Predictions for production of superheavy nuclei with Z=105-112 in hot fusion reactions

NUCLEAR PHYSICS AND INTERDISCIPLINARY RESEARCH

Predictions for production of superheavy nuclei with Z=105-112 in hot fusion reactions

Xiao-Bin Yu，

Long Zhu，

Zhi-Han Wu，

Fan Li，

Jun Su，

Chen-Chen Guo

Nuclear Science and Techniques

Vol.29, No.11

Article number 154

Published in print 01 Nov 2018

Available online 26 Sep 2018

DOI：10.1007/s41365-018-0501-2

63200

The effects of mass asymmetry on the production of superheavy nuclei (SHN), within the dinuclear system (DNS) model, are investigated in this study. It is observed that the fusion probability decreases with decreasing mass asymmetry. A total of 192 possible combinations of projectiles from O to Ti and targets with half-lives longer than 30 days for producing SHN ²⁶⁴Db, ²⁶⁵Db, ²⁶⁷Sg, ²⁶⁸Bh, ²⁶⁸Sg, ²⁶⁹Bh, ²⁷¹Hs, ²⁷¹Mt, ²⁷²Hs, ²⁷²Mt, ²⁷³Mt, ²⁷⁴Ds, ²⁷⁵Ds, ²⁷⁵Rg, ²⁷⁶Ds, ²⁷⁶Rg, ²⁷⁷Rg, ²⁷⁸Cn, ²⁷⁹Cn, and ²⁸⁰Cn are examined. Further, the optimal combinations and incident energies for synthesizing these nuclei are predicted. Most of the cross sections for production of SHN are larger than 10 pb; therefore, the process can be carried out with the available experimental equipment.

DNS modelSystematic studyFusion reactionSuperheavy nucleiEvaporation residue cross section

1 Introduction

In recent years, the synthesis of superheavy elements (SHEs) has been developed considerably, both experimentally and theoretically [1-3] and the Periodic Table of elements has been significantly extended. After the first successful synthesis of element 117 in 2010, all the elements in the seventh row of the Periodic Table have been discovered by mankind [3-10], which marks a great advancement in man’s cognition of the micro-world and a milestone in the evolution of the synthesis of SHEs. At present, efforts are being made to synthesize superheavy nuclei (SHN) experimentally. The elements from 107 to 113 were synthesized at GSI and RIKEN in cold fusion reactions [3-6], and the elements from 114 to 118 were produced at Dubna in hot fusion reactions using a neutron-rich projectile nucleus ⁴⁸Ca [1, 7-9]. Presently, scientists are interested in the production of SHEs with Z ≥ 119, which will be a tremendous breakthrough in the field of nuclear physics. However, in the synthesis of SHEs, the cross sections decrease with the increase in the charge number of the nuclei, and are close to or even far below the order of pb, which makes the process very difficult.

In addition, the production and measurement of the isotopes of already-known SHEs, which have not yet been synthesized, is important, as they can provide information on the trends of the decay properties along the neutron axis approaching the proposed neutron magic number, including the "island of stability". The synthesis of new SHN can greatly extend the map of the nuclides. According to the theory of nuclear structure [11-13], there is a double magic SHN, the nuclei in the neighborhood of which are relatively stable. In order to accurately locate the "island of stability", more experimental data needs to be available, therefore, the synthesis of more SHN is evidently important. At present, the main method used in the synthesis of SHN is the heavy-ion fusion evaporation reaction, hence, theoretical study of the process is essential for appropriate performance of the experiments [14-27]. Although, the ability to predict the production cross sections and incident energies is limited for theoretical models, it is still beneficial to investigate all the possible combinations systematically and predict the favorable ones for producing SHN [28].

In Fig. 1, the blue crosses represent the nuclei that will be investigated in this work. Due to the transition from the cold fusion reactions to hot fusion reactions, the SHN in this region are not synthesized yet. In this study, the effect of mass asymmetry on the fusion probability and cross sections of the reactions ²⁶Mg + ²⁴⁸Cm, ³⁶S + ²³⁸U, ⁴⁸Ca + ²²⁶Ra, which lead to the same compound nucleus ²⁷⁴HS*, are investigated first. In view of the long duration of the experiments and production rate, combinations of stable projectiles and targets with half-lives longer than 30 days are considered to be suitable. All possible combinations of projectiles from O to Ti and targets with half-lives longer than 30 days for producing SHN ²⁶⁴Db, ²⁶⁵Db, ²⁶⁷Sg, ²⁶⁸Bh, ²⁶⁸Sg, ²⁶⁹Bh, ²⁷¹Hs, ²⁷¹Mt, ²⁷²Hs, ²⁷²Mt, ²⁷³Mt, ²⁷⁴Ds, ²⁷⁵Ds, ²⁷⁵Rg, ²⁷⁶Ds, ²⁷⁶Rg, ²⁷⁷Rg, ²⁷⁸Cn, ²⁷⁹Cn, and ²⁸⁰Cn are examined and some optimal combinations and incident energies for synthesizing these nuclei are suggested.

