This paper reviews various results related to the single-particle structure in spherical and deformed nuclei, discussed from the viewpoint of the so-called shell-correction method. This method stresses the importance of large-scale nonuniformities in the energy distribution of the individual particles especially near the Fermi energy. The way in which these nonuniformities affect in an essential way many nuclear properties, such as the shape stiffness, the spatial density distribution, the total mass of the nucleus, the mass and inertia of the nuclear shape variations, etc. is also discussed. Against this background, the behavior of the nuclear deformation energy is described, in particular for larger distortions relevant to the fission process. In this connection, some qualitative singularities of the phenomenological liquid-drop deformation energy at large shape distortions are pointed out, and their possible implications for fission are discussed. As the problems considered cover a wide range of nuclear properties, this paper is not a review in the narrow sense of the word. Comparison with other approaches as well as historic references are given mainly to clarify specific points, because a complete review would be a monumental undertaking.

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Funny Hills: The Shell-Correction Approach to Nuclear Shell Effects and Its Applications to the Fission Process

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

https://t2.lanl.gov/nis/molleretal/publications/ADNDT-66-1997-131-text.pdf

S. Wycech

Papers

On the nuclear structure and stability of heavy and superheavy elements

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

Microscopic calculations of the inertial mass parameter for fissioning nuclei

On possibilities of narrow nuclear states of K

Hexadecapole equilibrium distortions of nuclei