In 1980 the anomalous sub-barrier fusion of two massive atomic nuclei was discovered. The author examines the experimental findings that the cross sections for sub-barrier fusion far exceed simple quantum tunnelling expectations, and the magnitude of the excess fusion is particularly sensitive to the valence structure of the collision partners. The phenomenon is interpreted as one which occurs when intrinsic degrees of freedom of the dinuclear system couple to the tunnelling degree of freedom. Several models, developed during the period from 1983-5, serve to illustrate the salient features of coupling-aided barrier penetration. The author discusses the nature of the couplings and the underlying dynamics, focusing attention on the quasi-elastic channels (inelastic scattering and nucleon transfer). Results of studies on quasi-elastic scattering and of the fusion partial-wave distributions, completed during the past three years, are then presented.

http://iopscience.iop.org/article/10.1088/0034-4885/51/8/001/pdf

Sub-barrier fusion of two nuclei

The heaviest known elements at present, the transactinides, ranging from element 104 to element 109, are the subject of this paper. It will start with a brief historical review on their investigation. A considerable part of this review will be devoted to the experimental methods developed to investigate the isotopes of these artificial elements, where the quantities produced are so small as to be measured in atoms. The major step forward in heavy element research was the finding that the nuclei at the top of the periodic table are unexpectedly stable against spontaneous fission, which has been explained by high ground-state shell effects. The experimental data will be compared with current predictions with the aim of learning about their predictive power. Finally, the limitations of the production of heavy elements by heavy ion fusion will be discussed.

https://iopscience.iop.org/article/10.1088/0034-4885/51/1/002/pdf

Recent advances in the discovery of transuranium elements

In parallel to the attempts to synthesize the heaviest nuclei, systematic studies have been made to obtain better understanding of the reaction aspects. The most comprehensive data have been taken for nearly mass-symmetric massive systems. They combine high Coulomb forces in the entrance channel with evaporation-residue cross sections which are high enough to be easily detectable. With these systems, rather cold compound nuclei can be produced, and even radiative fusion was observed. While one of the most salient features of the thoroughly studied fusion of light and medium-heavy systems is the enhanced sub-barrier fusion, the massive systems exhibit a considerable deficit of fusion above the expected potential barrier. This hindrance to fusion may be attributed to the dynamical evolution of the composite system which may lead to immediate reseparation. The experimental data reveal that the hindrance to fusion is strongly influenced by the nuclear structure of the reaction partners. The high fission competition in the evaporation cascade of fissile excited compound systems as deduced from measured evaporation-residue cross sections is compared with the expectations of the statistical model. Experimental evidence is presented.

https://iopscience.iop.org/article/10.1088/0034-4885/54/7/002/pdf

The conditions for the synthesis of heavy nuclei

Unstable heavy atomic nuclei not found in nature can be created by fusing two stable nuclei, in a process analogous to colliding charged droplets of liquid. Recently, the formation of a handful of super-heavy nuclei with atomic numbers 114 (ref. 1) and 116 (ref. 2) has been achieved by fusion of heavy nuclei. The electrostatic energy of such systems is very large (which is the reason super-heavy nuclei are unstable), so although the two nuclei may initially be captured by the nuclear potential, rather than fusing, they almost always separate after transfer of mass to the lighter nucleus. This process, called quasi-fission3,4, can inhibit fusion by many orders of magnitude. Understanding this inhibition may hold the key to forming more super-heavy elements. Theoretically, inhibition is predicted (ref. 5 and references therein) when the product Z1Z2 of the charges of the projectile and target nuclei is larger than about 1,600. Here we report measurements of three fusion reactions with Z1Z2 around half this value, each forming 216 88Ra. We find convincing model-independent evidence both of inhibition of fusion, and of the presence of quasi-fission. These results defy interpretation within the standard picture of nuclear fusion and fission.

