Regular Series


Vol. 34 (2003), No. 3, pp. 1639 – 1997


Professor Adam Sobiczewski: Seminal Contributions to Understanding and Predicting Nuclear Stability of the Heaviest Elements

abstract

Throughout his long career Adam Sobiczewski has made major contributions to the interpretation and understanding of experimental results on the synthesis and decay properties of the heaviest nuclei and to the development of theoretical methods for predicting properties of as yet undiscovered nuclei. He led the way in using a dynamical approach to macroscopic-microscopic calculations of spontaneous fission half-lives of deformed nuclei in a multi-dimensional deformation space without adjustable parameters. Examination of the well-deformed even-even nuclei with \(Z\)=104–114 and \(N\)=142–176 showed that inclusion of higher order deformations greatly increased the \(N\)=162 shell correction. Nuclei in the region of the doubly magic deformed nucleus \(^{270}\)108 were predicted to be much more stable than previously believed and significant deviations from the old rule of rapidly decreasing spontaneous-fission half-lives with increasing \(Z\) should occur. The impact and influence of these results on experimental investigations and the interactions between theory and experiment will be discussed.


Fission-Fragment Mass Distribution and Particle Evaporation at Low Energies

abstract

Fusion–fission dynamics is investigated with a special emphasis on fusion reactions at low energy for which shell effects and pairing correlations can play a crucial role leading in particular to multi-modal fission. To follow the dynamical evolution of an excited and rotating nucleus we solve a 2-dimensional Langevin equation taking explicitly light-particle evaporation into account. The confrontation theory-experiment is demonstrated to give interesting information on the model presented, its qualities as well as its shortcomings.


Model Experiments on Chemical Properties of Super Heavy Elements in Aqueous Solutions

abstract

This paper presents a brief review of model experiments on investigation of chemical properties of transactinide elements, ranging from 104 to 116. The possibilities of isolation of the nuclei of these elements from nuclear reaction products, using the ion-exchange method, are also considered.


The Study of Superheavy Elements at SHIP — Results and Developments

abstract

The nuclear shell model predicts that the next doubly magic shell-closure beyond \(^{208}\)Pb is at a proton number between \(Z = 114\) and 126 and at a neutron number \(N = 184\). The outstanding aim of experimental investigations is the exploration of this region of spherical ’Superheavy Elements’. This article describes the experiments that were performed recently at the GSI SHIP. They resulted in an unambiguous identification of elements 110 to 112. They were negative so far in searching for elements 113, 116, and 118. The measured decay data are compared with theoretical predictions. Some aspects concerning the reaction mechanism and the use of radioactive beams are also presented.


The Chemistry of Superheavy Elements

abstract

The chemistry of transactinide or superheavy elements has reached element 108. Preparations are under way to leap to element 112 and beyond. The current status of this atom-at-a-time chemical research and its future perspectives are reviewed from an experimental point of view together with some of the interesting results from \(n\)-rich nuclides near and at the N=162 neutron shell. Experimental techniques and important results enlightening typical chemical properties of elements 104 through 108 are presented in an exemplary way. From the results of these experiments it is justified to place these elements in the Periodic Table of the Elements into groups 4 through 8, respectively. However, mainly due to the influence of relativistic effects, it is no longer possible to deduce detailed chemical properties of these superheavy elements simply from this position.


Cluster Features in Reactions and Structure of Heavy Nuclei

abstract

Cluster effects in the structure of heavy nuclei are considered. The properties of the states of the alternating parity bands in Ra, Th, U and Pu isotopes are analyzed within a cluster model. The model is based on the assumption that cluster type shapes are produced by the motion of the nuclear system in the mass asymmetry coordinate. The results of calculations of the spin dependence of the parity splitting and of the electric multipole transition moments are in agreement with the experimental data.


Superheavy Elements Challenge Experimental and Theoretical Chemistry

abstract

When reflecting on the story of superheavy elements, the author, an experimenter, acknowledges the role, which the predictions of nuclear and chemical theories have played in ongoing studies. Today, the problems of major interest for experimental chemistry are the studies of elements 112 and 114 including their chemical identification. Advanced quantum chemistry calculations of atoms and molecules would be of much help. First experiments with element 112 evidence that the metal is much more volatile and inert than mercury.


Coherent Production of Compound Nuclear Resonances by Cold Neutrons

abstract

We consider the capture of a cold neutron (kinetic energy \(\lt 0,1\) meV) by a crystal in the case that, at first, by the emission of a phonon, the neutron is absorbed by one of the lattice nuclei forming a compound nuclear resonance. Subsequently, the resonance decays by the emission of a photon. The energy of the compound nuclear resonance must be very close to the neutron threshold, i.e. within the range of phonon energies (\(\lesssim 100\) meV), thus implying that the absorbing nuclei must be heavy actinides. We discuss the dependence of the capture process on the initial occupation pattern of phonons and, in particular, a mechanism of enhancing the absorption process.


