Nucleation and cluster formation in low-density nucleonic matter: A mechanism for ternary fission

Ternary fission yields in the reaction ${}^{241}\mathrm{Pu}$$(n_{th},f)$ are calculated using a new model which assumes a nucleation-time-moderated chemical equilibrium in the low-density matter which constitutes the neck region of the scissioning system. The temperature, density, proton fraction, and fission time required to fit the experimental data are derived and discussed. A reasonably good fit to the experimental data is obtained. This model provides a natural explanation for the observed yields of heavier isotopes relative to those of the lighter isotopes, the observation of low proton yields relative to ${}^2\mathrm{H}$ and ${}^3\mathrm{H}$ yields, and the nonobservation of ${}^3\mathrm{He}$, all features which are shared by similar thermal neutron-induced and spontaneous fissioning systems.

Figure 1

Relative yields of ternary cluster isotopes emitted in the fission of ${}^{242}$Pu. All yields are normalized to an assigned value of 10 000 for ${}^4$He. Symbols represent the yields. Lines are added to guide the eye. The vertical line indicates $N/Z$ of the ${}^{242}$Pu, 1.574.

Figure 2

Yield per fission as a function of mass ($A$) and charge ($Z$) of products. Solid points represent ${}^{241}\text{Pu}(n_{th},f)$ experimental yields from Koester et al. [9]. Lines are theoretical predictions from NSE calculation [7]. NSE parameters are $T=1.4\text{MeV}$, $\rho =4\times {10}^{-4}{\text{fm}}^{-3}$, and $Y_p=0.34$. (a) NSE calculation only. $M^2$ fit metric = 4.28. (b) NSE calculation with nucleation. Nucleation parameters are time $=6400\text{fm}/c$ and $A_c=5.4$. Fit metric $=1.18$.

Figure 3

Yield per fission as a function of the fragment mass number ($A$). Solid points represent ${}^{241}\text{Pu}(n_{th},f)$ experimental yields from Koester et al. [9]. Open data points are the result of NSE calculations [7] with the same parameters featured in the bottom panel of Fig. 2. $M^2$ fit metric $=0.561$.