Elsevier

Nuclear Physics A

Volume 183, Issue 2, 28 March 1972, Pages 371-389
Nuclear Physics A

A single-particle model calculation of total energy surfaces in heavy nuclei

https://doi.org/10.1016/0375-9474(72)90665-3Get rights and content

Abstract

The total energy surfaces for heavy nuclei have been calculated using a double-center oscillator, single-particle potential. The energy surfaces are calculated using the summation method of Nilsson in which the virial term, proportional to 〈TV〉, has been calculated explicitly. It is found that this term significantly influences the shape of the energy surface and the calculated height of the fission barrier. The fission barrier for 236U is reduced by 77 MeV with the inclusion of this term. Equilibrium deformations, fission barrier heights and shape isomer excitation energies for nuclei ranging from 230Th to 256Fm are calculated and compared with experimental data as well as other theoretical calculations. It is found that the calculated fission barrier heights are in reasonable agreement with the experimental data if the oscillator parameter, ħω0, is chosen so that the single-particle level density of the model equals that experimentally observed in the actinide region. Isomeric states, ranging in energy from 2 to 3 MeV, are predicted in nuclei from thorium to curium but are absent in the heavier elements. In thorium the calculations predict that the inner barrier is quite small and spontaneous fission would not likely be observed. In the heavier isotopes of uranium, the lighter isotopes of curium and virtually all of the isotopes of plutonium and americium, the calculated barriers are of nearly equal size. The outer barrier predicted in the heavier curium isotopes is small and observation of spontaneous fission might be quite difficult. It is shown that the energy surfaces are rather insensitive to the Nilsson spin-orbit parameter k. The quadrupole deformation of the ground state of the range of nuclei investigated is about β2 = 0.25 while that of the isomeric state is about β2 = 0.70.

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    ††

    Work supported in part by the US Atomic Energy Commission.

    To be submitted by David E. Maharry in partial fulfilment of the requirements for the degree of Doctor of Philosophy at the University of Kansas.

    Present address: Department of Physics, Franklin College, Franklin, Indiana.

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