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

TLDR

The shell‑correction method highlights large‑scale nonuniformities in single‑particle energies near the Fermi surface and, while covering a broad range of nuclear properties, is not a narrow review but rather a focused discussion with comparisons to other approaches. The paper reviews single‑particle structure in spherical and deformed nuclei from the perspective of the shell‑correction method. It explains how nonuniformities influence nuclear properties such as shape stiffness, density distribution, mass, and inertia, and describes the deformation energy behavior for large distortions relevant to fission. The study identifies qualitative singularities in the liquid‑drop deformation energy at large shape distortions and discusses their implications for fission.

Abstract

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.