Geometrical Relationships of Macroscopic Nuclear Physics

The aim of this book is to provide a single reference source for the wealth of geometrical formulae and relationships that have proven useful in the descrip­ tion of atomic nuclei and nuclear processes. While many of the sections may be useful to students and instructors it is not a text book but rather a reference book for experimentalists and theoreticians working in this field. In addition the authors have avoided critical assessment of the material presented except, of course, by variations in emphasis. The whole field of macroscopic (or Liquid Drop Model) nuclear physics has its origins in such early works as [Weizsacker 35] and [Bohr 39]. It continued to grow because of its success in explaining collective nuclear excitations [Bohr 52] and fission (see the series of papers culminating in [Cohen 62]). These develop­ ments correspond to the first maximum in the histogram below, showing the distribution by year of the articles cited in our Bibliography. After the Liquid Drop Model had been worked out in some detail the development of the Struti­ nsky approach [Strutinsky 68] (which associates single particle contributions to the binding energy with the shape of the nucleus) gave new life to the field. The growth of interest in heavy-ion reaction studies has also contributed.

1 Definition and Notation.- 1.1 Introduction.- 1.2 Nuclear Radius Constant.- 1.3 Geometrical Quantities.- 1.4 Surface Energies.- 1.5 Coulomb Energies.- 1.6 Curvature and Redistribution Energies, etc.- 1.7 Deformation Energies.- 1.8 Normal Modes and Dynamics.- 2 Characterization of Leptodermous Distributions.- 2.1 Introduction.- 2.2 The OriginaJ Surface Moments, Gm.- 2.3 The Surficial Moments, ?n.- 2.4 The Surface Shape Coefficients, ?n.- 2.5 Distributions Related by Folding.- 3 Folded Distributions.- 3.1 Definition.- 3.2 Normalization and Radial Moments.- 3.3 Multipole Moments.- 3.4 Moments of Inertia.- 3.5 Coulomb Energy.- 3.6 Specific Examples.- 4 Spllerically Symmetric Distributions.- 4.1 Sharp Sphere of Radius R.- 4.2 Diffuse Surface Distributions.- 5 Spheroidal Deformations.- 5.1 Spheroids.- 5.2 Nilsson Potential.- 6 Small Deformations.- 6.1 Spheroidal Expansion.- 6.2 Harmonic Expansions.- 6.3 Distorted Spheroids.- 6.4 Relations Between Small Shape Parameters.- 6.5 Triaxial Shapes.- 7 Large Deformations.- 7.1 Arbitrary Shapes.- 7.2 Generalized Spheroids.- 7.3 Cassinian Ovaloids.- 7.4 Matched Surfaces of Revolution.- 7.5 y-Family.- 8 Saddle Point Properties.- 8.1 Liquid Drop Barriers.- 8.2 Businaro-Gallone Point.- 8.3 Normal Modes.- 9 Separated Sllapes.- 9.1 Two Spheres.- 9.2 Two Spheroids.- 9.3 Two Distorted Spheres.- 9.4 Three Fragments.- 9.5 n-Spheres.- 10 Exotic Shapes.- 10.1 Toroids.- 10.2 Bubbles.- 11 Medium- and High-Energy Nuclear Collisions.- 11.1 Factorization.- 11.2 Different Approaches.- 11.3 Density Distributions.- Bibliograplly.- Citation Index.