Calculation Of Fission Barriers Research Articles

Calculation of fission barriers with the droplet model and folded Yukawa single-particle potential

Abstract Single-particle levels in a folded Yukawa potential are studied as functions of various types of distortions. Some level diagrams are plotted versus an elongation coordinate in the fission direction. The levels are also plotted as functions of the asymmetric coordinate ϵ 35 . The levels are labeled by their asymptotic quantum numbers.These diagrams thus show the calculated single-particle level structure at the second minimum and second peak in the fission barrier for nuclei in the actinide region. Fission barriers are calculated by the use of the macroscopic-microscopic method; the macroscopic part of the energy is obtained from the droplet model of Myers and Swiatecki. The relevant equilibrium points in the fission barrier are tabulated for the actinide elements and also for some lighter elements in the region 76 ≦ Z ≦ 84. The calculated energies of the equilibrium points reproduce experimental values to within an accuracy of 1 or 2 MeV. A detailed comparison is made between the three-quadratic-surface parametrization and the ϵ-coordinates in Nilsson's perturbed-spheroid parametrization.

Production of Superheavy Nuclei by Multiple Capture of Neutrons

A new calculation of fission barriers and neutron separation energies for heavy neutron-rich nuclei indicates that it is unlikely that superheavy nuclei can be produced either in the astrophysical r'' process or in man-made nuclear explosions. (auth)

The Importance of Delayed Fission in the Production of very Heavy and Superheavy Elements

Recent advances in the calculation of fission barriers and in the experimental determination of beta strength functions make it possible to derive reliable estimates of the effect of beta-delayed fission in the decay of very heavy nuclides far from the line of beta-stability. The model presented here is used to calculate the amount of delayed fission during the decay back of nuclides produced in the astrophysical decay r-process. An interesting feature of these calculations is that they reproduce the reversal of the odd-even effect found for the yield of beta-stable nuclides obtained in the thermonuclear explosions. The preliminary results from the r-process calculations indicate that the effect of delayed fission has to be considered when the yield of very heavy beta stable nuclides from this process is estimated.

Calculation of Fission Barriers for Heavy and Superheavy Nuclei

Calculation of Fission Barriers for Heavy and Superheavy Nuclei

New Calculation of Fission Barriers for Heavy and Superheavy Nuclei

On the basis of the macroscopic-microscopic method we have performed a new calculation of the nuclear potential energy of deformation for heavy and superheavy nuclei. Our primary emphasis has been to develop techniques that permit more accurate extrapolations both to the large deformations encountered in fission and heavy-ion reactions and to new regions of nuclei. With this purpose in mind, we specify the nuclear shape with five degrees of freedom, in terms of smoothly joined portions of three quadratic surfaces of revolution (e.g., two spheroids connected by a hyperboloidal neck). The single-particle potential is obtained by folding a Yukawa function with a uniform sharp-surface generating potential of appropriate shape. The parameters describing the potential are obtained from statistical (Thomas-Fermi) calculations that reproduce correctly the average trends throughout the Periodic Table of a variety of nuclear properties. To solve the Schr\"odinger equation for the single-particle energies and wave functions, we have used mainly an expansion of the wave function in a set of deformed harmonic-oscillator basis functions, but have also investigated a finite-difference method. Shell and pairing corrections are calculated from the single-particle energies by means of the methods developed by Strutinsky and added to the surface and Coulomb energies of the liquid-drop model to obtain the total potential energy of deformation.This approach is found to reproduce reasonably well the over-all trends of experimental fission-barrier heights of nuclei ranging from rare earths to actinides. The calculated fission barriers of actinide nuclei contain two peaks separated by a secondary minimum. The over-all variation in the relative heights of the two peaks agrees with experimental results, but the calculated first peak is somewhat low for thorium isotopes and somewhat high for curium isotopes. For the actinides the first saddle point is found to be symmetric in shape and the second saddle point asymmetric. The highest saddle point is asymmetric for $^{226}\mathrm{Ra}$ and $^{210}\mathrm{Po}$ and symmetric for $^{188}\mathrm{Os}$. The fission barriers of superheavy nuclei near $^{298}114$ are even higher than previously supposed. With respect to spontaneous fission, the island of superheavy nuclei is a mountain ridge extending from 114 protons to about 124 protons. The descent from the mountain down to the sea of instability is rather gentle for decreasing neutron numbers below 184, but is more rapid on the other three sides.