Spontaneous fission with $\beta$-parameterized quasimolecular shape

In the framework of a generalized liquid drop model (GLDM), a quasimolecular mechanism is introduced to describe the deformation of a nucleus in the procedure of nuclear fission or fusion. In order to more appropriately evaluate the shell correction on the fission or fusion path, the quasimolecular shape is described in terms of deformation parameters $\beta$ (i.e., so-called $\beta$ parameterized) by a transformation. For symmetric fission it is done analytically, whereas for asymmetric fission it is performed in a pure numerical way. Thereafter, for each quasimolecular shape, the shell correction can be calculated by the Strutinsky method where the single-particle energies are derived from a shell model in an axially deformed Woods–Saxon potential with the $\beta$-parameterized quasimolecular shape. We then use this recipe to predict the half-lives of several spontaneous fission channels for some heavy nuclei, and the results are in agreement with the experimental data.

Figure 1

The quasimolecular shapes in the fission procedure ${}^{256}\mathrm{Fm}\to {}^{128}\mathrm{Sn}+{}^{128}\mathrm{Sn}$. The shapes drawn by dashed red lines are obtained by using $\beta$ parameters, and those drawn by solid blue lines are plotted by using the original parameters $s$ where $s_1=s_2=s$.

Figure 2

Potential barrier of ${}^{256}\mathrm{Fm}\to {}^{128}\mathrm{Sn}+{}^{128}\mathrm{Sn}$.

Figure 3

The same as Fig. 1, but for ${}^{232}\mathrm{U}\to {}^{134}\mathrm{Te}+{}^{98}\mathrm{Zr}$.

Figure 4

The same as Fig. 1, but for ${}^{238}\mathrm{Pu}\to {}^{130}\mathrm{Sn}+{}^{108}\mathrm{Ru}$.

Figure 5

The same as Fig. 1, but for ${}^{243}\text{Am}\to {}^{133}\text{Sb}+{}^{110}\text{Ru}$.