Temperature and fissility dependence of fragment mass variance in heavy ion induced fission

Fission fragment mass and kinetic energy distributions have been measured in ${}^{12}\mathrm{C}+{}^{\mathit{nat}}\mathrm{Pb}$, ${}^{209}\mathrm{Bi}$, ${}^{235}\mathrm{U}$, and ${}^{11}\mathrm{B}+{}^{209}\mathrm{Bi}$ reactions at above barrier energies. The variance of the fragment mass distribution $\left({\sigma }_A^2\right)$ has been studied as a function of the temperature and fissility of the compound nucleus by analyzing the present results along with the available data from literature. It is observed that ${\sigma }_A^2$ increases exponentially with temperature as well as fissility of the compound nucleus. However, when data are analyzed with respect to the fragment temperature $\left(T_F\right)$, instead of the temperature of compound nucleus, the dependence of ${\sigma }_A^2$ on fissility is greatly reduced for a given value of $T_F$. The mass variance shows a universal dependence on $T_F$ irrespective of the fissility of the compound nucleus. This result implies that the mass variance is decided during the later stage of fission process and is related to the scission configuration of the fissioning nucleus.

Figure 1

Two-dimensional plot of the coincident fission events detected in the LAPSIC. The $X$ and $Y$ axes correspond to the pulse heights as observed in the $E$ and $\Delta E$ sections of the LAPSIC, respectively, for the ${}^{12}\mathrm{C}+{}^{235}\mathrm{U}$ system at $E_{\text{lab}}=76.0\mathrm{MeV}$.

Figure 2

(a) Average total kinetic energy $⟨TKE⟩$ as a function of $E_{\text{c.m.}}∕V_b$ for ${}^{12}\mathrm{C}+{}^{\mathit{nat}}\mathrm{Pb}$ (⋆), ${}^{209}\mathrm{Bi}$ (◻), ${}^{235}\mathrm{U}$ (◇), and the ${}^{11}\mathrm{B}+{}^{209}\mathrm{Bi}$ (엯) systems. Dashed lines show $⟨TKE⟩$ values expected from Viola’s systematics [21]. (b) Mass variance ${\sigma }_A^2$ as a function of $E_{\text{c.m.}}∕V_b$ for different systems as in (a).

Figure 3

Mass variance ${\sigma }_A^2$ as a function of compound nucleus temperature $\left(T_{\mathit{CN}}\right)$ for ${}^{11}\mathrm{B}+{}^{209}\mathrm{Bi}$ (엯), ${}^{12}\mathrm{C}+{}^{\mathit{nat}}\mathrm{Pb}$ (⋆), ${}^{12}\mathrm{C}+{}^{209}\mathrm{Bi}$ (◻), and ${}^{12}\mathrm{C}+{}^{235}\mathrm{U}$ (◇) systems in the present study along with the literature data for ${}^{12}\mathrm{C}+{}^{209}\mathrm{Bi}$ (◆), ${}^{16}\mathrm{O}+{}^{209}\mathrm{Bi}$ (⊕), ${}^{12}\mathrm{C}+{}^{232}\mathrm{Th}$ (▵), ${}^{16}\mathrm{O}+{}^{232}\mathrm{Th}$ (▴) [4], ${}^{238}\mathrm{U}+{}^{16}\mathrm{O}$ (●), ${}^{238}\mathrm{U}+{}^{26}\mathrm{Mg}$ (∎) [7], ${}^{32}\mathrm{S}+{}^{208}\mathrm{Pb}$ (+) [8], ${}^{16}\mathrm{O}+{}^{204}\mathrm{Pb}$ (▿), ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}$ (▾) [22], ${}^{30}\mathrm{Si}+{}^{186}\mathrm{W}$ (◀), ${}^{19}\mathrm{F}+{}^{197}\mathrm{Au}$ (◁), ${}^{12}\mathrm{C}+{}^{204}\mathrm{Pb}$ (▶) [5], ${}^4\mathrm{He}+{}^{209}\mathrm{Bi}$ (×), and ${}^4\mathrm{He}+{}^{197}\mathrm{Au}$ (▷) [23] systems.

Figure 4

Mass variance ${\sigma }_A^2$ as a function of fissility of the compound nucleus for the systems as in Fig. 3.

Figure 5

Mass variance ${\sigma }_A^2$ as a function of fragment temperature $T_F$ for the systems as in Fig. 3.