HEAVY-ELEMENT FISSION BARRIERS

P. MÖLLER and A. J. SIERK
Theoretical Division, Los Alamos National Laboratory, New Mexico 87545, USA

T. ICHIKAWA
RIKEN Nishina Center, Riken, Wako, Saitama, 351-0198, Japan

A. IWAMOTO
Japan Atomic Energy Agency (JAEA),
Tokai-mura, Naka-gun, Ibaraki, 319-1195, Japan

R. BENGTSSON, H. UHRENHOLT, and S. ÅBERG
Department of Mathematical Physics, Lund Institute of Technology,
SE-22100 Lund, Sweden

This paper was submitted to
PHYSICAL REVIEW C
on July 10, 2008 and resubmitted on March 3, 2009
It has been assigned Los Alamos National Laboratory Preprint No LA-UR-08-4190.



Abstract:

We present calculations of fission properties for heavy elements. The calculations are based on the macroscopic-microscopic finite-range liquid-drop model with a 2002 parameter set. For each nucleus we have calculated the potential energy in 3 different shape parameterizations: (1) for 5009325 different shapes in a five-dimensional deformation space given by the three-quadratic-surface parameterization, (2) for 10850 different shapes in a three-dimensional deformation space spanned by ε2, ε4, and γ in the Nilsson perturbed-spheroid parameterization, supplemented by a densely spaced grid in ε2, ε3, ε4, and ε6 for axially symmetric deformations in the neighborhood of the ground state, and (3) an axially symmetric multipole expansion of the shape of the nuclear surface using β2, β3, β4, and β6 for intermediate deformations. For a fissioning system it is always possible to define uniquely {\it one} saddle or fission threshold on the optimum trajectory between the ground state and separated fission fragments. We present such calculated barrier heights for 1585 nuclei from Z = 78 to Z = 125. Traditionally actinide barriers have been characterized in terms of a ``double-humped'' structure. Following this custom we present calculated energies of the first peak, second minimum, and second peak in the barrier for 135 actinide nuclei from Th to Es. However, for some of these nuclei which exhibit a more complex barrier structure there is no unique way to extract a double-humped structure from the calculations. We give examples of such more complex structures, in particular the structure of the outer barrier region near 232Th and the occurrence of multiple fission modes. Because our complete results are too extensive to present in a paper of this type our aim here is limited: (1) to fully present our model and the methods for determining the structure of the potential-energy surface, (2) to present fission thresholds for a large number of heavy elements, (3) to compare our results with the two-humped barrier structure deduced from experiment for actinide nuclei, and (4) to compare to additional fission-related data and to other fission models.
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The complete manuscript in color as a .ps.gz file is available for download.

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Table 2 (TABLE 2) , in computer-readable format, is available for download.
The format is (3I5,F10.2)
The variables are: Z, N, A, Bf


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Peter Moller
Last modified: Wed Mar 4 10:18:48 MST 2009