Figure 1:

(Color online) The nuclides in the superheavy area with Z = 105-118. The blue crosses represent the nuclei that will be investigated in this study.

The article is organized as follows: In Sec. 2, a description of the DNS model is given; The Sec. 3 details an analysis of the results of calculation and a prediction of the optimal combinations for synthesizing several SHN in the gap region; The Sec. 4 presents the summary and the prospects.

2 Theoretical description

According to the concept of the DNS model, the complete fusion reaction is described as a diffusion process. All the nucleons of the projectile are transferred to the target and form a compound nucleus. This process is accompanied by the dissipation of energy and angular momentum. The evaporation residue (ER) cross section of the superheavy nucleus under the incident energy E_c.m. in the center-of-mass frame can be written as [21, 24, 29-34]:

\begin{array}{l} σ_{ER} (E_{c .m .}) & = \frac{π ℏ^{2}}{2 μ E_{c .m .}} \sum_{J = 0}^{\infty} (2 J + 1) T (E_{c .m .,} J) \\ P_{CN} (E_{c .m .,} J) W_{sur} (E_{c .m .,} J), \end{array}

(1)

where, T(E_c.m., J) is the probability that the collision system overcomes the Coulomb barrier and forms the dinuclear system [35]. P_CN(E_c.m., J) is the fusion probability. W_sur(E_c.m., J) is the survival probability of the compound nucleus.

The fusion process described as a diffusion process, can be understood by numerically solving the master equations. The time evolution of the distribution probability function P(Z₁, N₁, t) for fragment 1 with the mass number A₁ and excitation energy E₁ at time t is described by the following master equations [17, 24]:

\begin{array}{l} \frac{d P (Z_{1}, N_{1}, t)}{d t} = \\ \sum_{Z_{1}^{'}} W_{Z_{1}, N_{1}; Z_{1}^{'}, N_{1}} (t) [d_{Z_{1}, N_{1}} P (Z_{1}^{'}, N_{1}, t) - \\ d_{Z_{1}^{'}, N_{1}} P (Z_{1}, N_{1}, t)] + \\ \sum_{N_{1}^{'}} W_{Z_{1}, N_{1}; Z_{1}, N_{1}^{'}} (t) [d_{Z_{1}, N_{1}} P (Z_{1}, N_{1}^{'}, t) - \\ d_{Z_{1}, N_{1}^{'}} P (Z_{1}, N_{1}, t)] - \\ [Λ_{Z_{1}, N_{1}, E_{1}, t}^{qf} (Θ) + Λ_{Z_{1}, N_{1}, E_{1}, t}^{fis} (Θ)] P (Z_{1}, N_{1}, t) . \end{array}

(2)

The potential energy surface (PES) of the DNS in the fusion process is defined as:

\begin{array}{l} U (Z_{1}, N_{1}; Z_{2}, N_{2}, & R) = E_{B} (Z_{1}, N_{1}) + E_{B} (Z_{2}, N_{2}) \\ - E_{B} (Z, N) + V_{C} (R) + V_{N} (R), \end{array}

(3)

where Z = Z₁ + Z₂ and N = N₁ + N₂. E_B(Zi,Ni) and E_B(Z,N) are the binding energies of the fragment i and the compound nucleus, respectively. V_C and V_N are the Coulomb potential and nuclear potential, respectively [24].

