Fusion and quasifission studies for the ${}^{40}\mathrm{Ca}+{}^{186}\mathrm{W},{}^{192}\mathrm{Os}$ reactions

Background: All elements above atomic number 113 have been synthesized using hot fusion reactions with calcium beams on statically deformed actinide target nuclei. Quasifission and fusion-fission are the two major mechanisms responsible for the very low production cross sections of superheavy elements.

Purpose: To achieve a quantitative measurement of capture and quasifission characteristics as a function of beam energy in reactions forming heavy compound systems using calcium beams as projectiles.

Methods: Fission fragment mass-angle distributions were measured for the two reactions ${}^{40}\mathrm{Ca}+{}^{186}\mathrm{W}$ and ${}^{40}\mathrm{C}+{}^{192}\mathrm{Os}$, populating ${}^{226}\mathrm{Pu}$ and ${}^{232}\mathrm{Cm}$ compound nuclei, respectively, using the Heavy Ion Accelerator Facility and CUBE spectrometer at the Australian National University. Mass ratio distributions, angular distributions, and total fission cross sections were obtained from the experimental data. Simulations to match the features of the experimental mass-angle distributions were performed using a classical phenomenological approach.

Results: Both ${}^{40}\mathrm{Ca}+{}^{186}\mathrm{W}$ and ${}^{40}\mathrm{C}+{}^{192}\mathrm{Os}$ reactions show strong mass-angle correlations at all energies measured. A maximum fusion probability of $60-70\%$ is estimated for the two reactions in the energy range of the present study. Coupled-channels calculations assuming standard Woods-Saxon potential parameters overpredict the capture cross sections. Large nuclear potential diffuseness parameters $\sim 1.5$ fm are required to fit the total capture cross sections. The presence of a weak mass-asymmetric quasifission component attributed to the higher angular momentum events can be reproduced with a shorter average sticking time but longer mass-equilibration time constant.

Conclusions: The deduced above-barrier capture cross sections suggest that the dissipative processes are already occurring outside the capture barrier. The mass-angle correlations indicate that a compact shape is not achieved for deformation aligned collisions with lower capture barriers. The average sticking time of fast quasifission events is ${10}^{-20}$ s.

Figure 1

Experimental MAD scatter plots for the ${}^{40}\mathrm{Ca}+{}^{186}\mathrm{W}$ reaction at different beam energies. The $E/V_B$ values and CN excitation energies ${\mathrm{E}}^{*}$ are given at the top of each plot. The corresponding projections of MADs [shown in panels (a)–(d)] onto the $M_R$ axis are shown in the lower panels (e)–(h). These projections represent the experimental $M_R$ distributions. The Gaussian distribution (red line) are the results of GEF calculations (see text).

Figure 2

Same as Fig. 1, but for the ${}^{40}\mathrm{Ca}+{}^{192}\mathrm{Os}$ reaction at different beam energies. The mass-asymmetric quasifission components present in the MADs are shown inside the black ellipses in panels (a)–(f). The Gaussian distributions (red line) are the results of GEF calculations (see text).

Figure 3

(a) The solid points represent the experimental ${\sigma }_{MR}$ values and the lines represent the ${\sigma }_{MR}$ values calculated using GEF model. (b) The minimum quasifission probability as a function of $E/V_B$ for the two reactions studied.

Figure 4

The angular distributions (center-of-mass) of the binary fragments from the (a) ${}^{40}\mathrm{Ca}+{}^{186}\mathrm{W}$ and (b) ${}^{40}\mathrm{Ca}+{}^{192}\mathrm{Os}$ reactions at different beam energies. The broken lines are the fits obtained using the TSM (see text).

Figure 5

Total fission cross sections for the ${}^{40}\mathrm{Ca}+{}^{186}\mathrm{W}$ and ${}^{40}\mathrm{Ca}+{}^{192}\mathrm{Os}$ reactions at different center-of-mass energies. The uncertainties are smaller than the symbols used.

Figure 6

Coupled-channels calculations for the ${}^{40}\mathrm{Ca}+{}^{192}\mathrm{Os}$ reactions with different potential parameters.

Figure 7

The Coulomb barrier as a function of different orientation angles of the (a) ${}^{186}\mathrm{W}$ and (b) ${}^{192}\mathrm{Os}$ nuclei relative to the beam direction, for the reactions studied.

Figure 8

(a) Experimental and (c) simulated MAD for the ${}^{40}\mathrm{Ca}+{}^{186}\mathrm{W}$ reaction at $E/V_B=0.98$. Simulations are performed assuming the standard mass-drift function and mass-equilibration time constant [1]. Quasielastic events are excluded in the MAD simulations shown in panel (c). (b) Experimental and simulated $M_R$ distributions for the ${}^{40}\mathrm{Ca}+{}^{186}\mathrm{W}$ reaction at same beam energy. (d) Experimental (black circle) and simulated (red square) angular distributions of the fragments with $M_R$ values between 0.25 and 0.5. The color scale for the counts in the MADs are the same as Fig. 1.

Figure 9

The (a) experimental and (c) simulated MAD including the mass-asymmetric component for the ${}^{40}\mathrm{Ca}+{}^{186}\mathrm{W}$ reaction at $E/V_B=0.98$. This mass-asymmetric component is generated from the lower barrier $\ell$ distribution with $\ell >40\hslash$. (b) Experimental and simulated $M_R$ distributions. (d) Experimental (black circle) and simulated (red square) angular distributions of the fragments with $M_R$ values betweem 0.25 and 0.5. The color scales for the counts in the MADs are the same as in Fig. 1.

Figure 10

Plots (a)–(c): Experimental MADs for the ${}^{40}\mathrm{Ca}+{}^{186}\mathrm{W}$ reaction at different beam energies. Plots (d)–(f): Corresponding simulated MADs for the same reaction. Plots (g)–(i): Experimental (black circles) and simulated (red squares) $M_R$ distributions. The same gating conditions used in Fig. 8 are followed to generate the $M_R$ distributions. Plots (j)–(l): Experimental (black circles) and simulated (red squares) angular distributions of the fragments with $M_R$ values between 0.25 and 0.5 with the same gating conditions as in Fig. 8. The weak mass asymmetric quasifission component present in the reaction are indicated inside the ellipse (black) in the experimental and simulated MADs. The color scale for the counts in the MADs are the same as Fig. 1.

Figure 11

Same as Fig. 10, but for the ${}^{40}\mathrm{Ca}+{}^{192}\mathrm{Os}$ reaction at different beam energies.