Fission fragment angular distribution in heavy-ion-induced fission with anomalous behavior

Fission fragment angular distribution in heavy-ion-induced fission reactions is of particular importance. Transition state theory is provided to determine the angular distribution of fission fragments which includes standard saddle-point statistical and standard scission-point statistical models. The standard saddle-point statistical model was not able to reproduce the experimental fission fragment angular anisotropies for several heavy-ion-induced fission systems. In contrast to the standard saddle-point model, the standard scission-point statistical model was fairly successful in the prediction of angular anisotropy in heavy-ion-induced fission reaction systems with an anomalous behavior in angular anisotropy of fission fragments, but this model is not widely used as the standard saddle-point statistical model. In this research, a generalized model is introduced for the prediction of fission fragments angular anisotropy in the heavy-ion-induced fission reaction systems having an anomalous behavior. For this purpose, we study the ${}^{14}\mathrm{N},{}^{16}\mathrm{O},{}^{19}\mathrm{F}+{}^{232}\mathrm{Th};{}^{16}\mathrm{O},{}^{19}\mathrm{F}+{}^{238}\mathrm{U};{}^{24}\mathrm{Mg},{}^{28}\mathrm{Si},{}^{32}\mathrm{S}+{}^{208}\mathrm{Pb};{}^{32}\mathrm{S}+{}^{197}\mathrm{Au}$; and ${}^{16}\mathrm{O}+{}^{248}\mathrm{Cm}$ reaction systems. Finally, it is shown that the presented model is much more successful than previous models.

Figure 1

The effective moments of inertia at the saddle point for the ${}^{32}\mathrm{S}+{}^{208}\mathrm{Pb}$ system. The continuous, dashed, and dot-dashed lines are the best fit on the experimental data, the calculated effective moments of inertia based on the USPS model, and the prediction of the RFRM, respectively. The experimental values of the effective moments of inertia denoted by circles and squares are taken from Refs. [17, 27], respectively.

Figure 2

Experimental fission fragment angular distributions for the induced fission of the ${}^{208}\mathrm{Pb}$ by different projectiles are compared with the predictions of the SSPS (dot-dashed curve), the SPS (dashed curve), and the USPS (continuous curve). (a) For the induced fission of the ${}^{208}\mathrm{Pb}$ target by ${}^{24}\mathrm{Mg}$, the experimental values of angular anisotropy are taken from Ref. [17]. (b) For the induced fission of the ${}^{208}\mathrm{Pb}$ target by ${}^{28}\mathrm{Si}$, the experimental values of angular anisotropy are taken from Ref. [17]. (c) For the induced fission of the ${}^{208}\mathrm{Pb}$ by ${}^{32}\mathrm{S}$, the experimental values of angular anisotropy denoted by circle and square points are taken from Refs. [17, 27], respectively.

Figure 3

Experimental fission fragment angular distributions for the induced fission of the ${}^{232}\mathrm{Th}$ by different projectiles are compared with the predictions of the SSPS (dot-dashed curve), the SPS (dashed curve), and the USPS (continuous curve). (a) For the induced fission of the ${}^{232}\mathrm{Th}$ target by ${}^{14}\mathrm{N}$, the experimental values of angular anisotropy denoted by triangles are taken from Ref. [28]. (b) For the induced fission of the ${}^{232}\mathrm{Th}$ target by ${}^{16}\mathrm{O}$, the experimental values of angular anisotropy denoted by circles and squares are taken from Refs. [17, 29], respectively. (c) For the induced fission of the ${}^{232}\mathrm{Th}$ target by ${}^{19}\mathrm{F}$, the experimental values of angular anisotropy denoted by circles are taken from Ref. [32].

Figure 4

Experimental fission fragment angular distributions for the induced fission of the ${}^{238}\mathrm{U}$ by different projectiles are compared with the predictions of the SSPS (dot-dashed curve), the SPS (dashed curve), and the USPS (continuous curve). (a) For the induced fission of the ${}^{238}\mathrm{U}$ target by ${}^{16}\mathrm{O}$, the experimental values of angular anisotropy denoted by squares and triangles are taken from Refs. [17, 30], respectively. (b) For the induced fission of the ${}^{238}\mathrm{U}$ target by ${}^{19}\mathrm{F}$, the experimental values of angular anisotropy denoted by circles are taken from Ref. [31].

Figure 5

Experimental fission fragment angular distributions for the induced fission of the ${}^{32}\mathrm{S}+{}^{197}\mathrm{Au}$ and ${}^{16}\mathrm{O}+{}^{248}\mathrm{Cm}$ reaction systems are compared with the predictions of the SSPS (dot-dashed curve), the SPS (dashed curve), and the USPS (continuous curve). (a) For the induced fission of ${}^{32}\mathrm{S}+{}^{197}\mathrm{Au}$, the experimental values of angular anisotropy denoted by circles are taken from Ref. [17]. (b) For the induced fission of ${}^{16}\mathrm{O}+{}^{248}\mathrm{Cm}$, the experimental values of angular anisotropy denoted by circles are taken from Ref. [17].