Unexpected inhibition of fusion in nucleus–nucleus collisions

We present a statistical-model description of fission, in the framework of compound-nucleus decay, which is found to simultaneously reproduce data from both heavy-ion-induced fusion reactions and proton-induced spallation reactions at around $1$ GeV. For the spallation reactions, the initial compound-nucleus population is predicted by the Li\`ege intranuclear cascade model. We are able to reproduce experimental fission probabilities and fission-fragment mass distributions in both reactions types with the same parameter sets. However, no unique parameter set was obtained for the fission probability. The introduction of fission transients can be offset by an increase of the ratio of level-density parameters for the saddle-point and ground-state configurations. Changes to the finite-range fission barriers could be offset by a scaling of the Bohr-Wheeler decay width as predicted by Kramers. The parameter sets presented allow accurate prediction of fission probabilities for excitation energies up to $300$ MeV and spins up to $60$ $\ensuremath{\hbar}$.

/pdf/unified-description-of-fission-in-fusion-and-spallation-20kjh2adrn.pdf

Unified description of fission in fusion and spallation reactions

A general method is presented for determining an equilibrium point on a potential energy surface subject to an arbitrary number of constraints. The method is then specialized to the calculation of a conditional saddle point in the liquid-drop model for which the constraint is the mass-asymmetry degree of freedom. This approach is useful for cases in which the mass asymmetry is not one of the chosen coordinates but instead is a function of these coordinates. Conditional saddle points are calculated for the liquid-drop and Yukawa-plus-exponential nuclear energy models, with the nuclear shape parametrized using both a three-quadratic-surface model and a Legendre polynomial expansion of the nuclear surface function. We show how the conditional saddle-point shapes and energies change as the fissility x and the mass asymmetry value ..cap alpha.. are varied. As ..cap alpha.. increases for fixed x, the saddle-point configurations effectively behave like lighter (less fissile) nuclei. For fissilities less than the Businaro-Gallone value (x/sub BG/), the conditional saddle-point energy always decreases with increasing ..cap alpha... For x>x/sub BG/, with increasing ..cap alpha.. the conditional saddle-point energy increases until it reaches the limit of the Businaro-Gallone peak, after which the energy decreases.

Conditional saddle-point configurations

We study the effect of the nuclear macroscopic energy, nuclear dissipation, and shape parametrization on dynamical thresholds for compound-nucleus formation in symmetric heavy-ion reactions. This is done by solving numerically classical equations of motion for head-on collisions to determine whether the dynamical trajectory in a multidimensional deformation space passes inside the fission saddle point and forms a compound nucleus, or whether it passes outside the fission saddle point and reseparates. Specifying the nuclear shape in terms of smoothly joined portions of three quadratic surfaces of revolution, we take into account three symmetric deformation coordinates. However, in some cases we reduce the number of coordinates to two by requiring the ends of the fusing system to be spherical in shape. The nuclear potential energy of deformation is determined in terms of a Coulomb energy and a nuclear macroscopic energy that is usually taken to be a double volume energy of a Yukawa-plus-exponential folding function, although a double volume integral of a single-Yukawa folding function and ordinary surface energy are also considered. The collective kinetic energy is calculated for incompressible, nearly irrotational flow by means of the Werner-Wheeler approximation. Four possibilities are studied for the transfer of collective kinetic energy into internalmore » single-particle excitation energy: (1) zero dissipation, (2) ordinary two-body viscosity, (3) one-body wall-formula dissipation, and (4) one-body wall-and-window dissipation. For systems with Z/sup 2//A larger than a threshold value (Z/sup 2//A)/sub thr/ which depends somewhat upon dissipation, the center-of-mass bombarding energy must exceed the maximum in the one-dimensional interaction barrier by an amount ..delta..E in order to form a compound nucleus.« less

K. Thomas

Papers

Conditional saddle-point configurations

Dynamical thresholds for compound-nucleus formation in symmetric heavy-ion reactions