Limits of Nuclear Stability

abstract

The modern version of the liquid-drop model (LSD) is compared with the macroscopic part of the binding energy evaluated within the Hartree–Fock–Bogoliubov procedure with the Gogny force and the relativistic mean field theory. The parameters of a liquid-drop like mass formula which approximate on the average the self-consistent results are compared with other models. The limits of nuclear stability predicted by these models are discussed.


Collective Quadrupole Excitations of Transactinide Nuclei

abstract

The quadrupole excitations of transuranic nuclei are described in the frame of the microscopic Bohr Hamiltonian modified by adding the coupling with the collective pairing vibrations. The energies of the states from the ground-state bands in U to No even–even isotopes as well as the \(B(\)E2\()\) transition probabilities are reproduced within the model containing no adjustable parameters.


Spontaneous Fission and \(\alpha \)-Decay Half-Lives of Superheavy Nuclei in Different Macroscopic Energy Models

abstract

Spontaneous fission half-lives (\(T_{\rm sf}\)) of the heaviest nuclei are calculated in the macroscopic-microscopic approach based on the deformed Woods-Saxon potential. Four different models of the macroscopic energy are examined and their influence on the results is discussed. The calculations of (\(T_{\rm sf})\) are performed within WKB approximation. Multi-dimensional dynamical-programming method (MDP) is applied to minimize the action integral in a 3-dimensional space of deformation parameters describing the nuclear shape \(\{\beta _2,\beta _4,\beta _6\}\).


Potential Energy Surface in Nucleus–Nucleus Collisions Corrected for Exact Nuclear Masses

abstract

A macroscopic model for calculating potential energy for nuclear shapes relevant in fusion and fission processes is presented. The potential energy is calculated as the sum of the Yukawa-plus-exponential folding potential and the Coulomb energy assuming realistic, diffuse charge distributions. Shape independent components (e.g. the Coulomb exchange and Wigner terms) in the Krappe–Nix–Sierk formulae for the total energy were combined and adjusted to the experimental ground state masses of the compound nucleus (for the mononuclear regime), and two separated nuclei (for the binary regime), and assumed to change in the transition region between these two regimes. We have used experimental data on heights of the saddle point (experimental fission barriers) and the interaction barrier (experimentally deduced fusion barriers) to verify our model calculations. Very good agreement with the fission barrier data proved correctness of our description of the shell-correction energies. Predictions of the interaction barriers also agree very well with experimental data. The calculated interaction barriers are significantly lower than those predicted with the “proximity potential”, and agree with the experimentally deduced fusion barriers.


On the Production of Superheavy Elements

abstract

How the Island behind the Swamp was drained and bridged by the discovery of Deformed Superheavy Elements is reported in a reminiscent introduction. What we know experimentally and theoretically on the nuclear structure of SHE is reported in the first section. The making of the elements with an analysis of production cross sections and its macroscopic limitation to \(Z\) = 112 + \(\varepsilon \) is presented in the second section. The break-down of fusion cross sections in the “Coulomb Falls” within a range of about 10 elements is introduced as the universal limiting phenomenon. How the nuclear structure of the collision partners modifies the on-set of this limitation is presented in Section 3. Reactions induced by deformed nuclei are pushed by side collisions to higher excitation energies (\(4n\)- and \(5n\)-channels), whereas reactions driven by the cluster-like, closed-shell nuclei, \(^{208}\)Pb\(_{126}\) and \(^{138}\)Ba\(_{82}\) , are kept at low excitation energies (\(1n\)- and \(2n\)-channels). The on-set of production limitation for deformed collision partners is moved to smaller effective fissilities \(x\) = 0.68 \(\leq \) 0.72, whereas for spherical clusters the on-set is delayed \(x\) = 0.76 \(\geq \) 0.72 and \(x\) = 0.79 \(\geq \) 0.72 for \(^{138}\)Ba and \(^{208}\)Pb, respectively. A short outlook, what should be done in the future, ends the article.


Barrier Distributions and Systematics of Fusion- and Capture Cross Sections

abstract

Methods of predicting ‘capture’ cross sections, i.e., cross sections for sticking of two colliding nuclei after overcoming the interaction barrier, are presented. Close links between the capture excitation functions and smearing of the interaction barrier are discussed. By using a new ‘polynomial fit’ method of determining \(d^2 (E\sigma )/dE^2\) values, the barrier distributions have been directly deduced for several precisely measured fusion excitation functions found in the literature, and compared with results of standard ‘point difference’ method. Existing data on near-barrier fusion- and capture excitation functions for about 50 medium and heavy nucleus–nucleus systems have been analyzed using a simple formula obtained assuming Gaussian shape of the barrier distribution. Systematics of the barrier distribution parameters, the mean barrier and width of the distribution, are presented and proposed to be used together with the closed-form ‘error function formula’ for predicting unknown capture cross sections in experiments on synthesis of super-heavy elements.


