Geometrical Relationships of Macroscopic Nuclear Physics

ISBN-13: 9783642830198 / Angielski / Miękka / 2011 / 141 str.

Rainer W. Hasse; William D. Myers

Opis

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."

Spis treści

1 Definition and Notation.- 1.1 Introduction.- 1.1.1 Liquid Drop Model.- 1.1.2 Droplet Model.- 1.2 Nuclear Radius Constant.- 1.3 Geometrical Quantities.- 1.3.1 Coordinate Systems.- 1.3.2 Radial Moments.- 1.3.3 Multipole Moments.- 1.3.4 Generalized Moments.- 1.3.5 Moments of Inertia.- 1.3.6 Other Moments.- 1.4 Surface Energies.- 1.4.1 Geometrical Surface Energy.- 1.4.2 Short Range Force Surface Energy.- 1.4.3 Proximity Energy.- 1.5 Coulomb Energies.- 1.5.1 Direct.- 1.5.2 Exchange.- 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.- 4.1.1 Uniform Density.- 4.1.2 Central Depression.- 4.2 Diffuse Surface Distributions.- 4.2.1 Leptodermous Distributions.- 4.2.2 Hill-Ford Distributions.- 4.2.3 Holodermous Distributions.- 4.2.4 Folded Distributions.- 5 Spheroidal Deformations.- 5.1 Spheroids.- 5.2 Nilsson Potential.- 6 Small Deformations.- 6.1 Spheroidal Expansion.- 6.2 Harmonic Expansions.- 6.2.1 ?n-Parameterization.- 6.2.2 ?n-Parameterization.- 6.2.3 ²n0-Parameterization.- 6.2.4 ?n-Parameterization.- 6.2.5 ?q-Parameterization.- 6.3 Distorted Spheroids.- 6.3.1 ?n-Parameterization.- 6.3.2 Spheroidal Coordinates.- 6.4 Relations Between Small Shape Parameters.- 6.5 Triaxial Shapes.- 6.5.1 Triaxial Ellipsoids.- 6.5.2 Bohr Parameterization.- 6.5.3 Higher Order Triaxial Shapes.- 7 Large Deformations.- 7.1 Arbitrary Shapes.- 7.1.1 Cylindrical Coordinates.- 7.1.2 Spherical Coordinates.- 7.2 Generalized Spheroids.- 7.2.1 Lawrence Shapes.- 7.2.2 Higher Algebraic Shapes.- 7.2.3 Funny Hills Parameterization.- 7.3 Cassinian Ovaloids.- 7.3.1 Symmetric Shapes.- 7.3.2, Distorted Shapes.- 7.3.3 Lemniscatoids.- 7.4 Matched Surfaces of Revolution.- 7.4.1 Matched Spheres.- 7.4.2 Dumbbells.- 7.4.3 Matched Quadratic Surfaces.- 7.4.4 Other Matched Surfaces.- 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.- 11.2.1 Fireball Model.- 11.2.2 Firestreak Model.- 11.2.3 Rows-on-Rows.- 11.2.4 Knock-on Collisions.- 11.3 Density Distributions.- 11.3.1 Density Projected on a Plane.- Bibliograplly.- Citation Index.