Fusion-fission in the reactions of the 58 Ni + 251 Cf and 64 Zn + 248 Cm combinations

Introduction : In the present study, we evaluate the nucleon evaporation, alpha decay, and fission widths in the fusion-fission of the 58 Ni+ 251 Cf and 64 Zn + 248 Cm reactions for the synthesis of the super-heavy 309 ; 312 126 nuclei. Methods : The feasibility of the synthesis of the 309 ; 312 126 isotopes via the mentioned systems is investigated based on the widths. The widths in the excitation energy range of E (cid:3) = 10 – 100 MeV are calculated in the scope of the statistical model, in which the level density is calculated by using the Fermi-gas model. By employing the LISE++ code, the level densities the compound nuclei, 309 ; 312 126 nuclei, are calculated to be about 10 5 – 10 50 (MeV (cid:0) 1 ) in the energy range of interest. Results : The lifetime of the compound nuclei, 309 ; 312 126 nuclei, which are estimated based on the total width, is about 10 (cid:0) 22 -10 (cid:0) 20 s. The fission has the largest width compared to those of the alpha decay and nucleon evaporations. Hence, the 58 Ni+ 251 Cf and 64 Zn + 248 Cm combinations are appropriate to the study of the mass distribution. In addition, the large alpha decay widths suggest the 309 ; 312 126 isotopes be the alpha-decay nuclei. Conclusion : The results are expected to be useful for considering measurements at facilities in the near future.


INTRODUCTION
Recently, super-heavy elements with atomic numbers 2 up to Z = 118 have been experimentally discovered 3 so far [1][2][3][4][5][6] . However, the number of isotopes is not 4 diversified, and the production mechanism of super-5 heavy nuclei has not been revealed up to date. It 6 is thought that, for heavy nuclei, the fusion mech-7 anism can be proceeded through three main stages: states. Therefore, it is necessary to study the probabil-20 ity of each stage to understand the interaction mech-21 anism of heavy nuclei. Notice that it is possible for 22 the appearance of the new doubling-magic numbers 23 during the fission of super-heavy nuclei. The fission 24 is also one of the routes reaching to the neutron-rich 25 heavy region. 26 It should be noted that the cross-section for the syn-27 thesis of new heavy elements with Z greater than 28 118, which is important for understanding the fusion 29 mechanism, has large uncertainty. Since the fusions 30 of the 58 Ni + 251 Cf and 64 Zn + 248 Cm combinations, 31 respectively, lead to the unknown 309,312 126 nuclei, 32 they can be candidates for discovering new super-33 heavy elements with the atomic numbers up to Z = 34 126. The cross-section relevant to the penetration of 35 the Coulomb barrier and leading to a contact between 36 two colliding nuclei (process (i)) can be precisely de-37 termined in a coupled-channel calculation 10,11 . The 38 probability of neutron emission from excited com-39 pound nuclei to form super-heavy nuclei can be cal-40 culated within a statistical model approach (process 41 (iii)) 12,13 . It is believed that the fusion-fission and 42 quasi-fission give different fission properties in these 43 reactions. Hence, the fusion probability can be deter-44 mined by evaluating the fusion-fission properties in 45 the fusions of the 58 Ni + 251 Cf and 64 Zn + 248 Cm sys-46 tems.

47
In order to investigate the mentioned problems, the 48 measurements of the concerned fusions are proposed 49 to obtain cross-sections of the synthesis of elements 50 with Z > 118 and to reveal the mass distribution in 51 the fission process. In the previous studies 7, 8 in which m i , s i , and E i are the mass, spin, and en-84 ergy of the emitted particle, respectively; E * and E Bi 85 denote the excitation energy of the compound nu-86 cleus and the threshold of the particle emission; i 87 is the cross-section for the compound-nuclide forma-88 tion via the channel of the emitted particle and daugh-89 ter nucleus; r i (E * D ) and r i (E * ) are the level densities 90 of the daughter and compound nuclei at excitation 91 energies E D * (after emission) and E * (before emis-92 sion), respectively.

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The fission width, which reflects the fission proba-94 bility of the compound nucleus, estimated based on 95 BohrWheeler method, is given by 13,15 : where B f is the fission barrier, which can be obtained 97 from Ref. 16,17 ; E and r f are the kinetic energy of the 98 fissioning system and the level density of the fission-99 ing nucleus 18 in the saddle configuration at given ex-100 citation energy, respectively. Subsequently, the total 101 width of the de-excitation is defined as: The level density, ρ(E * ), can be described in terms 103 of rotational (K rot. ) and vibrational (K vib. ) parame-104 ters, and the non-collective internal nuclear excita-105 tion, ρ int .(E * ), as 18-21 The coefficents of the rotational and vibrational effects 107 are given by The deformation-dependent function, f(β 2 ,β 4 ), is de-115 scribed in terms of the coefficients of quadrupole (β 2 ) 116 and octupole (β 4 ) deformations as The non-collective internal nuclear excitation is de- Since the lifetime reflects the existence of the com- can be determined based on the total width as

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The decay widths of neutron, proton, alpha, and fis-

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Since the rotation energy, E rot. , is much smaller than    As mentioned, the partial width of the alpha decay is   clei. In addition, it was found that the nucleon evapo-277 ration mechanism is also a mystery in the super-heavy 278 nuclide synthesis. Therefore, theoretical and experi-279 mental studies of the synthesis of super-heavy nuclei 280 are strongly suggested.

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The author declares that there is no conflict of interest 283 regarding the publication of this article.

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The ideas, calculations, data analysis, discussion of re-286 sults, and writing manuscript were performed by Dr.