Analysis of Nuclear Reactions Used for the Synthesis of Heavy and Superheavy Elements in the Framework of the Dinuclear System Concept

abstract

Reactions used for the synthesis of heavy and superheavy elements are analyzed within the framework of the dinuclear system concept. The important role of quasi- fission and the inner fusion potential barrier is emphasized. The results of calculation of the production cross sections for heavy and superheavy elements synthesized in cold and hot fusion reactions are given in comparison with experimental data. The minimum value of compound nucleus excitation energy is calculated for elements from \(104\) to \(114\), produced in cold fusion reactions. This article is a short survey of some results obtained by a group of physicists, using the dinuclear system concept.


On Nuclear Molecules Built up from \(^{132}\)Sn Components

abstract

The possible existence of nuclear quasi-molecules built up from \(^{132}\)Sn components is investigated. The crucial question is whether the extra stability of the doubly magic \(^{132}\)Sn nuclei makes them sufficiently rigid to be able to withstand the strains imposed by their mutual interactions. It is argued that if the simplest quasi-molecular dumbbell configuration were found to be (meta-)stable, then triangular and even tetrahedral structures might have comparable barriers against disintegration and comparable spontaneous fission lifetimes. These are estimated using simplifying assumptions. As regards the dumbbell’s stability, one may relate this to the existence of a potential energy pocket in the deformation energy landscape of a fissioning \(^{264}\)Fm nucleus, and to the presence of ‘bimodal’ fission in heavy Fm isotopes. Further experimental and theoretical studies of such systems may be relevant for answering the question concerning nuclear quasi-molecules.


Microscopic Description of Superheavy Nuclei with the Gogny Effective Interaction

abstract

An overview of the structure and stability properties of superheavy nuclei obtained from a microscopic approach employing the Gogny effective nucleon–nucleon interaction is presented. Shell gaps, fission barriers and stability against \(\alpha \)-decay are discussed and compared with experimental data and other theoretical approaches. In particular, a few \(\alpha \)-decay chains of odd nuclides observed in recent experiments are examined.


On Theoretical Problems in Synthesis of Superheavy Elements

abstract

Towards precise predictions of residue cross sections of the superheavy elements, recent theoretical developments of reaction mechanisms are presented, together with the remaining problems which give rise to ambiguities in absolute values of predicted cross sections.


The Discoveries of Bohrium, Hassium, Meitnerium, and the New Region of Deformed Shell Nuclei

abstract

The investigation of the light trans-actinide elements was not only exciting as it included the discovery of a number of new chemical elements. It led also to the discovery of a new region of shell nuclei existing beyond the macroscopic stability limit. Theory explained this in terms of a new shell region of deformed nuclei which bridge the trans-uranium nuclei and the predicted superheavy elements. This contribution will give a brief historic overview over these discoveries, experimental developments, and the impact on ongoing and future superheavy-element research.


The Single-Particle Densities in the Fission of \(^{258}\)Fm

abstract

The spontaneous fission of \(^{258}\)Fm has been analysed in the constrained Hartree–Fock–Bogolubov calculations. The bimodal fission in this nucleus has been explained. The single particle energies and densities on the fission path have been investigated. The pre-scission formation of the fission fragments have been found.


Properties of Light Hg, Pb and Po Isotopes

abstract

Quality of mass description for three different theoretical mass models is studied. Masses and deformations for Po, Pb and Hg isotopes are compared with experimental data. Gap in the proton single particle energy spectrum is discussed.


Nucleus–Nucleus Potential at Near-Barrier Energies from Selfconsistent Calculations

abstract

We determine the static nucleus–nucleus potential from Hartree-Fock (HF) calculations with the Skyrme interaction. To this aim, HF equations are solved on a spatial mesh, with the initial configuration consisting of target and projectile positioned at various relative distances. For a number of reaction partners, the calculated barrier heights reasonably well compare with those extracted from the measured fusion and capture cross sections. At smaller target-projectile distances, our results show the intrinsic barriers to heavy compound nucleus formation. We speculate on their possible connection with the fusion hindrance observed for large \(Z_{\rm T}Z_{\rm P}\).


Nuclear Matter Approach to the Interaction Potential Between Heavy Ions

abstract

A simple theory of the interaction potential between heavy ions \(\cal V\), based on the local density approach and the frozen density model, is presented for nuclei with neutron excess. The energy density needed for calculating \(\cal V\) is expressed in a simple way through the known properties of nuclear matter.


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