Nuclear shapes with reflection asymmetry

One of the earliest observations concerning the features of (binary) nuclear fission was the preference for breakup into two fragments of unequal mass. Many theoretical attempts to find an explanation in the framework of the liquid drop model (LDM) failed. Only in the late sixties, by adding shell corrections within Strutinsky's macroscopic- microscopic method, it was shown that the outer barrier for asymmetric shapes is lower than for symmetric ones. The equilibrium nuclear shapes in fission theory are usually obtained by minimizing the deformation energy for a given surface equation. We developed a method allowing to find out a saddle - point shape of a multifragment fission (number of fragments n ≥ 2) as a solution of an integro-differential equation; no a priori surface equation has to be given. Applications for fission into more than two or three fragments have been illustrated. One should mention that despite early theoretical predictions, the true ternary fission (with three identical fragments) was not experimentally detected until now. In the approach based on a pure LDM saddle - point shapes are always reflection symmetric: the deformation energy increases with the mass- asymmetry parameter η = (A1- A2)/ (A1+ A2). By adding the shell corrections δE, Edef = ELDM + δE, we can obtain the minima at a finite value of the mass asymmetry for binary fission. The phenomenological shell correction δE is inspired from the paper by Myers and Swiatecki (1966). Results are presented for saddle point shapes with reflection asymmetry in thorium and uranium even- mass isotopes with A = 226 - 238 and A = 230 - 238, respectively. In the absence of shell corrections the LDM saddle point shapes and energy barrier heights studied by Cohen and Swiatecki are well reproduced by the present method. (authors)