Competition between fusion-fission and quasifission processes in the ${}^{32}\mathrm{S}+{}^{184}\mathrm{W}$ reaction

The angular distributions of fission fragments for the ${}^{32}\mathrm{S}+{}^{184}\mathrm{W}$ reaction at center-of-mass energies of 118.8, 123.1, 127.3, 131.5, 135.8, 141.1, and 144.4 MeV are measured. The experimental fission excitation function is obtained. The anisotropy (${\mathcal{A}}_{\exp }$) is found by extrapolating each fission fragment angular distribution. The measured fission cross sections of the ${}^{32}\mathrm{S}+{}^{182,184}\mathrm{W}$ reaction are decomposed into fusion-fission, quasifission, and fast-fission contributions by the dinuclear system model (DNS). The angular momentum distributions of the dinuclear system and compound nucleus calculated by the DNS model are used to reproduce the experimental capture and fusion excitation functions for both reactions and quantities $K_0^2$, $\langle {\ell }^2\rangle$, and ${\mathcal{A}}_{\exp }$, which characterize angular distributions of the fission products at the considered range of beam energy. The total evaporation residue excitation function for the ${}^{32}\mathrm{S}+{}^{184}\mathrm{W}$ reaction calculated in the framework of the advanced statistical model is close to the available experimental data only up to about $E_{\mathrm{c}.\mathrm{m}.}\approx 160$ MeV. The underestimation of the experimental data at high excitation energies $E_{\mathrm{c}.\mathrm{m}.}>160$ MeV is explained by the fact that the statistical model cannot reproduce the cross section of evaporation residues formed by the nonequilibrium mechanism, that is, without formation of the compound nucleus in the statistical equilibrium state.

Figure 1

Scheme of the experimental setup for the measurements of fission fragment angular distribution of binary reaction products. See explanations in the text for details.

Figure 2

Fission fragment angular distributions for the ${}^{32}\mathrm{S}+{}^{184}\mathrm{W}$ reaction. Incident energies are shown in the figure. The experimental coincident data are shown with the fitting curve, which is used to determine the anisotropy ${\mathcal{A}}_{\exp }$ of the fragment angular distribution and mean square values of angular momentum from these events.

Figure 3

Illustration of capture path (dot-dashed line) into potential well (solid line) as the numerical solution of the equation of relative motion of colliding nuclei with the initial energy $E_{\mathrm{c}.\mathrm{m}.}=136.3$ MeV and $L=0$ for the ${}^{32}\mathrm{S}+{}^{184}\mathrm{W}$ reaction.

Figure 4

The potential energy surface for a dinuclear system leading to the formation of the ${}^{216}\mathrm{Th}{}^{*}$ CN as a function of the relative distance $R$ between centers of interacting nuclei and their charge numbers $Z$ (a); the nucleus-nucleus interaction potential $V(R)$ shifted on the $Q_{\mathit{gg}}$ value for the ${}^{32}\mathrm{S}+{}^{184}\mathrm{W}$ reaction (b); and the driving potential, $U_{\mathrm{dr}}(Z,R_m)$, which is a curve linking minimums corresponding to each charge asymmetry in the valley of the potential energy surface as a function of $Z$ (c).

Figure 5

Experimental excitation functions of capture obtained in this work (squares) and in Ref. [21] (open down triangles), of fusion obtained in Ref. [21] (solid down triangles), and of evaporation residues after emission of neutrons, protons, and $\alpha$ particles from the ${}^{216}\mathrm{Th}{}^{*}$ compound nucleus for the ${}^{32}\mathrm{S}+{}^{184}\mathrm{W}$ reaction [25] (open circles) are compared with theoretical results by the DNS model for the capture (dashed line), complete fusion (thin solid line), quasifission (dot-dashed line), fast fission (dot-dot-dashed line), and total evaporation residues (thick solid line). Theoretical values of fusion-fission and fusion cross sections are nearly equal because the total cross sections for the evaporation residues after emission of neutrons, protons, and $\alpha$ particles from the ${}^{216}\mathrm{Th}$${}^{*}$ compound nucleus are very small.

Figure 6

Comparison of the experimental excitation functions of fission (capture) obtained from Refs. [23] (stars), [22] (solid up triangles), and [24] (open squares) and of fusion obtained from Ref. [22] (open up triangles) for the ${}^{32}\mathrm{S}+{}^{182}\mathrm{W}$ reaction with theoretical results by the DNS model for the capture (dashed line), complete fusion (thin solid line), quasifission (dot-dashed line), and fast fission (dot-dot-dashed line). Theoretical values of fusion-fission and fusion cross sections are nearly equal because the calculated results of the total cross sections for the evaporation residues after emission of neutrons, protons, and $\alpha$ particles from the ${}^{214}\mathrm{Th}{}^{*}$ compound nucleus are small (thick solid line).

Figure 7

Theoretical values of the fusion probability $P_{\mathrm{CN}}$ for the ${}^{32}\mathrm{S}+{}^{182}\mathrm{W}$ (dashed line) and ${}^{32}\mathrm{S}+{}^{184}\mathrm{W}$ (solid line) reactions as a function of collision energy $E_{\mathrm{c}.\mathrm{m}.}$. The results of calculations with formula (2) in Ref. [39] are presented by the dot-dashed line.

Figure 8

Driving potential calculated for the two different values of the orientation angles of the target nucleus: ${\alpha }_T={15}^{°}$ (solid line) and ${\alpha }_T={45}^{°}$ (dot-dashed line) for the ${}^{32}\mathrm{S}+{}^{184}\mathrm{W}$ reaction.

Figure 9

The partial quasifission excitation function calculated at different values of the collision energy $E_{\mathrm{c}.\mathrm{m}.}$ for the ${}^{32}\mathrm{S}+{}^{184}\mathrm{W}$ reaction.

Figure 10

The presentation of the fusion probability $P_{\mathrm{CN}}$ for the ${}^{32}\mathrm{S}+{}^{184}\mathrm{W}$ reaction as a function of collision energy $E_{\mathrm{c}.\mathrm{m}.}$ and initial angular momentum $L$.

Figure 11

Comparison of the anisotropy measured (solid squares) in this work for the ${}^{32}\mathrm{S}+{}^{184}\mathrm{W}$ reaction with the theoretical results for the anisotropy of the quasifission (dashed line) and fusion-fission (solid line) fragments as a function of the center-of-mass energy (bottom axis) and excitation energy of CN (top axis). The averaged values of theoretical results are presented by the dot-dashed line.

Figure 12

Mean square value of the angular momentum (upper panel) versus the collision energy $E_{\mathrm{c}.\mathrm{m}.}$ for the ${}^{32}\mathrm{S}+{}^{184}\mathrm{W}$ reaction. The experimental data (solid squares) are shown in comparison with the results of the DNS model, which were obtained by averaging ${\ell }^2$ by partial cross sections of the quasifission (dashed line) and complete fusion (solid line) events. In the lower panel the experimental data of this work (solid squares) for $K_0^2$ are compared with our theoretical results.

Figure 13

Comparison of the experimental data from Ref. [22] for $K_0^2$ (solid squares) and anisotropy $\mathcal{A}$ with results of the DNS model (solid line).