After the capture process, the DNS is formed. For the formation of the compound nucleus (CN), the projectile should overcome the inner fusion barrier B_fus, defined as the difference between U_BG, the highest point called Businaro–Gallone (B.G.) point on the left of U(≤ta), and the potential at the entrance. Hence, summing up the probability on the left side of the B.G. point, the fusion probability of the DNS is given by [17, 28, 36],

\begin{array}{l} P_{CN} (J) = \sum_{Z_{1} = 1}^{Z_{BG}} \sum_{N_{1} = 1}^{N_{BG}} P (Z_{1}, N_{1}, E_{1} (J), τ_{int} (J)) . \end{array}

(4)

The compound nucleus formed in the fusion reaction is unstable because of its high excitation energy and usually cools down by emitting γ-rays, evaporating particles (neutrons, protons, α and other light charged particles) and fission [37-39]. This process is described by a statistical model. Subsequent to the fission of the composite nucleus, the survival probability of the SHN after evaporation of x neutrons (considering only neutron evaporation and fission), can be written as:

\begin{array}{l} W_{sur} (E_{CN}^{*}, x, J) = P (E_{CN}^{*}, x, J) \times \\ \prod_{i = 1}^{x} [\frac{Γ_{n} (E_{i}^{*}, J)}{Γ_{n} (E_{i}^{*}, J) + Γ_{f} (E_{i}^{*}, J)}], \end{array}

(5)

where J and $E_{CN}^{*}$ are the spin and excitation energies of the compound nucleus, respectively. The relationship between the excitation energy and incident energy in the center-of-mass frame is $E_{C N}^{*} = E_{c .m .} + Q$ . The nuclear ground state masses are taken from [40]. $Γ_{n} (E_{i}^{*}, J)$ and $Γ_{f} (E_{i}^{*}, J)$ are the widths of the ith neutron evaporation and fission, respectively. The solution is described later. $E_{i}^{*}$ is the excitation energy of the compound nucleus before evaporation of the ith neutron, which satisfies the following relation: $E_{i + 1}^{*} = E_{i}^{*} - B_{i}^{n} n - 2 T_{i}$ . $B_{i}^{n}$ is the evaporation energy of the ith neutron. Ti is the temperature before evaporation of the ith neutron, given by the relation $E_{i}^{*} = a T_{i}^{2} - T_{i}$ . The realization probability for neutron evaporation $P (E_{CN}^{*}, x, J)$ can be obtained from Ref. [34].

According to Weisskopf’s theory of evaporation, the evaporation width of the particle ν can be written as [41]:

\begin{array}{l} Γ_{ν} & (E^{*}, J) = \frac{(2 s_{ν} + 1) m_{ν}}{π^{2} ℏ^{2} ρ (E^{*}, J)} \times \\ \int_{I_{ν}} ε ρ (E^{*} - B_{ν} - ε, J) σ_{inv} (ε) d ε, \end{array}

(6)

where sν is the spin, mν is the reduced mass relative to the remaining nucleus, and Bν is the binding energy, of the evaporating particle ν. $I_{ν} = [0, E^{*} - B_{ν} - δ - \frac{1}{a}]$ . The mass table is obtained from Ref. [40]. δ = 0, Δ, 2Δ for odd-odd, odd-even, and even-even nuclei, $Δ = 11 / \sqrt{A}$ MeV. σ_inv is the inverse reaction cross section for a particle ν with channel energy ε [42]. For the neutron, it is given by $σ_{inv} = π R_{ν}^{2}$ . $R_{ν} = 1.16 [\sqrt[3]{A - 1} + 1]$ .

The width of fission is given by the Bohr-Wheeler formula [43]:

\begin{array}{l} Γ & _{f} (E^{*}, J) = \frac{1}{2 π ρ_{f} (E^{*}, J)} \times \\ \int_{I_{f}} \frac{ρ_{f} (E^{*} - B_{f} - ε, J) d ε}{1 + e x p [- 2 π (E^{*} - B_{f} - ε) / ℏ ω]} . \end{array}

(7)

Here $I_{f} = [0, E^{*} - B_{f} - δ - \frac{1}{a_{f}}]$ . B_f(E^*, J) is the fission barrier, which is of the form

\begin{array}{l} B_{f} (E^{*}, J) = B_{f}^{M} (E^{*} = 0, J) e x p (- \frac{E^{*}}{E_{D}}) . \end{array}

(8)

Here, E_D=20 MeV is the shell damping energy. $B_{f}^{M}$ is the shell correction energy which is taken from Ref. [40]. After obtaining the widths of neutron evaporation and fission, the final W_sur can be obtained from the Eq. (5).

