Fusion-fission of superheavy nuclei and clustering phenomena

Results of the study of mass-energy distributions of binary fragments for a wide range of nuclei with Z = 82-122 produced in reactions with heavy ions at energies close and below the Coulomb barrier are reported. The role of the shell effects, the influence of the entrance channel asymmetry and the deformations of colliding nuclei on the mechanism of the fusion-fission and quasifission processes are discussed. The observed peculiarities of the mass and energy distributions of reaction fragments are determined by the shell structure of the formed fragments.


Introduction
Nowadays more than 30 nuclei around the superheavy elements (SHE) region have been synthesized in fusion reactions of heavy nuclei. The existence of these nuclei is completely determined by proton and neutron closed shells at Z = 114-120 and N = 184 (island of stability). In the collisions of two massive nuclei many different reaction mechanisms such as elastic and inelastic scatterings, deep inelastic reactions, fusion and de-excitation of a compound nucleus, fusion-, quasi-and fast fission may take place. The existence of deep valleys on potential energy surface caused by shell effects is likely to be responsible for the manifestation of clustering phenomena in different reaction channels.
In low-energy collisions of heavy ions the quasifission (QF) process caused by the shell effects dominates hindering formation of compound nucleus [1]. QF is a transitional mechanism between deep-inelastic collisions and complete fusion, in which the composite system separates in two main fragments without forming a compound nucleus (CN). QF happens to be the most important mechanism that prevents the formation of SHE in the fusion of heavy nuclei. This paper presents the results of the study of mass-energy distributions of binary fragments for a wide range of nuclei with Z = 82-122 produced in reactions heavy ions at energies close and below the Coulomb barrier. Velocity vectors of binary reaction products were measured using the two-arm timeof-flight spectrometer CORSET [2].

Shell effects in quasifission
In the last decade a great success in the synthesis of SHE with Z = 112-118 was achieved bombarding actinide targets with 48 Ca ions (hot fusion reactions). In these reactions, in contrast to the cold fusion, neutron excess in the composite systems leads to difference in a cluster composition of the compound system (due to the neutron shell with N = 184) as well as in its decay products.
One can see from Figure 1 that mass-energy distributions of binary reaction products, obtained in the 48 Ca+ 208 Pb, 232 Th, 238 U, 244 Pu, 248 Cm reactions change from triangular shape for the reaction with spherical target 208 Pb [3], where CN-fission process dominates, to the wide two-humped shape in the case of reactions with actinide targets [4] determined by the QF process. This onset of quasifission for the latter reactions might be explained by the target deformation and, consequently, the orientation effect that favors the QF process which manly leads to the formation of the clusters in the exit channel of the reaction.
Generally, in heavy-ion-induced reactions the formation of asymmetric QF fragments is connected with the strong influence of the nuclear shell at Z = 82 and N = 126 (double magic lead). In fact for the 48 Ca + 232 Th and 48 Ca + 238 U reaction the maximum yield corresponds to fragments with masses around 208 u. However, in reactions with heavier targets the maximum is shifted up to 211 u for the reaction 48 Ca + 248 Cm. Notice, for the reaction 64 Ni + 238 U, the maximum yield of asymmetric QF fragments corresponds to the heavy mass 215 u. As it was shown in [5] the shells in light fragment at Z = 28 and N = 50 could be effective, together with the shell Z = 82 and N = 126, and could lead to the shift of the asymmetric QF peak.    calculated with NRV code [6] using the proximity model along with the experimental mass distributions are shown. A strong correlation between the maxima in mass distributions and the minima of the potential energy is likely to be responsible for the shift of the heavier mass asymmetric peaks. These effects on the fragments formation due to the nuclear shells are evidences of clustering phenomena. Another noticeable case of the importance of shell closures in driving the mass flow is reported in [7] for the system 88 Sr + 176 Yb.

Bimodal fission
The question about symmetric and asymmetric modes in low-energy nuclear fission arose immediately after the discovery of nuclear fission. The numerous theoretical works [8,9,10] showed that multimodality is caused by the valley structure of the deformation potential energy surface of a fissioning nucleus.
The phenomenon of bimodal fission, discovered in the 1980's for the case of spontaneous and lowenergy fission of nuclei in the Fm-Rf region [11], means the co-existence of two fission modes with different total kinetic energies for the same symmetric mass division. Bimodality is connected with a possibility for these nuclei to have in both fragments the number of neutrons and protons close to magic numbers Z = 50 and N = 82 (Super-Short (SS) mode). This possibility will sharply disappear when moving from Fm to more heavy nuclei. However, calculations show that the SS-valley should exist up to 270, 272 Hs and even 278, 290 Ds nuclei.

Superasymmetric fission
For the first time the superasymmetric mode was observed in the compound nuclei fission in Pb region [13]. The enhancement of the mass yield in the region 65-75 u for the light fragment in the fission of 213 At and 210 Po compound nuclei is connected with the influence of double magic Ni (Z = 28, N = 50) and double magic Sn (Z = 50, N = 82). Notice that in this case the ratio A H /A L  2, and the yield is around 0.01%. The superasymmetric fission mode with mass ratio of A H /A L  2.5, caused by the closed shells Z = 28 and N = 50, was also found in thermal-neutron-induced fission of actinides nuclei [14]. In this case only the light fragment is close to the double magic Ni and the yield of superasymmetric mode does not exceed 10 -4 %.
The mass and energy distributions of fragments obtained in the reaction 22 Ne + 238 U are shown in figures 6 and 7. The mass distribution of the symmetric fragments has a nearly Gaussian shape and the average TKE shows a parabolic dependence on fragment mass typical for fission of excited compound nuclei as established by the LDM, whereas in the mass region around 52/208 u (A H /A L  4.3), that corresponds to the formation of fissioning pair of two magic nuclei Ca/Pb, an increase of fragment yields was observed. Moreover the total kinetic energy for these fragments is found to be about ~30 MeV higher than predicted by the LDM. The higher TKE indicates that the asymmetric fragments originate from more compact scission configuration as compared to normal fission. In the low panel of figure 6 the experimental mass distribution together with the prediction of W. Greiner for thermal neutrons induced fission of 255 Fm is presented. According to this calculation the yield of about 0.01% is expected due to the influence of the closed shells, while for spontaneous fission of 255 Fm the yield of 10 -4 % is expected for this superasymmetric mode [15].  Ca + 208 Pb [3] and in spontaneous fission of 258 No and 262 No taken from [12].  In present work the superasymmetric mode with ratio A H /A L  4.3 caused by the influence of double magic Ca and double magic Pb has been observed in fission of excited 260 No * compound nucleus. At an excitation energy of 41 MeV the yield of these fragments is about 510 -2 %.

Conclusion
The clustering phenomena have a great impact on the heavy-ion reaction products. In the case of the quasifission process at least one of the fragment mass is determined mainly by nuclear shells with Z = 28, 82 and N = 50, 126; whereas in the case of the fusion-fission the nuclear shells with Z = 50 and N = 82 play an important role in the fragment formation.
The static deformation of the reaction partners is responsible for the evolution of the composite system and the appearing of the clusters in the exit channel for quasifission process.
The bimodal fission caused by clustering phenomena was observed for fission of superheavy nuclei 271, 274 Hs * and 256 No * . For the compound nucleus 260 No * formed in the reaction 22 Ne + 238 U at the initial excitation energy E * = 41 MeV the bimodal fission as well as superasymmetric fission with mass ratio A H /A L ≈ 4.3 were observed.