Isoscaling behavior in fission dynamics

The fission processes of ${}^{112}\mathrm{Sn}$+${}^{112}\mathrm{Sn}$ and ${}^{116}\mathrm{Sn}$+${}^{116}\mathrm{Sn}$ are simulated with the combination of the Langevin equation and the statistical decay model. The masses of two fission fragments are given by assuming the process of symmetric fission or asymmetric fission by Monte Carlo sampling with the Gaussian probability distribution. From the analysis of the isotopic/isotonic ratios of the fission fragments from both reactions, the isoscaling behavior has been observed and investigated in detail. Isoscaling parameters α and β are extracted as a function of the charge number and neutron number, respectively, in different widths of the sampling Gaussian probability distribution. It seems that α is sensitive to the width of fission probability distribution of the mass asymmetrical parameter, but β is not. Both α and β drop with increasing beam energy and reduced friction parameter.

Figure 1

Ratios of the pre-scission neutron number (a) and of the pre-scission proton number (b) between ${}^{116}\mathrm{Sn}$+${}^{116}\mathrm{Sn}$ and ${}^{112}\mathrm{Sn}$+${}^{112}\mathrm{Sn}$ as a function of beam energy ($E_{\mathrm{beam}}/A$).

Figure 2

(Color online) Fission-fragment mass distributions produced by the Langevin simulation for the reactions of ${}^{112}\mathrm{Sn}$+${}^{112}\mathrm{Sn}$ (open symbols) and ${}^{116}\mathrm{Sn}$+${}^{116}\mathrm{Sn}$ (filled symbols) at 8.4 MeV/nucleon with the different sampling width ${\sigma }_{{\alpha }_0}$ of Gaussian probability distribution.

Figure 3

(Color online) Isotopic (a) and isotonic (b) distributions of fission fragments in some given Z or N from the collisions of ${}^{116}\mathrm{Sn}$+${}^{116}\mathrm{Sn}$ (filled symbols) and of ${}^{112}\mathrm{Sn}$+${}^{112}\mathrm{Sn}$ (open symbols) at 8.4 MeV/nucleon. ${\sigma }_{{\alpha }_0}=$ 0.06. Notice that the $x$-axis scale is different.

Figure 4

(Color online) Square of full width of the isotopic (a) and isotonic (b) distribution as a function of Z and N, respectively, in different ${\sigma }_{{\alpha }_0}$. The width is the average value of the two systems (they are almost the same for both systems).

Figure 5

(Color online) Extracted mean temperature of fissioning nuclei of two reaction systems as a function of their charge number (a) or neutron number (b).

Figure 6

(Color online)Values of $(N_Z){}_2-(N_Z){}_1$ (a) and $|(N_N){}_2-(N_N){}_1|$ (b) as a function of Z and N of the fission fragments, respectively, between ${}^{116}\mathrm{Sn}$+${}^{116}\mathrm{Sn}$ and ${}^{112}\mathrm{Sn}$+${}^{112}\mathrm{Sn}$ with different ${\sigma }_{{\alpha }_0}$.

Figure 7

(Color online) (a) Calculated neutron numbers as a function of the charge numbers for the fissioning nuclei of two reaction systems. (b) Difference of the neutron number of the fissioning nuclei between two reaction systems as a function of the charge number for the fissioning nuclei. Lines represent two-order polynomial fits in (a) and a linear fit in (b).

Figure 8

(Color online) Isotopic yield ratio of fission fragments between ${}^{116}\mathrm{Sn}$+${}^{116}\mathrm{Sn}$ and ${}^{112}\mathrm{Sn}$+${}^{112}\mathrm{Sn}$ in the Langevin model with ${\sigma }_{{\alpha }_0}=0.06$ and $E_{\mathrm{beam}}$/A = 8.4 MeV. Different symbols from left to right represent the calculated results for the isotopes from Z = 37 to 59. The lines represent exponential fits to guide the eye.

Figure 9

(Color online) Same as Fig. 8, but for the isotonic yield ratio and N = 46–73.

Figure 10

(Color online) (a) Isoscaling parameter α as a function of Z in the different Gaussian widths ${\sigma }_{{\alpha }_0}$ of the mass asymmetry parameter ${\alpha }_0$ for fission fragments; (b) same as (a), but for $\frac{[(N_Z){}_2-(N_Z){}_1]}{{\sigma }_Z^2}$.

Figure 11

(Color online) (a) Isoscaling parameter $\left|\beta \right|$ as a function of Z in the different Gaussian widths ${\sigma }_{{\alpha }_0}$ of the mass asymmetry parameter ${\alpha }_0$ for fission fragments; (b) same as (a), but for $\left|\frac{(N_N){}_2-(N_N){}_1}{{\sigma }_N^2}\right|$.

Figure 12

(Color online) Isoscaling parameter α (a) and $\left|\beta \right|$ (b) as functions of beam energy for the fragments Z = 44–54 and N = 58–68, respectively. The width ${\sigma }_{{\alpha }_0}$ of the Gaussian probability is 0.06.

Figure 13

(Color online) Same as Fig. 12, but plotted against the reduced friction parameter ${\beta }_0$.