Rotational energy and limits to fusion reactions between two nuclei

The energy balance of the fusion process between two nuclei is discussed with respect to the rotational energy. Two energy regimes are obtained. In the first regime the increase of rotational energy of the compound system as function of incident energy is governed by the moment of inertia of the two-fragment system at the barrier configuration. The faster increase of rotational energy of the compound system is furnished by theQ-value. In a sliding collision only part of theQ-value can be converted into rotational energy. Therefore, the Yrast limit in the population of the compound nucleus cannot be reached. When this source of energy is exhausted at a certain angular momentum, a second regime is obtained; then the increase of angular momentum and rotational energy as function of incident energy must be determined by the moment of inertia of the compound system.     

The role of the entrance channel in the fusion of massive nuclei

The role of the entrance channel in the fusion-fission reactions leading to nearly the same superheavy compound nucleus is studied in the framework of dynamic model. The calculations are done for ⁴⁸Ca +²⁴⁴Pu and ^74,76Ge +²⁰⁸Pb reactions which could lead to formation of superheavy element Z = 114. It is shown that for these reactions there is an energy window for the values of the bombarding energy at which a capture probability is sufficiently large. Together with the restriction coming from the intrinsic barrier for fusion, it helps to find an optimal value of the bombarding energy for a given projectile--target combination. Received: 15 July 1998     

The interaction and fusion of arbitrarily oriented deformed nuclei

The fusion/capture cross sections between various deformed nuclei are calculated. It is shown that quadrupole and hexadecapole deformations of heavy nuclei are important for evaluating the barrier height, capture well depth, and fusion/capture cross sections of heavy nuclei. It is found that calculations of the capture cross section of two heavy deformed nuclei must be performed with averaging over all possible mutual orientations of the colliding nuclei.     

Sub-barrier fusion processes: The case of weakly-bound nuclei

This lecture reviews the main aspects associated with fusion processes between heavy ions at energies below the Coulomb barrier. We discuss in particular the novel features arising in the case of fusion with weakly-bound nuclei. The role of continuum states and the coupling to break-up channels are particularly emphasized.     

Interaction and fusion of deformed nuclei

It is shown that the height of the barrier and its position, as well the depth of the capture well, are highly sensitive to the relative orientation of colliding strongly deformed nuclei. It is found that the fusion/capture cross sections and the nucleus-nucleus potential for heavy nuclear systems depend greatly on the magnitude and sign of the quadrupole deformation of nuclear surfaces. In order to describe correctly the cross section for the capture of heavy strongly deformed nuclei, it is necessary to perform averaging over all three angles that describe their relative orientation. Allowance for a hexadecapole deformation leads to a significant increase in the capture cross section for very heavy nucleus-nucleus systems.     

Fission dynamics of hot nuclei

Experimental evidence accumulated during the last two decades indicates that the fission of excited heavy nuclei involves a dissipative dynamical process. We shall briefly review the relevant dynamical model, namely the Langevin equations for fission. Statistical model predictions using the Kramers’ fission width will also be discussed.     

核对称轴不同相对取向对熔合动力学的影响

计算了核对称轴不同相对取向时的熔合位垒.基于双核模型观念，考虑了熔合与准裂变的竞争，通过数值法求解主方程，计算了⁷⁶Ge+²⁰⁸Pb，⁴⁸Ca+²⁴⁴Pu核对称轴不同相对取向对熔合概率的影响，探索了最有利于超重元素合成的弹靶相对取向.取向不同时，对熔合反应的影响较大，计算结果表明弹靶碰撞为腰对腰时，更有利于发生熔合反应. 关键词： 超重元素 熔合概率 变形核 方向角度     

Transfer and fusion reactions of unstable nuclei

The transfer and fusion reactions are studied for reactions between a stable and an unstable nucleus with neutron skin, taking as examples the reactions ^16,28O+⁴⁰Ca. The two-dimensional time-dependent Hartree-Fock method is used. It is shown that, in such reactions, the nucleon transfer is enhanced enormously for both protons and neutrons. The neutron skin does not enhance the fusion cross section contrary to the usual expectation.     

What is the most realistic mechanism of the compound nucleus formation in the complete fusion of two massive nuclei?

An attempt has been made to reveal the most realistic picture of the mechanism of the compound nucleus formation in complete fusion of two massive nuclei.     

Reaction dynamics with exotic nuclei

We review the new possibilities offered by the reaction dynamics of asymmetric heavy-ion collisions, using stable and unstable beams. We show that it represents a rather unique tool to probe regions of highly asymmetric nuclear matter (ANM) in compressed as well as dilute phases, and to test the in-medium isovector interaction for high-momentum nucleons. The focus is on a detailed study of the symmetry term of the nuclear equation of state (EOS) in regions far away from saturation conditions but always under laboratory controlled conditions.

