Going beyond statistical models for fission in the Businaro-Gallone region

Dynamical calculations based on a four-dimensional stochastic Langevin approach are used to study fission in the Businaro-Gallone region. The use of such a model to map the Businaro-Gallone transition is proposed for the first time, exploiting recent theoretical developments and computing resources. The significance of the approach is supported by a systematic comparison with measurements for a set of systems. Experimental observations on fission-fragment charge distributions, which remained unexplained within a unified framework so far, are described by the dynamical model in a consistent manner. A detailed analysis reveals the interplay of dynamical effects, going beyond statistical-models interpretation and suggesting to revisit the commonly admitted idea about the prevalence of static effects in the Businaro-Gallone region.

Figure 1

Fission barrier height in the ($L,q_3$) plane for a sample of nuclei. The barrier is derived from the FRLDM potential energy landscape and is defined as the difference between the potential at the ground-state equilibrium and the conditional ($q_3$-constrained) saddle point. The figure is borrowed from Ref. [13].

Figure 2

(Top row) Fission barrier height as a function of $q_3$ for a sample of nuclei for (a) $L=0\hslash$ and (b) $L=40\hslash$. (Bottom row) Fission barrier height as a function of $q_3$ for a sample of $L$ values for (c) ${}^{102}\mathrm{Rh}$ and (d) ${}^{110}\mathrm{Sn}$.

Figure 3

Stiffness $d^{2}V\left(q_3\right)/d{q}_3^2{\mid }_{q_3=0}$ as a function of $L$ for a sample of nuclei, i.e., $\chi$ values (a), and as a function of $\chi$ for a sample of $L$ values (b). Arrows localize the crossing of the BG point.

Figure 4

Measured (symbols) and calculated (curves) fragment $Z$ distribution for fission of ${}^{110}\mathrm{Sn}$, induced as specified in Table 1. The calculated distribution is shown for $L_{\max }=70\hslash$ (solid line) and $L_{\max }=50\hslash$ (dashed line). Theory is normalized to experiment to focus on the shape of the distributions. Staggering in the calculated curves is attributable to statistics. The inset shows gemini++ [24] predictions for $L=50\hslash$ (dashed line) and $L=70\hslash$ (solid line).

Figure 5

Measured (symbols) and calculated (curves) fragment $Z$ distribution for fission of ${}^{102}\mathrm{Rh}$, induced as specified in Table 1 at two beam energies. The calculations are done for $L_{\max }=40\hslash$. Theory is normalized to experiment to focus on the shape of the distributions. Staggering in the calculated curves is attributable to statistics. The yields of the $E_{\mathrm{lab}}=8.4 A\mathrm{MeV}$ run are arbitrarily scaled for legibility. Dashed curves show the corresponding gemini++ [24] predictions.

Figure 6

Calculated correlation between fragment $Z$ and CN angular momentum for fission of ${}^{102}\mathrm{Rh}$, induced at $E_{\mathrm{lab}}=8.4 A\mathrm{MeV}$ (top) and $E_{\mathrm{lab}}=11.4 A\mathrm{MeV}$ (bottom).

Figure 7

Calculated fragment $Z$ (top) and time (bottom) distributions for fission events of ${}^{102}\mathrm{Rh}$, induced at $E_{\mathrm{lab}}=8.4 A\mathrm{MeV}$ (a),(c) and $E_{\mathrm{lab}}=11.4 A\mathrm{MeV}$ (b),(d). The integral distributions (solid lines) are decomposed into the contributions from events with (dotted lines) and without (dashed lines) pre-scission evaporation.

Figure 8

Potential energy landscape in the ($q_1,q_3$) plane for ${}^{102}\mathrm{Rh}$ at $L=60\hslash$. Energies are given relative to the spherical minimum for $L=0\hslash$.

Figure 9

Measured (symbols) and calculated (curves) fragment $Z$ distribution for the reactions listed in Table 1. Yields are arbitrarily scaled for legibility.