Fusion In Collisions Research Articles

Contributions of quasifission and fusion-fission in the Mg24 + Hf178 reaction at 145 MeV laboratory beam energy using the Boltzmann-Uehling-Uhlenbeck model

Background: Understanding the mechanism of the quasifission reaction is important, because it is an essential competitor to the fusion reaction leading to superheavy elements. However, it is a challenge to separate the quasifission and fusion-fission components.Purpose: This paper provides a dynamics description of the $^{24}\mathrm{Mg}+^{178}\mathrm{Hf}$ reaction at laboratory beam energy of 145 MeV, and studies contributions of quasifission and fusion-fission in the reaction.Method: The Boltzmann-Uehling-Uhlenbeck model is improved to study the heavy-ion collision at incident energy near the Coulomb barrier. A method is developed to determine the window of the dinuclear system during the evolution.Results: It is shown that the fusion occurs with a large percentage in the central collision, and the quasiinelastic scattering occurs mainly in the peripheral collision. The quasifission competes with the fusion in collisions with small impact parameters. It is found that the cross sections of quasifission decrease and those of fusion increase with increasing surface energy or incompressibility. The mass-angular correlation of the quasifission events shows the mass asymmetry. The fragments emitted at the front angle are targetlike fragments and those at the back angle are projectilelike fragments. Furthermore, the differential cross sections at the angles ${0}^{\ensuremath{\circ}}$ and ${180}^{\ensuremath{\circ}}$ are larger than that at ${90}^{\ensuremath{\circ}}$.Conclusions: By comparing the calculations of the mass distribution and mass-angular correlation to the data, it is deduced that the compound nucleus fission plays a main role and accounts for the characteristic of fragment observables in the $^{24}\mathrm{Mg}+^{178}\mathrm{Hf}$ reaction at laboratory beam energy of 145 MeV.

Fusion processes in collisions of Li6 beams on heavy targets

We discuss a recently introduced model to evaluate complete and incomplete fusion in collisions of weakly bound nuclei. We propose a modification of the imaginary potential to deal with cross sections at energies well below the Coulomb barrier, and discuss the relation between the cross sections provided by a continuum discretized coupled-channel calculation and the ones measured in actual experiments. The new version of the model is used to make predictions of fusion cross sections in collisions of $^{6}\mathrm{Li}$ with a few heavy targets, and the results are compared to the available data. The overall agreement between theory and experiment is quite good.

Theory of complete and incomplete fusion of weakly bound systems

We propose a new method to evaluate complete and incomplete fusion in collisions of weakly bound nuclei. The method is applied to the Li7+209Bi system and the results are compared to experimental data. The overall agreement between theory and experiment is extremely good, above and below the Coulomb barrier. This suggests that 7Li breakup is the mechanism responsible for the suppression of complete fusion in this collision. We point out that this conclusion is not inconsistent with the assumption that the suppression arises from stripping processes, provided that they correspond to transfer reactions to the continuum of the target.

Semiclassical calculations of complete and incomplete fusion in collisions of weakly bound nuclei

We use an improved version of the semiclassical method described in Refs. [1,2,3] to evaluate fusion cross sections in collisions of weakly bound nuclei. This version takes into account the static effects of the low breakup threshold, uses better bin states in the discretization of the continuum and avoids the excitation of closed channels. The population of these channels is a consequence of the violation of energy conservation, which is inherent in the semiclassical method. The method is employed to evaluate complete fusion and total fusion cross section in collisions of the weakly bound 6,7Li projectiles with 159Tb and 197Au targets, for which data is available. The overall agreement between theory and experiment is fairly good.

Aneutronic Fusion in Collision of Oppositely Directed Plasmoids

Tri-Alpha and Helion energy companies have proposed an approach as the near future fusion reactor. The method used in this kind of reactor for attaining high fusion yield is based on the formation and throwing of two plasmoids toward each other. In this study, the optimized reaction rate for interpenetration of two head on colliding plasmoids is investigated. Calculations are performed by supposing the velocity of plasmoids ions as Maxwellian distribution function. Fusion output-to-input power ratio (Q factor) was computed by evaluation of the velocity-averaged cross sections and also ion−electron and ion−ion Coulomb power loss. A fluid model including a computational code has been used for the precise calculations of fusion power balance. The optimum interpenetration velocity and plasmoids parameters required to reach the ignition are studied for aneutronic fusion fuels, such as p–11B and D–3He, as well as D−T and D−D fuels. The results of investigation show that the breakeven is attainable in specific collision velocity and plasma temperature for each fuel. Also, the plasma density has to be around 1020 ions/cm3.

Relaxation times and modes of disturbed aggregate distribution in micellar solutions with fusion and fission of micelles.

