Potential Energy Surfaces for the Fission of the Actinide Nuclei

Abstract

Collective potential energy surfaces have been systematically calculated for the symmet­ ric fission of the five isotopes of the elements Th, Pu, Cm, Cf, Fm and No and the eight isotopes of the element U. The calculation is performed on the basis of Strutinsky's pre­ scription in which the liquid drop model of v. Groote and Hilf and the modified two-center harmonic oscillator shell model are used for macroscopic and microscopic parts, respectively. Effects of mass asymmetry at the second saddle point are investigated. The properties of the ground state, the second minim urn and the first and second saddle points along the static fission path are discussed in comparison with the results of Moller and Nix. The structure of the potential energy surface is found to come mainly from the shell structure which is strongly related to the distance between the mass centers of the nascent fragments. Special attentions are given to the fragment mass distributions and the constancy of the heavy fragment masses is partially explained on the basis of the properties of the second barrier. § I. Introduction Since the late 1960's, a renewed interest has been aroused 111 the structure of the potential energy surface for the fission process. It was motivated mainly by the discoveries of the fission isomer!) and the related resonant structure of the fission cross section. 2J The calculation based on the liquid drop model was proved not to be able to reproduce these featuers and in 1967 a new method for the calculation of the potential energy-- the macroscopic-microscopic model'J __ was proposed. Since then, calculations based on this model have been widely made and the fission isomer has been theoretically explained as a shape isomer. It is caused by the shell structure of a largely deformed nucleus and the fact that the shell structure appears at such a large deformation has made a drastic change m our knowledge of the nuclear structure. 4J The structure of the potential energy surfaces of the heavy nuclei is at present fairly well known. 5 J~sJ For the actinide nuclei, a typical feature is that there exists a second minimum and as a result the fission barrier is split into two, the inner barrier and the outer barrier. The calculated heights of these barriers and the second minimum were compared with the experimental data and overall agreement