3 Results and discussion

In order to investigate qualitatively the effects of mass asymmetry on the fusion probability, the driving potential, which is the minimum value of PES for combinations with the same mass asymmetry, is shown in Fig. 2, as a function of mass asymmetry for the reactions ²⁶Mg + ²⁴⁸Cm, ³⁶S + ²³⁸U, and ⁴⁸Ca + ²²⁶Ra, leading to the same compound nucleus ²⁷⁴Hs*. Although the systems evolve in both the proton and neutron degrees of freedom, the mass asymmetry can still be a good collective degree for estimating the fusion probability. The B.G. point is shown in this figure. The blue arrow indicates the inner fusion barrier B_fus for the reaction ⁴⁸Ca + ²²⁶Ra. The inner fusion barrier plays a main role in the competition between quasifission and complete fusion. According to the results of the calculation, the inner fusion barriers for the reactions ³⁶S + ²³⁸U and ⁴⁸Ca + ²²⁶Ra are B_{fus, S} = 3.6 MeV and B_{fus, Ca} = 8.6 MeV, respectively. It is observed that the injection point of the reaction ²⁶Mg + ²⁴⁸Cm is located on the left side of the B.G. point, therefore, the fusion probability for ²⁶Mg + ²⁴⁸Cm would be much larger than that of the other two reactions.

Figure 2:

(Color online) The driving potential of ²⁷⁴HS* presented as a function of mass asymmetry. The black arrow indicates the B.G. point. The injection points for the reactions ²⁶MG + ²⁴⁸Cm, ³⁶S + ²³⁸U, and ⁴⁸Ca + ²²⁶Ra are denoted by a triangle, solid circle, and square, respectively.

Figure 3 presents the fusion probabilities as a function of the excitation energy of the compound nucleus in the reactions ²⁶Mg + ²⁴⁸Cm, ³⁶S + ²³⁸U, and ⁴⁸Ca + ²²⁶Ra. It can be seen from the calculated results that with the same excitation energy, the fusion probability decreases with decreasing mass asymmetry. This is because a near symmetric system can overcome a high inner fusion barrier for forming a compound nucleus by nucleon transfer. The fusion probability for the reaction ²⁶Mg + ²⁴⁸Cm, is close to 1 and much larger than that of the other two reactions. It can also be seen that the fusion probabilities for all the reactions increase with increasing energy.

Figure 3:

(Color online) The fusion probability for reactions ²⁶Mg + ²⁴⁸Cm, ³⁶S + ²³⁸U, and ⁴⁸Ca + ²²⁶Ra.

Figure 4 shows the excitation functions for the reactions ²⁶Mg + ²⁴⁸Cm, ³⁶S + ²³⁸U, and ⁴⁸Ca + ²²⁶Ra. The available experimental data [44-46], which is indicated by points, is also shown. The curves show the results of calculation for different evaporation channels. It can be seen that the calculations duly authenticate the experimental data.

Figure 4:

(Color online) The excitation functions for the reactions ²⁶Mg + ²⁴⁸Cm (a), ³⁶S + ²³⁸U (b), and ⁴⁸Ca + ²²⁶Ra (c). The purple dotted lines, red solid lines, black dashed lines, and blue dash-dotted lines represent 2n, 3n, 4n, and 5n evaporation channels, respectively. The red squares, black circles, and blue diamonds represent the experimental data of 3n, 4n, and 5n evaporation channels respectively [44-46].

The excitation functions for the reactions ²²Ne + ²⁵⁴Cf, ²⁶Mg + ²⁵⁰Cm, and ⁴⁸Ca + ²²⁸Ra are shown in Fig. 5. All the reactions lead to the same compound nucleus, ²⁷⁶Hs*. It can be seen that the cross sections decrease with decreasing mass asymmetry.

Figure 5:

(Color online) The excitation functions for the reactions ²²Ne + ²⁵⁴Cf (a), ²⁶Mg + ²⁵⁰Cm (b), and ⁴⁸Ca + ²²⁸Ra (c).

However, it cannot be presumed that the reaction with larger value of mass asymmetry is better for producing SHN. For systems with larger values of mass asymmetry, the reactions are usually very hot. Therefore, in the de-excitation process, many neutrons evaporate. This actually limits the neutron richness of the synthesized SHN. Moreover, due to the limitation of the target, the projectile cannot be very light. In addition, the mass asymmetry not only affects the fusion probability, but also has an impact on the probability of the capture and survival stages. Therefore, in this study, all the possible combinations are examined systematically, with stable projectiles of Z=8-22 and targets with half-lives longer than 30 days, for synthesizing the unknown SHN, as shown in Fig. 1.

