Study of Superdeformation with Skyrme - Hartree - Fock Method

In the last decade superdeformed (SD) bands have been studied extensively both experimentally and theoretically. Since the rst observation in 152 Dy in 1986 1) , SD bands have been found in four mass regions, i.e., A 80 2) , 130 3;4) , 150 and 190 5). Although these SD bands have been observed only at high spins so far, they may be present at zero spin, too, like ssion iso-mers in actinide nuclei: The familiar generic argument on the strong shell eect at axis ratio 2:1 6) does not assume rotations. If non-ssile SD isomers exist at zero spin, they may be utilized to develop new experimental methods to study exotic states, in a similar manner as short-lived high-spin isomers are planned to be utilized as projectiles of fusion reactions in order to populate very high-spin near-yrast states 7). They will also be useful to test theoretical models whether the models can describe correctly the large deformations of rare-earth nuclei without further complications due to rotation. In this paper, we employ the Skyrme-Hartree-Fock method to study the SD states at zero spin. First, we compare various Skyrme force parameter sets to see whether they can reproduce the extrapolated excita-tion energy of the SD band head of 194 Hg. Second, we study ssion isomers in 236;238 U. Third, we systematically search large-deformation solutions with the SkM 3 force. The feature of our calculations is that the single-particle wavefunctions are expressed in a three-dimensional Cartesian-mesh representation 8). This representation enables one to obtain solutions of various shapes (including SD) without preparing a basis spe-cic to each shape. Solving the mean-eld equations in this representation requires, however, a large amount of computation which can be accomplished only with present supercomputers. determined the excitation energies and the spins of a SD band in 194 Hg down to I = 8 +. By extrapolating the spectrum to I = 0, they could predict reliably the excitation energy of the band head to be 6.017 MeV In table 1, we show the excitation energy E 3 of the SD band-head state calculated with various Skyrme force parameter sets. From macroscopic point of view, the softness to deformation is determined by the small-ness of the surface energy coecient a s specic to each force. The SkM 3 is a force adjusted so as to reproduce the ssion barrier height of 240 Pu and thus expected to …