Calculated fission properties of the heaviest elements

Abstract

Experimental results on the fission properties of nuclei close to 264Fm show sudden and large changes with a change of only one or two neutrons or protons. The nucleus 258Fm, for instance, undergoes symmetric fission with a half-life of about 0.4ms and a kinetic-energy distribution peaked at about 235 MeV whereas 256Fm undergoes asymmetric fission with a half-life of about 3 h and a kinetic-energy distribution peaked at about 200 MeV. Qualitatively, these sudden changes have been postulated to be due to the emergence of fragment shells in symmetric-fission products close to 132Sn. Here we present a quantitative calculation that shows where high-kinetic-energy symmetric fission occurs and why it is associated with a sudden and large decrease in fission half-lives. We base our study on calculations of potential-energy surfaces in the macroscopicmicroscopic model and a semi-empirical model for the nuclear inertia. For the macroscopic part we use a Yukawa-plus-exponential (finite-range) model and for the microscopic part a folded-Yukawa (diffuse-surface) single-particle potential. We use the three-quadratic-surface parameterization to generate the shapes for which the potential-energy surfaces are calculated. The use of this parameterization and the use of the finite-range macroscopic model allows for the study of two touching spheres and similar shapes. Since these shapes are thought to correspond to the scission shapes for the high-kinetic-energy events it is of crucial importance that a continuous sequence of shapes leading from the nuclear ground state to these configurations can be studied within the framework of the model. We present the results of the calculations in terms of potential-energy surfaces and fission half-lives for heavy even nuclei. The surfaces are displayed in the form of contour diagrams as functions of two moments of the shape. They clearly show the appearance of a second fission valley, which leads to scission configurations close to two touching spheres, for fissioning systems in the vicinity of 264Fm. Fission through this new valley leads to much shorter fission half-lives than fission through the old valley. The reason is that the inertia associated with motion in the new valley is much smaller than in the old valley. The large decrease in the inertia is the reason for the unexpectedly short half-life for 258Fm. Earlier, it had appeared that the short half-life was due to the disappearance of the second peak in the barrier below the nuclear ground-state energy. However, we find that the second peak is still about 3 MeV above the ground state in the new valley for 258Fm and that the short half-life is instead due mainly to the lower inertia in the new valley.