Exploring quasifission characteristics for ${}^{34}\text{S}+{}^{232}\text{Th}$ forming ${}^{266}\mathrm{Sg}$

Background: Fission fragments from heavy ion collisions with actinide nuclei show mass-asymmetric and mass-symmetric components. The relative probabilities of these two components vary rapidly with beam energy with respect to the capture barrier, indicating a strong dependence on the alignment of the deformed nucleus with the partner in the collisions.

Purpose: To study the characteristics of the mass-asymmetric quasifission component by reproducing the experimental mass-angle distributions to investigate mass evolution and sticking times.

Methods: Fission fragment mass-angle distributions were measured for the ${}^{34}\text{S}+{}^{232}\text{Th}$ reaction. Simulations to match the measurements were made by using a classical phenomenological approach. Mass ratio distributions and angular distributions of the mass-asymmetric quasifission component were simultaneously fit to constrain the free parameters used in the simulation.

Results: The mass-asymmetric quasifission component—predominantly originating from tip (axial) collisions with the prolate deformed ${}^{232}\text{Th}$—is found to be peaked near $A=200$ at all energies and center-of-mass angles. A Monte Carlo model using the standard mass equilibration time constant of $5.2\times {10}^{-21}$ s predicts more symmetric mass splits. Three different hypotheses assuming (i) a mass halt at $A=200$, (ii) a slower mass equilibration time, or (iii) a Fermi-type mass drift function reproduced the main experimental features.

Conclusions: In tip collisions for the ${}^{34}\text{S}+{}^{232}\text{Th}$ reaction, mass-asymmetric fission with $A\sim 200$ is the dominant outcome. The average sticking time is found to be $\sim 7\times {10}^{-21}$ s, independent of the scenario used for mass evolution.

Figure 1

Upper panels (a) to (f) show ${\mathrm{v}}_{\parallel }-{\mathrm{v}}_{\text{cn}}$ versus ${\mathrm{v}}_{\perp }$ scatter plot for all fission events, at different beam energies. The $E/V_B$ values (${\mathrm{V}}_B=154.8\text{MeV}$) and CN excitation energies $E^{*}$ are given at the top of each plot. Central panels (g) to (l) show experimental MAD scatter plots for ${}^{34}\text{S}+{}^{232}\text{Th}$ reactions at different energies. Lower panels (m) to (r) show the corresponding projected $M_R$ distributions of the mirrored MADs shown in panels (g) to (l). The angular window (${45}^{\circ }<{\theta }_{\mathrm{c}.\mathrm{m}.}<{135}^{\circ }$) used for producing these $M_R$ distributions is indicated in panel (k).

Figure 2

Unsymmetrized $M_R$ distribution of the fragments from ${}^{34}\text{S}+{}^{232}\text{Th}$ at $E^{*}=42.5$ MeV, for ${90}^{\circ }\le {\theta }_{\mathrm{c}.\mathrm{m}.}\le {135}^{\circ }$. The red dashed and green dot-dashed lines correspond to individual Gaussian fits while the solid blue line represents the overall fit.

Figure 3

Average mass ratio of the heavy asymmetric fragments and symmetric fragments measured as a function of $E/V_B$. Dot-dashed (red) line represents pre-evaporation mass $A=133$ (symmetric fission) and upper and lower broken lines (black) represent $A=208$ and 200, respectively and the solid (blue) line represents the entrance channel mass asymmetry. Upward arrows represent three data points selected for the theoretical simulations discussed in Sec. 5.

Figure 4

The dependence on the center-of-mass angle (${\theta }_{\mathrm{c}.\mathrm{m}.}$) of the average mass ratio for the heavy asymmetric and symmetric fragments for the ${}^{34}\text{S}+{}^{232}\text{Th}$ reaction at the three lowest measured energies. Vertical bars indicate the widths (${\sigma }_{MR}$) of the Gaussian fits.

Figure 5

Typical angular momentum-distributions generated for the axial and equatorial collisions for the ${}^{34}\text{S}+{}^{232}\text{Th}$ reaction at $E/V_B=0.98$, where $L$ and ${\sigma }_L$ are the angular momentum and partial-wave cross sections, respectively.

