Fragment-Shell Influences in Nuclear Fission

Potential-energy surfaces and shell-correction-energy surfaces for nuclei in the $A\ensuremath{\simeq}200$ region and for actinide ($A\ensuremath{\gtrsim}230$) have been calculated in the improved two-center model. These surfaces are shown in a two-dimensional representation as a function of the elongation and the constriction of the nuclear shape. Both the ground-state shell corrections and the fission barriers in the $A\ensuremath{\cong}200$ region agree well with experiment. It is found that the saddlepoint position in this region is shifted significantly towards smaller deformations compared with the liquid-drop-model prediction, this shift arising from a very pronounced valley in the shell-correction surface at the position of the liquid-drop-model saddle point. The implications of this finding for a nuclear mass formula and for the application of the liquid-drop model to fission of these nuclei are discussed. In both mass regions ($A\ensuremath{\cong}200 \mathrm{and} A\ensuremath{\gtrsim}230$) the shell corrections alone show pronounced structure which changes slowly with mass number. At small deformations, up to the region of the second maximum in the potential, this structure is determined by the compound-nucleus shell structure. At larger deformations this structure is shown to arise from the shell structure of the nascent fragments, thus establishing the importance of fragment shells early in the fission process for the entire mass range $A\ensuremath{\gtrsim}200$. As a consequence of these studies the regions of validity for the liquid-drop model in describing nuclear fission are explained. Finally, it is shown that the recently observed symmetry in the mass distribution of $^{257}\mathrm{Fm}$ is due to the approach to the nucleus $^{264}\mathrm{Fm}$, which can split symmetrically into the two energetically strongly favored $^{132}\mathrm{Sn}$ nuclei.