Sub-barrier quasifission in heavy element formation reactions with deformed actinide target nuclei

Background: The formation of superheavy elements (SHEs) by fusion of two massive nuclei is severely inhibited by the competing quasifission process. Low excitation energies favor SHE survival against fusion-fission competition. In “cold” fusion with spherical target nuclei near ${}^{208}\mathrm{Pb}$, SHE yields are largest at beam energies significantly below the average capture barrier. In “hot” fusion with statically deformed actinide nuclei, this is not the case. Here the elongated deformation-aligned configurations in sub-barrier capture reactions inhibits fusion (formation of a compact compound nucleus), instead favoring rapid reseparation through quasifission.

Purpose: To determine the probabilities of fast and slow quasifission in reactions with prolate statically deformed actinide nuclei, through measurement and quantitative analysis of the dependence of quasifission characteristics at beam energies spanning the average capture barrier energy.

Methods: The Australian National University Heavy Ion Accelerator Facility and CUBE fission spectrometer have been used to measure fission and quasifission mass and angle distributions for reactions with projectiles from C to S, bombarding Th and U target nuclei.

Results: Mass-asymmetric quasifission occurring on a fast time scale, associated with collisions with the tips of the prolate actinide nuclei, shows a rapid increase in probability with increasing projectile charge, the transition being centered around projectile atomic number $Z_{\mathrm{P}}=14$. For mass-symmetric fission events, deviations of angular anisotropies from expectations for fusion fission, indicating a component of slower quasifission, suggest a similar transition, but centered around $Z_{\mathrm{P}}\sim 8$.

Conclusions: Collisions with the tips of statically deformed prolate actinide nuclei show evidence for two distinct quasifission processes of different time scales. Their probabilities both increase rapidly with the projectile charge. The probability of fusion can be severely suppressed by these two quasifission processes, since the sub-barrier heavy element yield is likely to be determined by the product of the probabilities of surviving each quasifission process.

Figure 1

The upper panels show the measured mass-angle distributions of FMT events for the reaction ${}^{34}\mathrm{S}+{}^{232}\mathrm{Th}$, forming ${}^{266}\mathrm{Sg}$, at the indicated center-of-mass bombarding energy $E_{\mathrm{c}.\mathrm{m}.}$. The ratio $E/V_{\mathrm{B}}$ (independent of the reference frame) is also given, where the average barrier energy $V_{\mathrm{B}}$ is 153.5 MeV in the c.m. frame. The intensity scale is counts, proportional to $d^2\sigma /d\theta d{M}_R$. The lower panels show the projected mass-ratio ($M_{\mathrm{R}}$) spectra for the angular range ${45}^{\circ }<{\theta }_{c.m.}<{135}^{\circ }$. The counts have been multiplied by the indicated scale factors. A transition occurs from predominantly mass-asymmetric quasifission at sub-barrier energies to apparently mass-symmetric fission at $E>V_{\mathrm{B}}$. The MADs show that the mass-asymmetric component has a very fast time scale, while the component peaked at symmetry shows a significant mass-angle correlation, inconsistent with fusion fission.

Figure 2

As in Fig. 1 for the reaction ${}^{28}\mathrm{Si}+{}^{238}\mathrm{U}$, also forming ${}^{266}\mathrm{Sg}$. The average barrier energy $V_{\mathrm{B}}$ was taken as 139.5 MeV. The mass-asymmetric quasifission component is weaker in this reaction.

Figure 3

As in Fig. 1 for the reaction ${}^{30}\mathrm{Si}+{}^{232}\mathrm{Th}$, forming ${}^{262}\mathrm{Rf}$. The average barrier energy $V_{\mathrm{B}}$ was taken as 135.7 MeV. The mass-angle correlation of the mass-symmetric component is weaker in the reactions forming ${}^{262}\mathrm{Rf}$.

Figure 4

As in Fig. 1 for the reaction ${}^{24}\mathrm{Mg}+{}^{238}\mathrm{U}$, forming ${}^{262}\mathrm{Rf}$. The average barrier energy $V_{\mathrm{B}}$ was taken as 119.7 MeV. The mass-asymmetric quasifission component is weaker than in the ${}^{30}\mathrm{Si}+{}^{232}\mathrm{Th}$ reaction forming ${}^{262}\mathrm{Rf}$.

Figure 5

The root-mean-square (RMS) value of the $M_{\mathrm{R}}$ spectra for all four reactions evaluated over the range $0.17<M_{\mathrm{R}}<0.83$. They are plotted as a function of $E/V_{\mathrm{B}}$. The expectation for fusion fission is approximately 0.07. The results show a smooth energy dependence, and are correlated strongly with the atomic number of the projectile $Z_{\mathrm{P}}$ and with $E/V_{\mathrm{B}}$.

