All possible ternary fragmentations of ${}^{252}\mathrm{Cf}$ in collinear configuration

All possible ternary fragmentations in fission of ${}^{252}\mathrm{Cf}$ are studied in collinear configuration within a spherical approximation using the recently proposed “three cluster model.” The potential energy surface of collinear configuration exhibits a strong valley around ${}^{48}\mathrm{Ca}$ and its neighboring nuclei ${}^{50}\mathrm{Ca}$, ${}^{54}\mathrm{Ti}$, and ${}^{60}\mathrm{Cr}$. Such strong minima are not seen in the potential energy surface of an equatorial configuration. As a consequence of strong minima in the potential, the overall relative yield is higher for the ternary fragmentation with ${}^{48}\mathrm{Ca}$, ${}^{50}\mathrm{Ca}$, ${}^{54}\mathrm{Ti}$, ${}^{60}\mathrm{Cr}$, and ${}^{82}\mathrm{Ge}$ as the third fragment. The results of potential energy and relative yield calculations reveal that collinear configuration increases the probability of emission of heavy fragments like ${}^{48}\mathrm{Ca}$ (doubly magic nucleus) and its neighboring nuclei as the third fragment. The obtained results indicate that the collinear configuration is the preferred configuration for intermediate nuclei (${}^{48}\mathrm{Ca}$, ${}^{50}\mathrm{Ca}$, ${}^{54}\mathrm{Ti}$, and ${}^{60}\mathrm{Cr}$) as the third fragment in particle accompanied fission while the equatorial configuration may be a preferred configuration for light nuclei (${}^4\mathrm{He}$, ${}^{10}\mathrm{Be}$) as the third fragment.

Figure 1

Schematic touching configurations of three spherical nuclei (a) in the case of equatorial emission and (b) in the case of collinear emission.

Figure 2

The ternary fragmentation potential for collinear emission of fragments in ternary fission of ${}^{252}\mathrm{Cf}$ nucleus for different third fragments with mass number ${\mathrm{A}}_3$ $=$ 48 plotted as a function of fragment mass number ${\mathrm{A}}_2$.

Figure 3

The ternary fragmentation potential for collinear emission of fragments in ternary fission of ${}^{252}\mathrm{Cf}$ nucleus for different third fragments with mass number$A_3=84$ plotted as a function of fragment charge number $Z_3$.

Figure 4

A comparison between the mass and charge minimized ternary fragmentation potential of the most probable configuration in (a) equatorial and (b) collinear emission of fragments in the ternary fission of ${}^{252}\mathrm{Cf}$ for $A_3=1$ to 84 plotted as a function of third particle mass number ${\mathrm{A}}_3$.

Figure 5

The scattering potential for equatorial and collinear emission of fragmentation ${}^{132}\mathrm{Sn}+{}^{72}\mathrm{Ni}+{}^{48}\mathrm{Ca}$ in ternary fission of a ${}^{252}\mathrm{Cf}$ nucleus plotted as a function of surface separation.

Figure 6

The potential barrier height for all possible mass and charge minimized ternary fragmentations corresponding to equatorial and collinear emission of ${}^{252}\mathrm{Cf}$ nucleus plotted as a function of fragment mass number $A_3$.

Figure 7

The potential barrier position for all possible mass and charge minimized ternary fragmentation corresponding to equatorial and collinear emission of a ${}^{252}\mathrm{Cf}$ nucleus is plotted as a function of fragment mass number $A_3$.

Figure 8

The penetration probability calculated for equatorial and collinear emission of fragments in ternary fission of a ${}^{252}\mathrm{Cf}$ nucleus for fixed third fragment $A_3={}^{48}\mathrm{Ca}$.

Figure 9

The individual relative yields of different charge minimized ternary fragmentation with $A_3$ $=$ ${}^{34}\mathrm{Si}$, ${}^{40}\mathrm{S}$, ${}^{48}\mathrm{Ca}$, ${}^{50}\mathrm{Ca}$, ${}^{60}\mathrm{Cr}$, and ${}^{82}\mathrm{Ge}$ are plotted as a function of fragment mass number ($A_2$) in panels (a), (b), (c), (d), (e), and (f), respectively. The most probable configurations $A_1$ and $A_2$ are labeled.

Figure 10

The overall relative yields of the ternary fission fragmentation of ${}^{252}\mathrm{Cf}$, accompanied with all possible charge minimized third fragments $A_3=1$ to 84 plotted as a function of third fragment mass number $A_3$.

Figure 11

A comparison between the overall relative yield calculated for equatorial and collinear emission of fragments in ternary fission of ${}^{252}\mathrm{Cf}$ plotted as a function of third fragment mass number $A_3$.

Figure 12

The relative yield calculated for equatorial and collinear emission of fragments in $\alpha$ accompanied fission of ${}^{252}\mathrm{Cf}$ are compared with the experimental data.