Measurement of mass and total kinetic energy distributions for the ${}^{12}\mathrm{C}+{}^{175}\mathrm{Lu}$ system

Fission fragment mass and total kinetic energy (TKE) distributions were measured for ${}^{12}\mathrm{C}+{}^{175}\mathrm{Lu}$ system at excitation energies down to 16.7 MeV above the saddle point. The overall mass and TKE distributions could be fitted with single Gaussian functions. The observed width of the mass and TKE distributions agree well with the systematics based on liquid drop (LD) behavior. The average TKE also shows parabolic dependence on fragment mass, as expected from LD behavior. Small contributions due to microscopic corrections from $Z\approx 38$ and 45 shells can be extracted, if the widths of the LD component are fixed from systematics. Contrary to the theoretical predictions of substantial contributions from microscopic corrections, dominance of liquid drop behavior was observed.

Figure 1

Correlation plots for the (a) times of flight ($T_1$ and $T_2$), (b) folding angle (${\theta }_1+{\theta }_2$) and total azimuthal angle (${\varphi }_1+{\varphi }_2$), (c) parallel and perpendicular components of velocity ($V_{\parallel }$ and $V_{\perp }$), and (d) mass-angle distribution (MAD) for the ${}^{12}\mathrm{C}+{}^{175}\mathrm{Lu}$ system at $E_{\mathrm{Lab}}=65$ MeV. The $V_{\parallel }$ is normalized by the velocity of the center of mass ($V_{CN}$). Plots (b)–(d) are generated for fission events.

Figure 2

Left panels (a)–(d): The fragment mass-TKE correlations along with TKE profile (black open circle). The black solid line is the LD-predicted mass dependence of TKE [38].

Right panels (e)–(h): The experimental TKE distributions are compared with the single Gaussian fits (solid line). To use the same color gradient, the distributions are normalized to 200% and the normalization factors are mentioned in the brackets.

Figure 3

The experimental mass distributions (a)–(d) for the ${}^{12}\mathrm{C}+{}^{175}\mathrm{Lu}$ reaction from the present measurement (filled circles) and (e)–(f) for the $p+{}^{186}\mathrm{Os}$ reaction [10] (open circles) are plotted with increasing excitation energy at the saddle point ($E_{\mathrm{sad}}$) from bottom to top panels. The solid lines show the multi-Gaussian (MG) fits to the data along with different fissioning modes corresponding to macroscopic liquid drop component (violet shaded region) and microscopic component due to $Z\approx 38$ (yellow shaded region) and $Z\approx 45$ (red shaded region) shells. The dot-dashed line is the single Gaussian (SG) fit to the data. The corresponding ${\chi }^2$ and the number of degrees of freedom (ndf) are also mentioned.

Figure 4

The extracted mass widths from single Gaussian fits (${\sigma }_M$) are plotted as a function of temperature at the saddle point ($T$) for present measurement ${}^{12}\mathrm{C}+{}^{175}\mathrm{Lu}$ (filled circles) and $p$ $+$ ${}^{186}\mathrm{Os}$ [10] (open circles). The solid line is the description using Eq. (2).

Figure 5

Comparison of the available theoretical predictions for fission fragment mass distribution of ${}^{187}\mathrm{Ir}$. The predictions of the macroscopic-microscopic model (M-M) [27], GEF (Version 2021/1.1) [46], and improved scission point model (ISP) [47] are shown in dot-dot-dashed, solid, and dashed lines, respectively. The numbers in the brackets represent the excitation energy above the saddle point.