Exploration of Optimum Shape in Symmetric Fission

Abstract：

In this paper the large deformation of symmetric fission is described by a biquadratic surface revolution instead of several quadratic equations. Based on the standard liquid model, variation calculation of the deformation energy is performed and thereby, a better shape with a group of coefficients {bi} than the Cassinian ovaloid is obtained. The shape with {bi} has lower deformation energy than that of the Cassinian ovaloid at the same separation distance between C.M. of half bcxiies. The applicability of this so-called shape optimum II with {bi} is examined in the mass range A=208-308. The fission barrier for shape optimum II is lower and thinner than that of the ovaloid, because after the saddle point the potential descends more rapidly. There are significant differences of deformation energy between the shape optimum II and the ovaloid when the neck in the middle appears. The neck cross section of shape optimum II is larger than that of the ovaloid before the scission point is reached, but they are equal or thinner near this point.