The cross sections of different projectile-target combinations are compared to obtain the optimal ones for synthesizing the unknown SHN, as shown in Figs. 6, 7, 8, 9 and 10. It can be seen that for producing most of these nuclei, the maximal ER cross sections are larger than 10 pb. For example, for producing the ²⁶⁸Sg, the ER cross section is close to 1 nb in the reaction ¹⁸O + ²⁵⁴Es → ²⁶⁸Sg + 4n with an incident energy of 82.87 MeV. Moreover, for producing the ²⁶⁴Db, ²⁶⁵Db, ²⁶⁷Sg, ²⁶⁸Bh, ²⁶⁹Bh, ²⁷¹Hs, ²⁷¹Mt, ²⁷²Hs, ²⁷²Mt, ²⁷³Mt, ²⁷⁴Ds, 275Rg, ²⁷⁵Ds, ²⁷⁶Ds, ²⁷⁶Rg, ²⁷⁷Rg, the most promising reactions are ¹⁸O + ²⁴⁹Bk → ²⁶⁴Db + 3n (12 pb at 79.36 MeV), ¹⁹F + ²⁵⁰Cm → ²⁶⁵Db + 4n (5.6 pb at 89.55 MeV), ¹⁷O + ²⁵⁴Cf → ²⁶⁷Sg + 4n (82 pb at 82.01 MeV), ¹⁸O + ²⁵⁴Es → ²⁶⁸Bh + 4n (160 pb at 84.22 MeV), ¹⁸O + ²⁵⁵Es → ²⁶⁹Bh + 4n (770 pb at 84 MeV), ¹⁸O + ²⁵⁷Fm → ²⁷¹Hs + 4n (520 pb at 84.56 MeV), ²²Ne + ²⁵²Es → ²⁷¹Mt + 3n (190 pb at 99.25 MeV), ²²Ne + ²⁵⁴Cf → ²⁷²Hs + 4n (190 pb at 101.87 MeV), ³²Si + ²⁴³Am → ²⁷²Mt + 3n (51 pb at 134.9 MeV), ²²Ne + ²⁵⁵Es → ²⁷³Mt + 4n (140 pb at 103.52 MeV), ²¹Ne + ²⁵⁷Fm → ²⁷⁴Ds + 4n (23 pb at 104.13 MeV), ³⁰Si + ²⁴⁸Bk → ²⁷⁵Rg + 3n (20 pb at 137.64 MeV), ²²Ne + ²⁵⁷Fm → ²⁷⁵Ds + 4n (20 pb at 104.92 MeV), ²²Ne + ²⁵⁷Fm → ²⁷⁶Ds + 3n (9.2 pb at 99.92 MeV), ³²Si + ²⁴⁷Bk → ²⁷⁶Rg + 3n (10 pb at 139.94 MeV), and ³²Si + ²⁴⁸Bk → ²⁷⁷Rg + 3n (18 pb at 139.31 MeV), respectively. However, it can be seen that for synthesis of ^278-280Cn the ER cross sections are approximately 1 pb, therefore, the reaction is still feasible with the available experimental equipment. The maximal evaporation cross sections, optimal incident energies, and corresponding evaporation channels are deduced and presented clearly in Table. 1. It is found that for synthesizing the isotopes ²⁶⁷Sg and ²⁶⁸Sg, the target ²⁵⁴Cf can be used. The ¹⁸O is predicted as a projectile, for producing both the isotopes ²⁶⁸Bh and ²⁶⁹Bh. In addition, the combinations of projectile and target are the same for synthesizing the ²⁷⁵Ds and ²⁷⁶Ds, but in different evaporation channels.

The optimal combinations for synthesis of SHN in the gap.

