Experimental study of the quasifission, fusion-fission, and de-excitation of Cf compound nuclei

Background: The fusion-evaporation reaction at energies around the Coulomb barrier is presently the only way to produce the heaviest elements. However, formation of evaporation residues is strongly hindered due to the competing fusion-fission and quasifission processes. Presently, a full understanding of these processes and their relationships has not been reached.

Purpose: This work aims to use new fission measurements and existing evaporation residue and fission excitation function data for reactions forming Cf isotopes to investigate the dependence of the quasifission probability and characteristics on the identities of the two colliding nuclei in heavy element formation reactions.

Method: Using the Australian National University's 14UD electrostatic accelerator and CUBE detector array, fission fragments from the ${}^{12}\mathrm{C}+{}^{235}\mathrm{U}$, ${}^{34}\mathrm{S}+{}^{208}\mathrm{Pb}$, ${}^{36}\mathrm{S}+{}^{206}\mathrm{Pb}$, ${}^{36}\mathrm{S}+{}^{208}\mathrm{Pb}$, and ${}^{44}\mathrm{Ca}+{}^{198}\mathrm{Pt}$ reactions were measured. Mass and angle distributions of fission fragments were extracted and compared to investigate the presence and characteristics of quasifission.

Results: Mass-angle-correlated fission fragments were observed for the ${}^{44}\mathrm{Ca}+{}^{198}\mathrm{Pt}$ reaction; no correlation was observed in the other reactions measured. Flat-topped fission-fragment mass distributions were observed for ${}^{12}\mathrm{C}+{}^{235}\mathrm{U}$ at compound-nucleus excitation energies from 28 to 52 MeV. Less pronounced flat-topped distributions were observed, with very similar shapes, for all three sulfur-induced reactions at excitation energies lower than 45 MeV.

Conclusions: A high probability of long-time-scale quasifission seems necessary to explain both the fission and evaporation residue data for the ${}^{34}\mathrm{S}+{}^{208}\mathrm{Pb}$ and ${}^{36}\mathrm{S}+{}^{206}\mathrm{Pb}$ reactions. Flat-topped mass distributions observed for ${}^{12}\mathrm{C}$- and ${}^{34,36}\mathrm{S}$-induced reactions are suggested to originate both from late-chance fusion-fission at low excitation energies and the persistence of shell effects at the higher energies associated with quasifission.

Figure 1

Experimental (symbols) capture and ER cross sections following neutron evaporation as a function of excitation energy for the reactions ${}^{36}\mathrm{S}+{}^{206}\mathrm{Pb}$ and ${}^{34}\mathrm{S}+{}^{208}\mathrm{Pb}$, both forming the same CN ${}^{242}{\mathrm{Cf}}^{*}$ [25]. The downward arrow marks the upper cross-section limit. Theoretical ER cross sections indicated by solid lines were calculated assuming that no quasifission is present in either reaction ($P_{\mathrm{CN}}=1$). The dotted line represents calculations for ${}^{34}\mathrm{S}+{}^{208}\mathrm{Pb}$ assuming that $P_{\mathrm{CN}}$ is 10 times smaller ($P_{\mathrm{CN}}=0.1)$.

Figure 2

Measured mass and angle distributions of fission fragments from the reactions ${}^{12}\mathrm{C}+{}^{235}\mathrm{U}$, ${}^{36}\mathrm{S}+{}^{206}\mathrm{Pb}$, ${}^{34}\mathrm{S}+{}^{208}\mathrm{Pb}$, and ${}^{44}\mathrm{Ca}+{}^{198}\mathrm{Pt}$ are shown in the $M_R$ and ${\theta }_{\mathrm{c}.\mathrm{m}.}$ plane. Below each MAD plot the projection of the MAD onto the $M_R$ axis is shown (see text). Excitation energies of the corresponding CN (${}^{242}\mathrm{Cf}$ and ${}^{247}\mathrm{Cf}$) are given.

Figure 3

Experimental $M_R$ distributions of fission fragments originating from the ${}^{12}\mathrm{C}+{}^{235}\mathrm{U}$, ${}^{36}\mathrm{S}+{}^{208}\mathrm{Pb}$, ${}^{36}\mathrm{S}+{}^{206}\mathrm{Pb}$, and ${}^{34}\mathrm{S}+{}^{208}\mathrm{Pb}$ reactions leading to ${}^{247}{\mathrm{Cf}}^{*}$, ${}^{244}{\mathrm{Cf}}^{*}$, and ${}^{242}{\mathrm{Cf}}^{*}$ are shown by histograms. Excitation energies of the corresponding CN are given. The smooth lines in red show best-fitting Gaussian functions.

Figure 4

Experimental (symbols) and calculated (lines) mean square deviations (a), mean squared angular momenta (b), and ${({\sigma }_{\mathrm{RMS}}/{\sigma }_{\mathrm{gaus}})}_{\mathrm{norm}.}$ (c) values. The dotted line in panel (c) indicates the value 1 for the ratio.

Figure 5

Schematic representation of multichance fission in ${}^{247}{\mathrm{Cf}}^{*}$. Mass distributions calculated using the the general fission model code gef are shown in gray (see text).

Figure 6

(a) Mass distribution of fission fragments of ${}^{244}{\mathrm{Cf}}^{*}$ [63] and (b) ${}^{242}{\mathrm{Cf}}^{*}$ [62] following electron capture decay of ${}^{244}\mathrm{Es}$ and ${}^{242}\mathrm{Es}$ (see text) and of ${}^{242}{\mathrm{Cf}}^{*}$ produced via ${}^{34}\mathrm{S}+{}^{208}\mathrm{Pb}$ at ${\mathrm{E}}^{*}=52.2$ MeV (c). (a, b) Experimental data are marked by circles; blue shaded distributions correspond to results of gef calculations (see text) at 10 MeV. Gaussian fits with ${\sigma }_{\mathrm{MR}}=0.03$ are shown by red lines. (c) The experimental distribution (black histogram) and gef results (blue shaded spectrum) at 52 MeV are shown.

Figure 7

The experimental data as presented in Fig. 3, now fitted by three Gaussians. The smooth lines in red show the sum of the three Gaussian functions and the smooth lines in blue show the two Gaussians corresponding to the mass-asymmetric split. Expected numbers of neutrons emitted before formation of the ER are also shown on the right.

Figure 8

Top panel: Extracted fractions of the mass-asymmetric fission component of the $M_R$ distributions for ${}^{242}{\mathrm{Cf}}^{*}$, ${}^{244}{\mathrm{Cf}}^{*}$, and ${}^{247}{\mathrm{Cf}}^{*}$. Bottom panel: Survival probabilities, $W_{\mathrm{CN}},$ of the ${}^{242}{\mathrm{Cf}}^{*}$ CN formed in ${}^{34}\mathrm{S}+{}^{208}\mathrm{Pb}$ and ${}^{36}\mathrm{S}+{}^{206}\mathrm{Pb}$ reactions. These values were extracted using the data shown in Fig. 1, which was taken from Refs. [25, 36].