Figure 6

Representative measured mass-angle distributions for the ${}^{34}\mathrm{S}+{}^{232}\mathrm{Th}$ reaction at below-, near- and above-barrier energies in panels (a)–(c) respectively. Simulations including separate components for axial (tip) collisions and equatorial collisions are shown in panels (d)–(f). Simulation parameters were adjusted to give a good representation of the measurements over the experimentally measured coverage (see text). Panels (g)–(i) show the ratio of the simulated events in the experimental angular range to the total, thus providing the detection efficiency for a given mass ratio. At the near-barrier energy the fast mass-asymmetric quasifission events are peaked within the detector coverage, giving a high efficiency.

Figure 7

Representative mass-ratio spectra (blue circles) for the reactions and energies indicated, corrected for detection efficiency as determined in Fig. 6. With the goal of extracting relative yields of the symmetric-peaked and mass-asymmetric components, the mass-symmetric yield was matched to a Gaussian (red curve). Subtracting this gives the residuals (magenta squares). These in turn were fitted with Gaussians (black curves). The ratio of asymmetric to symmetric fission yields were then determined for all measurements (see text).

Figure 8

Ratio of the mass-asymmetric to symmetric-peaked fission yields for the ${}^{34}\mathrm{S}+{}^{232}\mathrm{Th}$ reaction as a function of $E/V_{\mathrm{B}}$. Experimental results with efficiency correction are shown by the red diamonds, and without by yellow diamonds in panel (a). To illustrate the sensitivity of the energy dependence to model parameters, panels (a)–(c) show calculations for different values of the assumed probability of fast mass-asymmetric quasifission ($P_{\mathrm{FQF}}$) in axial (tip) collisions. In each panel calculations for a range of angles ${\theta }_{\mathrm{FQF}}$ dividing axial from equatorial collisions are shown. Chi-squared analysis gave the best fitting model parameters (see text).

Figure 9

At the top is a sketch of the simple ansatz used to model the ratio between fast mass-asymmetric quasifission and symmetric-peaked fission. Axial collisions up to a limiting angle ${\theta }_{\mathrm{FQF}}$ are assumed to result in fast quasifission with probability $P_{\mathrm{FQF}}$. Other collisions are taken to result in symmetric-peaked fissionlike events. The schematic illustration below shows $P_{\mathrm{FQF}}$ as a function of $\theta$, with the sharp cutoff of $P_{\mathrm{FQF}}$ shown by the red dotted line. A more realistic smooth cutoff (green dashed line) can be approximated by a stepped function, but use of this makes little change to the results (see text).

Figure 10

As in Fig. 8, for the other three reactions studied. Here a fixed value of ${\theta }_{\mathrm{FQF}}={20}^{\circ }$ is used, and calculations for various values of $P_{\mathrm{FQF}}$ are shown. As for the ${}^{34}\mathrm{S}+{}^{232}\mathrm{Th}$ data, a chi-squared fit gave best values of ${\theta }_{\mathrm{FQF}}$ and $P_{\mathrm{FQF}}$.

Figure 11

Results of application of the fast quasifission anzatz (illustrated again at the top) to the four reactions, as a function of projectile atomic number $Z_{\mathrm{P}}$. Panel (a) shows the best-fitting values of ${\theta }_{\mathrm{FQF}}$. Experimental uncertainties (from the chi-squared analysis) prevent definitive determination of the dependence on $Z_{\mathrm{P}}$, though the data are consistent with an increasing trend, which might be expected. Panel (b) shows the dependence of $P_{\mathrm{FQF}}$ on $Z_{\mathrm{P}}$ (circles and triangles for Th and U respectively). A rapid rise is seen, as expected even from the raw $M_{\mathrm{R}}$ spectra. Also shown are the probabilities for slow quasifission estimated from the angular distributions of the symmetric-peaked fission (see Sec. 3c).

Figure 12

Measured angular distributions from this work, for FMT fission in the ${}^{19}\mathrm{F}+{}^{232}\mathrm{Th}$ reaction, at the indicated c.m. energies. Fits to the distributions using the transition state model formalism are shown by the dashed lines, where $K_0$ was a free parameter. The different colored symbols serve to correlate the data with the c.m. energies. The anisotropies were determined from the ratio of the value of the fit at ${180}^{\circ }$ to that at ${90}^{\circ }$.

Figure 13

Cross sections for FMT fission (orange points) for the ${}^{19}\mathrm{F}+{}^{232}\mathrm{Th}$ reaction, as a function of $E/V_{\mathrm{B}}$. The average barrier energy $V_{\mathrm{B}}$ was determined to be 89.5 MeV. Also shown are estimated cross sections for fission events where most of the mass of the projectile was not absorbed, most likely following transfer reactions. The cross section of transfer fission exceeds that of FMT fission at around $E/V_{\mathrm{B}}=0.90$, and at $E/V_{\mathrm{B}}=0.80$, it is difficult to identify reliably the FMT fission events.

Figure 14

Symmetric-peaked fission angular anisotropies $A$ as a function of $E/V_{\mathrm{B}}$ for the indicated reactions. The curves represent TSM calculations of fusion-fission anisotropies. They are color coded to the reaction symbol.