Longitudinal ternary fission

The longitudinal ternary fission is studied using the generalized liquid drop model. The proximity energy and the charge and mass asymmetries are taken into account. Spherical parent and daughter nuclei are considered. The shape sequence selected to simulate the quasimolecular three-body shapes is built from different but connected elliptic half lemniscatoids. The potential barriers are much lower when the central fragment is the smallest one and particularly when it is an $\alpha$ particle. The $2\alpha$ emission can be described as a particular prolate fission with emission of two particles at the tips of the deformed nucleus. The associated potential barriers are high and thin.

Figure 1

Simulation of a fusion and binary compact fission.

Figure 2

Shape evolution from the spherical parent nucleus to three aligned spherical nuclei, the left and right nuclei being identical, the central fragment being the smallest one.

Figure 3

Shape evolution from the spherical parent nucleus to three aligned spherical nuclei, the left and right nuclei being identical, the central fragment being the biggest one.

Figure 4

Simulation of the double-$\alpha$ decay of ${}^{224}\mathrm{Ra}$ like a very asymmetric ternary fission.

Figure 5

$h_1$ and $h_2$ are the maximal distances on the $X$ axis. $c_1$ and $c_2$ are the two elongations on the deformation axis. $d$ is the distance between the center of mass and the plan of the neck.

Figure 6

Potential barriers of the longitudinal ternary fission of ${}^{210}\mathrm{Ra}$ leading to a central fragment of ${}^{182}\mathrm{Os}, {}^{154}\mathrm{Gd}, {}^{86}\mathrm{Zr}$, and ${}^{28}\mathrm{Mg}$.

Figure 7

Potential barriers of the longitudinal ternary fission of ${}^{60}\mathrm{Zn}$ leading to a central fragment of ${}^{36}\mathrm{Ar}, {}^{20}\mathrm{Ne}, {}^{12}\mathrm{C}$, and ${}^4\mathrm{He}$.

Figure 8

Potential barriers governing the $2\alpha$ radioactivity of ${}^{224}\mathrm{Ra}, {}^{220}\mathrm{Rn}, {}^{216}\mathrm{Rn}$, and ${}^{200}\mathrm{Rn}$. It is supposed that the $2\alpha$'s are emitted at ${180}^{\circ }$ of each other at the tips of the deformed parent nucleus.