Figure 6

TDHF calculations of moments of inertia, normalized by the moment of inertia of a rigid sphere, $I_0$, as a function of time in zeptoseconds, for different beam energies (center-of-mass). The orientation (axial or equatorial) and average angular-momentum value used in each case are indicated. The average value of $I/I_0$ between 2 zs and 13 zs was used in the quasifission simulations.

Figure 7

(a) Typical sticking-time distribution with parameters $(p,s,e)=(12,4,10)$ zs as indicated (see text; Sec. 5 E). (b) $M_R$ evolution as a function of time following Eq. (4), with an initial time delay of 1 zs.

Figure 8

(a) Experimental MAD at $E/V_B=0.93$ (excluding the quasi-elastics). (b) MAD simulated (excluding quasi-elastics) for the same $E/V_B$ assuming the exponential mass drift as given in Eq. (4). (c) $M_R$ distributions of the experimental (filled black circles) and simulated (open red squares) MADs between the angular window ${45}^{\circ }$ and ${135}^{\circ }$. The angular window used is shown as a rectangle in Fig. 8. (d) Angular distributions of the mass-asymmetric quasifission component present in this reaction. The angular and $M_R$ window used are shown as rectangles in Fig. 8.

Figure 9

Top Panels (a) to (c) show experimental MAD scatter plots for the ${}^{34}\text{S}+{}^{232}\text{Th}$ reaction at different $E/V_B$, showing $M_R$ values between 0.16 and 0.84. Panels (d) to (f) show simulated MADs at the same $E/V_B$ values and $M_R$ range, assuming mass evolution only to $A=200$. Panels (g) to (i) show projected $M_R$ distributions of experimental (filled black circles) and simulated (open red squares) MADs within the angular window ${45}^{\circ }$ and ${135}^{\circ }$. The angular window used is shown as a rectangle in panels (b) and (e). Bottom panels (j) and (k) show angular distributions of mass-asymmetric quasifission events from experimental (filled black circles) and simulated (open red squares) MADs at $E/V_B=0.93$ and 0.98. The events are selected between the angular window ${45}^{\circ }$ and ${135}^{\circ }$ and $M_R$ window 0.16 and 0.36, represented as rectangles in Figs. 9 and 9. Bottom panel (l) shows mean $M_R$ as a function of center-of-mass angle at $E/V_B=1.08$.

Figure 10

(a) Mass drift as a function of time in Tōke's picture [3], and three new scenarios presented in this work. The shaded region represents the average sticking time observed in this work (see Table 1). Panels (b)–(d) show the sticking-time distributions of fast events at different $E/V_B$ values as a function of time.

Figure 11

Top panels (a) to (c) show experimental MAD scatter plots for the ${}^{34}\text{S}+{}^{232}\text{Th}$ reaction at different $E/V_B$, showing $M_R$ values between 0.16 and 0.84. Panels (d) to (f) show simulated MADs assuming longer mass equilibration time for fast collisions. Panels (g) to (i) show projected $M_R$ distributions of experimental (filled black circles) and simulated (open red squares) MADs. The angular and $M_R$ ranges used are indicated in panel (h). Bottom panels (j) and (k) show angular distributions of mass-asymmetric quasifission events from experimental (filled black circles) and simulated (open red squares) MADs at $E/V_B=0.93$ and 0.98 for the angular and $M_R$ windows indicated in panel (j). Bottom panel (l) shows mean $M_R$ as a function of center-of-mass angle at $E/V_B=1.08$.

Figure 12

Top panels (a) to (c) show experimental MAD scatter plots for the ${}^{34}\text{S}+{}^{232}\text{Th}$ reaction at different $E/V_B$, showing $M_R$ values between 0.16 and 0.84. Panels (d) to (f) show simulated MADs assuming a Fermi-type mass-drift function for slow and fast events. Panels (g) to (i) show projected $M_R$ distributions of experimental (filled black circles) and simulated (open red squares) MADs. The angular and $M_R$ ranges used are indicated in panel (h). Bottom panels (j) and (k) show angular distributions of mass-asymmetric quasifission events from experimental (filled black circles) and simulated (open red squares) MADs at $E/V_B=0.93$ and 0.98 for the angular and $M_R$ windows indicated in panel (j). Bottom panel (l) shows mean $M_R$ as a function of center-of-mass angle at $E/V_B=1.08$.