Temperature of low-energy ternary fission from the dependence of particle yields on the mass of the fissioning system

In thermal neutron-induced and spontaneous fission the addition of two neutrons to a neutron-even system produces only minor changes to the shape, kinetic energy, and temperature of the scission configuration. If these changes are assumed negligible and if ternary fission is associated with a statistical process then the ratio of ternary fission yields for systems differing by two atomic mass units can be used to infer a nuclear temperature. The yields of hydrogen, helium, lithium, and beryllium isotopes ejected perpendicular to the direction of the main fragments from ${}^{233,235}\mathrm{U}(n_{\mathrm{th}},f)$, ${}^{239,241}\mathrm{Pu}(n_{\mathrm{th}},f)$, and ${}^{250,252}\mathrm{Cf}$ spontaneous fission give a nuclear temperature $T=1.24\pm 0.10\text{MeV}$. The yield of polar $\alpha$ particles from ${}^{233,235}\mathrm{U}(n_{\mathrm{th}},f)$ give $T=1.13\pm 0.24\text{MeV}$. These results are in agreement with other inferred low-energy ternary fission temperatures and support the idea that both equatorial and polar ternary fission involve a statistical process where the ejected particles are in equilibrium with a heat bath with a temperature slightly hotter than 1 MeV.

Figure 1

The ${}^{233,235}\mathrm{U}(n_{\mathrm{th}},f)$ (open squares); ${}^{239,241}\mathrm{Pu}(n_{\mathrm{th}},f)$ (solid diamonds); and ${}^{250,252}\mathrm{Cf}$ (open triangles) spontaneous fission equatorial ternary fission yield ratios, $Y(A_f+2)/Y(A_f)$, versus $A_{\mathrm{LCP}}+2$$(Z_{\mathrm{LCP}}-$1). These yield ratios were determined by a combination of various experimental results [11, 12, 13, 14, 15, 16, 17, 18]. The solid curves show a model calculation (see text).

Figure 2

Measured $\alpha$-particle yield ratios versus $A_f$ for spontaneous fission (triangles) and thermal-neutron-induced fission reactions (squares). These yield ratios were determined by a combination of various experimental results [2, 15, 16, 17, 18, 20]. Some of the points have been shifted by not more than 0.4 atomic mass units to avoid clutter. The horizontal line shows the uncertainty weighted average at a yield ratio of 0.825.