Thermodynamic properties of ANM are surveyed starting from non-relativistic and relativistic effective interactions. In the relativistic case, the role of the isovector–scalar δ-meson is stressed. The qualitative new features of the liquid–gas phase transition, “diffusive” instability and isospin distillation, are discussed. The results of ab initio simulations of n-rich, n-poor, heavy-ion collisions, using stochastic isospin-dependent transport equations, are analyzed as a function of beam energy and centrality. The isospin dynamics plays an important role in all steps of the reaction, from prompt nucleon emissions to the final fragments. The isospin diffusion is also of large interest, due to the interplay of asymmetry and density gradients. In relativistic collisions, the possibility of a direct study of the covariant structure of the effective nucleon interaction is shown. Results are discussed for particle production, collective flows and isotransparency.

Perspectives of further developments of the field, in theory as well as in experiment, are presented.     

Chiral dynamics of hadrons in nuclei

In this talk I report on selected topics of hadron modification in the nuclear medium using the chiral unitary approach to describe the dynamics of the problems. I shall mention how antikaons, η and φ are modified in the medium and will report upon different experiments done or planned to measure the φ width in the medium.     

Statistical properties of fusion reactions involving deformed nuclei

The statistical properties of the ¹⁶⁵Ho(α,2nγ) ¹⁶⁷Tm reaction were investigated. It was found that both the slopes of the excitation functions and the side-feeding intensities are independent of the K quantum number. Regular behaviour of these quantities as a function of the spin I and of the excitation energies of the observed levels provide a means for spin assignments, just as for spherical nuclei. The analysis, in the present case, however, is much more involved.     

Fission dynamics of excited nuclei within the liquid-drop model

We evaluate the temperature T_scis at the scission point and the saddle-to-scission time τ_scis for the fission of heated nuclei. We use classical Lagrange-like equations of motion within the liquid-drop model. The nuclear surface is parameterized by a two-parameter family of the Lawrence shapes. Conservative forces are defined through the free energy of the nucleus at finite temperatures. We use the friction tensor that is derived from the Navier-Stokes momentum-flux tensor and which takes into account the boundary conditions at the nuclear surface. The scission line is determined from the instability condition of the nuclear shape with respect to variations of the neck radius. A numerical solution to the dynamical equations is obtained for the ²³⁶U nucleus. The viscosity coefficient μ is deduced from a comparison of experimental data on the kinetic energy of fission fragments with the computed one. It is found that μ obtained by using our approach deviates significantly from μ of the standard hydrodynamic model.     

Production of super-heavy nuclei in cold fusion reactions

A model for cold-fusion reactions related to the synthesis of super-heavy nuclei in collisions of heavy projectile-nuclei with a ²⁰⁸Pb target nucleus is discussed.In the framework of this model,the production of the com-pound nucleus by two paths,the di-nuclear system path and the fusion path,are taken into account simultaneously.The formation of the compound nucleus in the framework of the di-nuclear system is related to the transfer of nucle-ons from the light nucleus to the heavy one.The fusion path is linked to the sequential evolution of the nuclear shape from the system of contacting nuclei to the compound nucleus.It is shown that the compound nucleus is mainly formed by the fusion path in cold-fusion reactions.The landscape of the potential energy related to the fusion path is discussed in detail.This landscape for very heavy nucleus-nucleus systems has an intermediate state,which is linked to the formation of both the compound nucleus and the quasi-fission fragments.The decay of the intermediate state is taken into account in the calculation of the compound nucleus production cross sections and the quasi-fission cross sections.The values of the cold-fusion cross sections obtained in the model agree well with the experimental data.     

The finite size effects in fusion of deformed nuclei at incident energies near the barrier

By the end of the last century, the precision of heavy-ion-fusion cross-section measurement had been increased up to 1%. This allowed the measured cross sections to be converted into experimental fusion-barrier distributions. In the experimental analysis, the barrier distributions were analyzed using a Woods-Saxon shape for the nuclear part of the bare nucleus-nucleus potential. This potential was defined along the line joining the centers of the two nuclei (“centerline potential”), which, for deformed nuclei, contradicts the short-range character of the nucleon-nucleon (N N) nuclear interaction. We present the results of our theoretical study of the significant deviations of the simplified potential from a “realistic” nuclear potential. The finite-size effects on the potential for deformed nuclei were first investigated in an approximate geometrical way. Then a more rigorous approach, namely, a semimicroscopic double-folding model, was applied to calculate the nucleus-nucleus potential. The angle-dependent fusion barriers calculated with a simple delta-function-like exchange term of the N N M3Y interaction was found to be very similar to those calculated with a finite-range expression. This circumstance enables us to perform rather quick calculations of the fusion cross sections and the corresponding barrier distributions. Comparison of the results with the experimental data showed that the finite-size effects are substantial and cannot be ignored in a quantitative analysis of experimental fusion cross sections and barrier distributions. The text was submitted by the authors in English.