*ON	2*BC	2*EC	ECN^*(E_c.m.)	2*σ_{ER, max}(pb)
²⁶⁴Db	¹⁸O + ²⁴⁹Bk	3n	36 (79.36)	1.2 × 10¹
²⁶⁵Db	¹⁹F + ²⁵⁰Cm	4n	44 (89.55)	5.6
²⁶⁷Sg	¹⁷O + ²⁵⁴Cf	4n	40 (82.01)	8.2 × 10¹
²⁶⁸Sg	¹⁸O + ²⁵⁴Cf	4n	39 (82.87)	9.2 × 10²
²⁶⁸Bh	¹⁸O + ²⁵⁴Es	4n	39 (84.22)	1.6 × 10²
²⁶⁹Bh	¹⁸O + ²⁵⁵Es	4n	39 (84.00)	7.7 × 10²
²⁷¹Hs	¹⁸O + ²⁵⁷Fm	4n	38 (84.56)	5.2 × 10²
²⁷¹Mt	²²Ne + ²⁵²Es	3n	34 (99.25)	1.9 × 10²
²⁷²Hs	²²Ne + ²⁵⁴Cf	4n	39 (101.87)	1.9 × 10²
²⁷²Mt	³²Si + ²⁴³Am	3n	32 (134.9)	5.1 × 10¹
²⁷³Mt	²²Ne + ²⁵⁵Es	4n	39 (103.52)	1.4 × 10²
²⁷⁴Ds	²¹Ne + ²⁵⁷Fm	4n	43 (104.13)	2.3 × 10¹
²⁷⁵Rg	³⁰Si + ²⁴⁸Bk	3n	33 (137.64)	2.0 × 10¹
²⁷⁵Ds	²²Ne + ²⁵⁷Fm	4n	39 (104.92)	2.0 × 10¹
²⁷⁶Ds	²²Ne + ²⁵⁷Fm	3n	34 (99.92)	9.2
²⁷⁶Rg	³²Si + ²⁴⁷Bk	3n	32 (139.94)	1.0 × 10¹
²⁷⁷Rg	³²Si + ²⁴⁸Bk	3n	32 (139.31)	1.8 × 10¹
²⁷⁸Cn	³⁰Si + ²⁵¹Cf	3n	35 (140.57)	1.7
²⁷⁹Cn	³⁰Si + ²⁵²Cf	3n	36 (140.22)	1.1
²⁸⁰Cn	³⁰Si + ²⁵⁴Cf	4n	43 (144.86)	3.0

ON: Objective Nucleus

Figure 6:

(Color online) The excitation functions for synthesizing ²⁶⁴Db (a), ²⁶⁵Db (b), ²⁶⁷Sg (c), and ²⁶⁸Sg (d). The purple dotted lines, red solid lines, black dashed lines, and blue dash-dotted lines represent the 2n, 3n, 4n, and 5n evaporation channels, respectively. The red squares, black circles, and blue diamonds represent the experimental data of the 3n, 4n, and 5n evaporation channels, respectively. The red diamonds represent the largest cross sections.

Figure 7:

(Color online) The same as Fig. 5, but for ²⁶⁸Bh, ²⁶⁹Bh, ²⁷¹Hs, and ²⁷¹Mt.

Figure 8:

(Color online) The same as Fig. 6, but for ²⁷²Hs, ²⁷²Mt, ²⁷³Mt, and ²⁷⁴Ds.

Figure 9:

(Color online) The same as Fig. 6, but for ²⁷⁵Rg, ²⁷⁵Ds, ²⁷⁶Ds, and ²⁷⁶Rg.

Figure 10:

(Color online) The same as Fig. 6, but for ²⁷⁷Rg, ²⁷⁸Cn, ²⁷⁹Cn, and ²⁸⁰Cn.

4 Summary

The production of several SHN was investigated systematically within the dinuclear system model. The mass asymmetry effects were studied and it was observed that the fusion probabilities decreased with decreasing mass asymmetry. Suitable reactions for producing SHN in the gap region, as shown in Fig. 1, were predicted by reviewing the stable beam induced hot fusion reactions, and 192 possible combinations with projectiles from O to Ti and targets with half-lives longer than 30 days, for producing SHN ²⁶⁴Db, ²⁶⁵Db, ²⁶⁷Sg, ²⁶⁸Bh, ²⁶⁸Sg, ²⁶⁹Bh, ²⁷¹Hs, ²⁷¹Mt, ²⁷²Hs, ²⁷²Mt, ²⁷³Mt, ²⁷⁴Ds, ²⁷⁵Ds, ²⁷⁵Rg, ²⁷⁶Ds, ²⁷⁶Rg, ²⁷⁷Rg, ²⁷⁸Cn, ²⁷⁹Cn, and ²⁸⁰Cn were examined. The optimal combinations and incident energies for synthesizing these nuclei were predicted. It was found that the production cross sections, for synthesizing most of these SHN, were larger than 10 pb. The predicted cross section was 920 pb for the production of ²⁶⁸Sg; hence, the reaction could be carried out with the available experimental equipment. In future, it would be necessary to carry out systematic calculations on the production of SHN within other theoretical models so that a comparison of the predicted favorable reactions among the different models can provide valuable information regarding the experimental procedure.

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