. We discuss how these reactions can affect the centrality dependence and the rapidity distributions of the ? yield.     

Coulomb distortions in heavy-ion reactions

In heavy-ion scattering the Coulomb potential deviates from the potential of two point charges since vibrations, rotations and giant resonances are excited in both projectile and target nuclei as a result of their mutual electrostatic forces. In this paper this effect is calculated using a classical model. The adiabatic and the dynamical solutions of the problem are compared and discussed.     

Neutron-to-proton ratios in heavy-ion reactions

An expression for determining then/p ratio in heavy-ion reactions has been tested using recently published data. The agreement between the calculated and measured ratios is satisfactory.     

Kinematical effects in heavy-ion reactions

Transfer reactions between heavy ions at energies well above the Coulomb barrier have a large cross-section only, if certain kinematical conditions are satisfied. These relate the Q-value of the reaction to the angular momentum of the transferred nucleons in the initial and final nuclei.     

Charge distribution in heavy-ion reactions

Marked oscillations are seen in the differential cross section of charge distributions in high-energy heavy-ion reactions with massive projectiles. It is suggested that this can be explained by a simple quantum mechanical potential model over an “enlarged” Hilbert space.     

Application of the extended Barshay-Temmer theorem to heavy-ion reactions

The reactions ¹⁰B+¹²C, ¹⁴N+¹⁶O leading to various final states in the isobaric mass systems 11, 13 and 15, respectively, have been investigated experimentally. These measurements provide a number of applications for the extended Barshay-Temmer theorem.     

Light particles in low-energy heavy-ion reactions

Conclusions Study of the mechanism of the light particle emission in heavy-ion reactions brought several trends in heavy-ion reactions. They indicate an extraordinary importance of the energies not more than 5 MeV above the Coulomb barrier, where many characteristics change rapidly.Some imagination on the relative role of different mechanisms was obtained from the analysis of¹⁹⁷Au(²²Ne, ) reaction at 178 MeV.It is a pleasure to express sincere gratitude to V. D. Tonnev, in collaboration with whom many results discussed here were obtained.It is a pleasure to express sincere gratitude to V. D. Tonnev, in collaboration with whom many results discussed here were obtained.     

Interfering transfer processes in heavy-ion reactions

Heavy-ion reactions in which two different transfer processes may interfere are analyzed. Angular distributions of the reactions ¹⁴C(¹⁶O, ¹⁷O)¹³C and ¹⁴C(¹⁶O, ¹⁸O)¹²C were measured at incident energies of 20, 25 and 30 MeV. The strong oscillations observed at the Coulomb barrier together with a backward rise at higher energies are taken as evidence for the superposition of two competing transfer reactions. DWBA calculations for the two single transfer processes were performed using the fixed-range approximation, and the two transition amplitudes were summed coherently. The experimental angular distributions are well reproduced. The DWBA also explains the disappearance of the interference structures for higher transferred angular momenta l. Data on the reaction ¹¹B(¹⁶O, ¹⁵N)¹²C measured earlier are included in the analysis in order to show the systematic dependence on l-values.     

Pauli blocking potential applied to heavy-ion fusion reactions

In this study, the Pauli blocking potential between two colliding nuclei in the density overlapping region is applied to describe the heavy nuclei fusion process. Inspired by the Pauli blocking effect in the \begin{document}$ \alpha $\end{document}-decay of heavy nuclei, the Pauli blocking potential of single nucleon from the surrounding matter is obtained. In fusion reactions with strong density overlap, the Pauli blocking potential between the projectile and target can be constructed using a single folding model. By considering this potential, the double folding model with a new parameter set is employed to analyze the fusion processes of 95 systems. A wider Coulomb barrier and shallower potential pocket are formed in the inner part of the potential between the two colliding nuclei, compared to that calculated using the Akyüz-Winther potential. The fusion hindrance phenomena at deep sub-barrier energies are described well for fusion systems \begin{document}$ ^{16} $\end{document}O + \begin{document}$ ^{208} $\end{document}Pb and \begin{document}$ ^{58} $\end{document}Ni + \begin{document}$ ^{58} $\end{document}Ni.     

Channel-coupling effects in heavy-ion fusion reactions

A coupled-channel framework for fusion reactions is considered where an ingoing-wave boundary condition allows the effect of strong coupling in the barrier region to be studied. It is shown analytically within the sudden limit and, more generally, with model calculations that the couplings to reaction channels act to enhance the transmission through the barrier at low energies. This appears to be a natural mechanism for explaining the relatively large sub-barrier heavy-ion fusion cross sections which have recently been observed.     

Non-orthogonality effects in heavy-ion transfer reactions

Calculations are made of the effects arising from the non-orthogonality of channel states in heavy-ion neutron transfer reactions, as well as the associated elastic-scattering processes. A single iteration is performed upon the integral equations associated with the coupled-channel treatment of the transfer process. The reactions considered are ¹³C(¹⁶O, ¹⁷O)¹²C leading to the ground state and first excited state of ¹⁷O and the ²⁹Si(¹⁶O, ¹⁷O)²⁸Si reaction leading to the first excited state of ¹⁷O. Corrections are found to be as large as 10 % at angles where the cross sections are sizeable. Similar results are obtained for the elastic-scattering processes. The choice of reactions was made so as to emphasise the importance of these corrections.Consideration of the errors associated with the depiction of bound states in terms of a sum of Hankel functions and the use of a local-momentum approximation for the channel motion suggests that the figure for the correction represents an upper bound.     

Particle-wave ambiguities in the interpretation of heavy-ion reactions

The relations between the partial wave scattering amplitudes in l-space and the reaction cross section angular distributions are derived in the limits of classical and diffractive scattering. It is shown that a measurement of the angular distribution of a “quasi-elastic” heavy ion reaction does not permit an unambiquous inference of the reaction's partial-wave amplitudes, even for large l. The ambiguities are illustrated with DWBA calculations.