The nuclear shell model predicts that the next doubly magic shell closure beyond ${}^{208}\mathrm{Pb}$ 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 (SHE's). This article describes the experimental methods that led to the identification of elements 107 to 112 at GSI, Darmstadt. Excitation functions were measured for the one-neutron evaporation channel of cold-fusion reactions using lead and bismuth targets. The maximum cross section was measured at beam energies well below a fusion barrier estimated in one dimension. These studies indicate that the transfer of nucleons is an important process for the initiation of fusion. The recent efforts at JINR, Dubna, to investigate the hot-fusion reaction for the production of SHE's using actinide targets are also presented. First results were obtained on the synthesis of neutron-rich isotopes of elements 112 and 114. However, the most surprising result was achieved in 1999 at LBNL, Berkeley. In a study of the reaction ${}^{86}{\mathrm{K}\mathrm{r}+}^{208}{\mathrm{Pb}\ensuremath{\rightarrow}}^{294}{118}^{*},$ three decay chains were measured and assigned to the superheavy nucleus ${}^{293}118.$ The decay data reveal that, for the heaviest elements, the dominant decay mode is alpha emission, not fission. The results are discussed in the framework of theoretical models. This article also presents plans for the further development of the experimental setup and the application of new techniques. At a higher sensitivity, the exploration of the region of spherical SHE's now seems to be feasible, more than 30 years after its prediction.

The discovery of the heaviest elements

Nuclear ground-state masses and deformations: FRDM(2012)

We present calculations of fission properties for heavy elements. The calculations are based on the macroscopic-microscopic finite-range liquid-drop model with a 2002 parameter set. For each nucleus we have calculated the potential energy in three different shape parametrizations: (1) for 5 009 325 different shapes in a five-dimensional deformation space given by the three-quadratic-surface parametrization, (2) for 10 850 different shapes in a three-dimensional deformation space spanned by epsilon(2), epsilon(4), and gamma in the Nilsson perturbed-spheroid parametrization, supplemented by a densely spaced grid in epsilon(2), epsilon(3), epsilon(4), and epsilon(6) for axially symmetric deformations in the neighborhood of the ground state, and (3) an axially symmetric multipole expansion of the shape of the nuclear surface using beta(2), beta(3), beta(4), and beta(6) for intermediate deformations. For a fissioning system, it is always possible to define uniquely one saddle or fission threshold on the optimum trajectory between the ground state and separated fission fragments. We present such calculated barrier heights for 1585 nuclei from Z=78 to Z=125. Traditionally, actinide barriers have been characterized in terms of a "double-humped" structure. Following this custom we present calculated energies of the first peak, second minimum, and second peak in the barrier for 135 actinide nuclei from Th to Es. However, for some of these nuclei which exhibit a more complex barrier structure, there is no unique way to extract a double-humped structure from the calculations. We give examples of such more complex structures, in particular the structure of the outer barrier region near Th-232 and the occurrence of multiple fission modes. Because our complete results are too extensive to present in a paper of this type, our aim here is limited: (1) to fully present our model and the methods for determining the structure of the potential-energy surface, (2) to present fission thresholds for a large number of heavy elements, (3) to compare our results with the two-humped barrier structure deduced from experiment for actinide nuclei, and (4) to compare to additional fission-related data and other fission models. . (Less)

Heavy-element fission barriers

A review of the discovery and investigation of the ?island of stability? of super-heavy nuclei at the separator DGFRS (FLNR, JINR) in the fusion reactions of 48Ca projectiles with target nuclei 238U-249Cf is presented. The synthesis of the heaviest nuclei, their decay properties, and methods of identification are discussed. The role of shell effects in the stability of super-heavy nuclei is demonstrated by comparison of the experimental data and results of theoretical calculations. The radioactive properties of the new nuclei, the isotopes of elements 112?118 as well as of their decay products, give evidence of the significant increase of the stability of the heavy nuclei with rise of their neutron number and approaching magic number N = 184.

https://iopscience.iop.org/article/10.1088/0034-4885/78/3/036301/pdf

Super-heavy element research

Description of structure and properties of superheavy nuclei

https://escholarship.org/content/qt59h9f0kv/qt59h9f0kv.pdf?t=p0jvaz

On the spontaneous fission of nuclei with Z near 114 and N near 184

The spontaneous-fission process for doubly even nuclei with Z> or =92 is studied in a semiempirical WKB framework. One-dimensional fission barrier potentials are established from theoretical deformation-energy surfaces based on the droplet model and the modified-oscillator model. The effects of axial asymmetry as well as reflection asymmetry have been taken into account. Macroscopic (irrotational flow) inertial-mass functions and, alternatively, microscopic (cranking model) inertial mass parameters have been employed for the calculation of the fission half-lives. With one over-all normalization parameter it is possible to fit the experimental half-lives to within a factor of 20 on the average. The resulting effective inertial-mass functions are used to estimate the stability of the transactinide elements. Only minor differences with previous estimates for the r process and superheavy nuclei are encountered. (AIP)

/pdf/spontaneous-fission-half-lives-for-even-nuclei-with-z-92-4gueicawz1.pdf

Spontaneous-fission half-lives for even nuclei with Z>92

http://lup.lub.lu.se/search/ws/files/5391129/3459066.pdf

Hexadecapole equilibrium distortions of nuclei

https://portal.research.lu.se/portal/files/5297081/3459049.pdf

A Sobiczewski

Papers

On the spontaneous fission of nuclei with Z near 114 and N near 184

Spontaneous-fission half-lives for even nuclei with Z>92

Hexadecapole equilibrium distortions of nuclei

Nonperturbative treatment of the P3 degree of freedom of the nuclear potential at equilibrium and fission distortions