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Title: Saddle point shapes of nuclei

Abstract

Very general reflection asymmetrical saddle point nuclear shapes are obtained by solving an integro-differential equation without being necessary to specify a certain parametrization. This equation is derived as an Euler-Lagrange relationship associated to the variational problem of minimizing the potential energy with constraints (constant volume and given deformation parameter). The mass asymmetry in binary cold fission of Th and U isotopes is explained as the result of adding a phenomenological shell correction to the liquid drop model deformation energy. Applications to ternary fission are outlined.

Authors:
 [1];  [2];  [1];  [3]
  1. Horia Hulubei National Institute of Physics and Nuclear Engineering (IFIN-HH), Bucharest-Magurele (Romania)
  2. (Germany)
  3. Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe University, Frankfurt (Germany)
Publication Date:
OSTI Identifier:
21057109
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 899; Journal Issue: 1; Conference: 6. international conference of the Balkan Physical Union, Istanbul (Turkey), 22-26 Aug 2006; Other Information: DOI: 10.1063/1.2733031; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; ASYMMETRY; COLD FISSION; CORRECTIONS; EUROPIUM; INTEGRO-DIFFERENTIAL EQUATIONS; LIQUID DROP MODEL; NUCLEAR DEFORMATION; NUCLEAR STRUCTURE; NUCLEI; POTENTIAL ENERGY; RADIOISOTOPES; TERNARY FISSION; THORIUM ISOTOPES; URANIUM ISOTOPES; VARIATIONAL METHODS

Citation Formats

Poenaru, D. N., Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe University, Frankfurt, Plonski, I. H., and Greiner, W. Saddle point shapes of nuclei. United States: N. p., 2007. Web. doi:10.1063/1.2733031.
Poenaru, D. N., Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe University, Frankfurt, Plonski, I. H., & Greiner, W. Saddle point shapes of nuclei. United States. doi:10.1063/1.2733031.
Poenaru, D. N., Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe University, Frankfurt, Plonski, I. H., and Greiner, W. Mon . "Saddle point shapes of nuclei". United States. doi:10.1063/1.2733031.
@article{osti_21057109,
title = {Saddle point shapes of nuclei},
author = {Poenaru, D. N. and Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe University, Frankfurt and Plonski, I. H. and Greiner, W.},
abstractNote = {Very general reflection asymmetrical saddle point nuclear shapes are obtained by solving an integro-differential equation without being necessary to specify a certain parametrization. This equation is derived as an Euler-Lagrange relationship associated to the variational problem of minimizing the potential energy with constraints (constant volume and given deformation parameter). The mass asymmetry in binary cold fission of Th and U isotopes is explained as the result of adding a phenomenological shell correction to the liquid drop model deformation energy. Applications to ternary fission are outlined.},
doi = {10.1063/1.2733031},
journal = {AIP Conference Proceedings},
number = 1,
volume = 899,
place = {United States},
year = {Mon Apr 23 00:00:00 EDT 2007},
month = {Mon Apr 23 00:00:00 EDT 2007}
}
  • The potential energy of deformation of an idealized, uniformly charged liquid drop is considered. Evidence is discussed for a discontinuous or almost discontinuous behavior of the family of equilibrium configurations of a charged drop (so-called saddle point shapes'') in the neighborhood of a certain critical value of the charge. This evidence, based on several sets of semiquantitative estimates of the deformation energy of a drop, suggests a rapid change in the appearance of the saddle point shapes-- from that of two fragrnents connected by a neck, to that of a cylinder with rounded ends--in a narrow range of charge values.more » When applied to nuclei this evidence suggests a qualitative change in the properties of fission in that part of the periodic table where the value of Z/sup 2//A is around 35. The physical reason for this behavior of a charged drop is discussed with reference to questions of the stability of spherical and elongated configurations, as well as configurations in which the drop is disintegrated into two or more fragments. The discussion is made with the aid of the concept of points of bifurcation'' in families of equilibrium configurations. One such bifurcation occurs where the conventional symmetric family of saddle point shapes loses stability against asymmetric distortions. This is estimated to take place at a critical charge corresponding to medium weight nuclei with Z/sup 2//A values of about 20 or 25. The significance of this critical region for the definition of fission as a process distinct from spallation'' is discussed. Some of the estimates are made with the aid of the configuration of tangent spheroids. Formulas for evaluating the electrostatic interaction of such spheroids are discussed, and tables of the surface and electrostatic energies (separated into the selfenergies of the fragments and their interaction energy) are given for equal and unequal spheroids with various eccentricities. (auth)« less