Saddle-point shapes and fission barriers of rotating nuclei

This article reviews the work relating to the development of a rotating liquid drop model together with a chronology of its confrontation with the experimental interpretation of data. It is brought out that the zero temperature rotating finite range model is quite successful in the interpretation of data obtained from heavy ion-induced reactions. Operated by Martin Marietta Energy Systems, Inc., under contract DE-AC05-840R21400 with the U.S. Department of Energy.     

Electromagnetic decay of hot rotating nuclei

A theory of strength functions for electromagnetic multipole emission is developed. It combines the finite-temperature cranked Hartree-Fock-Bogoliubov formalism with the random-phase approximation, and is free of spurious contributions. Numerical results for ¹⁶⁴Er based on the Kumar-Baranger hamiltonian are presented. They display sizeable fluctuations of the matrix elements for the statistical transitions (contrary to the statistical model), and underline the important role of M1 transitions for good rotors.     

Lowering of calculated fission barriers of superheavy nuclei

The effect of angular momentum explicit conservation is evaluated in the framework of models which utilize single-particle wavefunctions to calculate fission barriers. Using simple assumptions, and extrapolating from known data, the calculated syperheavy barriers are lowered by 2 – 2.5 MeV. Fission barriers for the actinides are unaffected.     

Statistical fluctuations in hot rotating nuclei

Thermal fluctuations in angular momentum due to excitation is investigated. Shape changes or structural rearrangement are observed as a consequence of fluctuation in second moment of spin. The uncertainty in angular momentum is considerably enhanced due to thermal fluctuation and is strongly dependent on spin and structural changes.     

Evaporation and fission of hot metallic clusters and hot nuclei

Evaporation and fission of metallic clusters are described by models developed in nuclear physics which are appropriately modified. Results of calculations for evaporation rates, appearance sizes and fission times (with and without viscosity) are presented. Presented at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997.     

Temperature-dependent Hartree-Fock-Bogoliubov calculations in hot rotating nuclei

Cranked temperature-dependent Hartree-Fock-Bogoliubov (CTHFB) equations in the rotating frame are solved numerically for a realistic case in the rare-earth region, the nucleus ¹⁶⁴Er. The behavior of pairing correlations, shape degrees of freedom and other physical quantities are discussed as a function of angular momentum and temperature.     

Langevin fission dynamics of hot rotating nuclei: Systematic application to Z 2/A=34–42 heavy nuclei

A stochastic approach that treats fission dynamics on the basis of three-dimensional Langevin equations is used to calculate the mass-energy distributions of fragments originating from the fission of compound nuclei whose fissility parameter lies in the range Z ²/A=34–42. In these calculations, use was made of the liquid-drop model allowing for finite-range nuclear forces and the diffuseness of the nuclear surface in calculating the potential energy and a modified one-body mechanism of viscosity in describing dissipation. The emission of light prescission particles is taken into account on the basis of the statistical model. The calculations performed within three-dimensional Langevin dynamics reproduce well all parameters of the experimental mass-energy distributions of fission fragments and all parameters of the prefission-neutron multiplicity for various parameters of the compound nucleus. The inclusion of the third collective coordinate in the Langevin equations leads to a considerable increase (by up to 40–50%) in the variances of mass-energy distributions in relation to what was previously obtained from two-dimensional Langevin calculations. For the parameters of the mass-energy distributions of fission fragments and the parameters of the prefission-neutron multiplicity to be reproduced simultaneously, the reduction coefficient K _s must be diminished at least by a factor of 2(0.2≤K _s ≤0.5) in relation to that in the case of total one-body viscosity (K _s =1).     

Two-phase model of rotating nuclei

Using the generator-coordinate method a model is formulated in which the nucleus is treated as a triaxial rotator with coupled normal and superconductive phases. Averaging the model hamiltonian over coherent states the effects of different orientations of the mass quadrupoloid with respect to the angular momentum are studied in the case of ^{156, 166}Er nuclei.     

Static and statistical properties of hot rotating nuclei in a macroscopic temperature-dependent finite-range model

A macroscopic temperature-dependent model that takes into account nuclear forces of finite range is used to calculate the static and statistical properties of hot rotating compound nuclei. The level-density parameter is approximated by an expression of the leptodermous type. The resulting expansion coefficients are in good agreement with their counterparts proposed previously by A. V. Ignatyuk and his colleagues. The effect of taking simultaneously into account the temperature of a nucleus and its angular momentum on the quantities under study, such as the heights and positions of fission barriers and the effective moments of inertia of nuclei at the barrier, is considered, and the importance of doing this is demonstrated. The fissility parameter (Z²/A)_crit and the position of the Businaro-Gallone point are studied versus temperature. It is found that, with increasing temperature, both parameters are shifted to the region of lighter nuclei. It is shown that the inclusion of temperature leads to qualitatively the same effects as the inclusion of the angular momentum of a nucleus, but, quantitatively, thermal excitation leads to smaller effects than rotational excitation.     

Giant-dipole resonance and the deformation of hot,rotating nuclei

The development of nuclear shapes under the extreme conditions of high angular momentum and/or temperature is examined. Scaling properties are used to demonstrate universal properties of both thermal expectation values of nuclear shapes as well as the minima of the free energy, which can be used to understand the Jacobi transition. A universal correlation between the width of the giant-dipole resonance and quadrupole deformation is found, providing a novel probe to measure the nuclear deformation in hot nuclei.     

Novel features of the fragment mass variance in fission of hot nuclei

On the basis of data obtained by the incomplete fusion reactions ⁷Li(43A MeV)+²³²Th and ¹⁴N(34A MeV)+¹⁹⁷Au, the energy dependence of the variance (σ _M ² ) of the fragment mass in fission of highly heated nuclei has been investigated for total excitation energies E _tot ^* ranging from 50 up to 350 MeV. The dependence σ _M ² E _tot ^* shows some unexpected features when E _tot ^* exceeds a value of about 70 MeV. After this value, the steady increase of σ _M ² expected from its temperature dependence changes to some kind of plateau between 100 and 200 MeV. Further on, at E _tot ^* in excess of about 250 MeV, the variance is found to increase again sharply. In order to analyze this behavior quantitatively, a dynamical stochastic model has been developed. The model employs the one-body dissipation mechanism and describes the decay of highly excited and rotating nuclei by fission and light-particle evaporation. It satisfactorily explains the measured prior-to-scission neutron multiplicities and the experimental mass variances up to E _tot ^* ?250 MeV, but the stochastic treatment does not reveal any increase in σ _M ² at higher excitation energies in contradiction with the data.