We have performed direct numerical calculations of the kinetics of relaxation in the system of surfactant spherical micelles under joint action of the molecular mechanism with capture and emission of individual surfactant molecules by molecular aggregates and the mechanism of fusion and fission of the aggregates. As a basis, we have taken the difference equations of aggregation and fragmentation in the form of the generalized kinetic Smoluchowski equations for aggregate concentrations. The calculations have been made with using the droplet model of molecular surfactant aggregates and two modified Smoluchowski models for the coefficients of aggregate-monomer and aggregate-aggregate fusions which take into account the effects of the aggregate size and presence of hydrophobic spots on the aggregate surface. A full set of relaxation times and corresponding relaxation modes for nonequilibrium aggregate distribution in the aggregation number has been found. The dependencies of these relaxation times and modes on the total concentration of surfactant in the solution and the special parameter controlling the probability of fusion in collisions of micelles with other micelles have been studied.

Dynamical approach to heavy ion-induced fission

Deep inelastic collisions (DICs) can compete strongly with fusion in collisions of heavy nuclei. However, standard coupled-channels calculations do not take DIC processes into account. As a result, calculations have been shown to overestimate the fusion cross-sections, resulting in a discrepancy between experimental data and theoretical calculations, particularly at energies above the fusion barrier. To investigate this discrepancy, we conducted a series of experiments using the ANU 14UD tandem accelerator and the CUBE 2-body fission spectrometer to examine the competition between transfer/DIC and fusion. In particular, fusion-fission and 3-body fission yields have been extracted for 34 S + 232 Th and 40 Ca + 232 Th systems. This work shows that the transfer-fission probability is enhanced relative to fusion-fission for 40 Ca + 232 Th, when compared to 34 S+ 232 Th. It is suggested that the enhancement of this DIC process in 40 Ca + 232 Th is linked to an increase in the density overlap of the colliding nuclei as a function of the charge product and contributes to fusion hindrance.

An inquiry on hindrance to heavy-ion sub-barrier fusion

Since more than a decade the phenomenon of hindrance to fusion in collisions of heavy-ions at energies much lower than the Coulomb barrier is systematically investigated both experimentally and theoretically. The accumulated data for fusion excitation functions is not confirming a unique trend for the cross-section reduction with decreasing energy. I review shortly the theoretical contribution I did together with my collaborators, aiming to explain this new low-energy phenomenon based on the inclusion of an additional repulsion due to the incompressibility of nuclear matter in the nuclear interaction of two strongly overlapping nuclei. I show that for reactions at extremely low energy, the hindrance to fusion is mainly caused by a thicker Coulomb barrier due to the incompressibility of nuclear matter. A strict association of a maximum in the astrophysical S-factor near the threshold to the onset of hindrance is discarded by our long series of studies on the subject. We succeeded to obtain an excellent agreement to the fusion cross-sections data for a significative number of systems: medium-heavy projectile-target combinations, medium-heavy projectile and medium-light target, medium-light projectile and target, light projectile and heavy target. Fusion reactions relevant for the carbon and oxygen burning cycles in highly evolved stars are also set under scrutiny and we conclude that hindrance is absent in this case.

Structure effects and dynamics in fusion reactions of light weakly bound nuclei

The study of fusion in collision around the Coulomb barrier, induced by radioactive or stable weakly bound nuclei, has been the subject of many experiments in the last years. From a semiclassical point of view, direct processes like break-up or transfer may be favoured by the low binding energies and one might also expect suppressed fusion cross section due to the competition with the break-up. However, according to the Coupled Channel calculations (CC), it is well known that the presence of strong open reaction channels can be responsible for a fusion cross-section enhancement with respect to the single barrier penetration calculations and the break-up should be included in such calculations. In order to further investigate on this topic, the 6Li+64Zn collision has been studied at several energies around the Coulomb barrier, to extract the total fusion and the total reaction cross sections and to study the energy dependence of the optical model potential.

Dynamical effects in the fusion hindrance

It is well known that there is a hindrance to fusion in collisions with heavy nuclei that plays a decisive role in synthesis of the super-heavy elements (SHE). The origin of the fusion hindrance is nowadays qualitatively understood but there are still quantitative ambiguities on the dynamics of the fusion mechanism and the predictions need to be assessed. In this communication, we stress the fact that dynamical effects play a crucial role in the amplitude of the reduction of the fusion probability. We found that the fast evolution of the neck degree of freedom affects the slow radial motion, i.e., the fusioning motion, through a dynamical coupling. We showed that we could do a so-called adiabatic elimination of the fast variable in the coupled equation, resulting in an effective one-dimensional equation for the radial motion with a shift of the starting point. This treatment of the dynamical coupling leads to a larger hindrance.

Observation of molecular fusion and deep inelastic scattering in C60++C60 collisions.

Direct experimental evidence is obtained for the occurrence of fusion in collisions between two ${\mathrm{C}}_{60}$ molecules at collision energies of 200 to 500 eV in the center-of-mass frame of reference. The ${\mathrm{C}}_{120}^{+}$ formed at 200 and 250 eV collision energy has a lifetime of more than 70 \ensuremath{\mu}s with high internal energy. Results are in good qualitative agreement with recent molecular dynamics simulations combined with density functional theory.