Influence of fusion dynamics on fission observables: A multidimensional analysis

An attempt to unfold the respective influence of the fusion and fission stages on typical fission observables, and namely the neutron prescission multiplicity, is proposed. A four-dimensional dynamical stochastic Langevin model is used to calculate the decay by fission of excited compound nuclei produced in a wide set of heavy-ion collisions. The comparison of the results from such a calculation and experimental data is discussed, guided by predictions of the dynamical deterministic HICOL code for the compound-nucleus formation time. While the dependence of the latter on the entrance-channel properties can straigthforwardly explain some observations, a complex interplay between the various parameters of the reaction is found to occur in other cases. A multidimensional analysis of the respective role of these parameters, including entrance-channel asymmetry, bombarding energy, compound-nucleus fissility, angular momentum, and excitation energy, is proposed. It is shown that, depending on the size of the system, apparent inconsistencies may be deduced when projecting onto specific ordering parameters. The work suggests the possibility of delicate compensation effects in governing the measured fission observables, thereby highlighting the necessity of a multidimensional discussion.

Figure 1

Correlation between experimental neutron prescission multiplicities $M_n^{\text{pre}}$ with (a) $\alpha /{\alpha }_{\text{BG}}$ and $E^{*}$, and with (b) $\chi$ and $E^{*}$. For experimental points, we refer to Table 1. Error bars are omitted for clarity. Lines connect different energy points for a given reaction. The same color (shade of gray) is employed for reaction couples leading to the same CN. Systems below (above) the BG transition are shown with circles (squares).

Figure 2

(a) Calculated dependence of the formation time $t_{\text{fo}}$ on entrance-channel asymmetry $\alpha /{\alpha }_{\text{BG}}$ and energy with respect to the Coulomb barrier $E_{\text{cm}}/V_b$, as obtained from HICOL. (b) Calculated dependence of the neutron prescission multiplicity $M_n^{\text{pre}}$ on CN excitation energy $E^{*}$ and mean angular momentum $\langle L\rangle$, as obtained from the stochastic Langevin code. The reactions presented in the plots are listed in Table 1. Lines connect different energy points for a given reaction. The same color (shade of gray) is employed for reaction couples leading to the same CN. Systems below (above) the BG transition are shown with circles (squares).

Figure 3

(a) Difference between the formation times $t_{\text{fo}}$ (integrated over $L$) below ($<\text{BG}$) and above ($>\text{BG}$) the BG asymmetry ${\alpha }_{\text{BG}}$ as function of $E^{*}$ for the reaction couples leading to a given CN and considered in Fig. 2; different symbols are used for different couples. (b) Similar to panel (a) for the difference between the mean angular momenta $\langle L\rangle$.

Figure 4

Calculated dependence of the neutron prescission multiplicity $M_n^{\text{pre}}$ on $\chi$ and $E^{*}$ as obtained from the stochastic Langevin code for the same set of reactions than in Fig. 1. Lines connect different energy points for a given reaction. The same color (shade of gray) is employed for reaction couples leading to the same CN. Systems below (above) the BG transition are shown with circles (squares).

Figure 5

Neutron prescission multiplicity $M_n^{\text{pre}}$ as function of excitation energy for various reactions. Each panel corresponds to a specific CN: (a) ${}^{216}\mathrm{Ra}$, (b) ${}^{248}\mathrm{Cf}$, (c) ${}^{213}\mathrm{Fr}$, and (d) ${}^{198}\mathrm{Pb}$, populated by means of two entrance channels. The experimental $M_n^{\text{pre}}$ (open symbols) are compared with dynamical Langevin CN-decay calculations (full symbols). For each couple of reactions, the system with largest (smallest) $\alpha /{\alpha }_{\text{BG}}$ is shown with a red dashed (blue full) line.

Figure 6

Correlation between CN angular momentum $L$ and neutron prescission multiplicity $M_n^{\text{pre}}$ as calculated from the CN decay stochastic Langevin model. The first and second rows each display two reactions leading to a specific CN (${}^{248}\mathrm{Cf}$ and ${}^{206}\mathrm{Po}$, respectively) at similar $E^{*}$. The last row considers one reaction system at two different $E^{*}$. In each case, the predicted mean $M_n^{\text{pre}}$ is indicated also.

Figure 7

Neutron prescission multiplicity $M_n^{\text{pre}}$ as calculated from the CN decay stochastic Langevin model for the ${}^{20}\mathrm{Ne}+{}^{159}\mathrm{Tb}$ reaction as function of CN excitation energy. The calculation, including the full theoretical $L$ distribution is shown with (red) dots, while calculations from selected $L$ values—45 and 70 $\hslash$—are displayed with open (blue) squares and (green) triangles, respectively. Experimental data wherever available are shown as well [31].