Introduction

As the center of the “island of stability" was predicted to be at Z = 114 and N = 184 by the macroscopic-microscopic model [1-5], reaching the next shell closure has been a major goal in nuclear physics. Various theoretical methods, including the Skyrme-Hartree-Fock approach and relativistic mean-field model, have predicted the proton and neutron shells at Z = 114, 120, 124, or 126 and N = 184 [3-13]. In recent years, superheavy elements with proton numbers up to Z = 118 have been synthesized via fusion reactions [14-25], along with the discovery of many new superheavy nuclei [26-33]. Despite these achievements, the neutron-rich superheavy nuclei region remains unknown.

The existence of superheavy nuclei with Z ≥ 104 is mainly attributed to shell-structure effects. This information has led to the investigation of superheavy isotopes near the shell closure. Nevertheless, the experimental feasibility to the “island of stability" via the stable beam-induced hot fusion reactions encounters challenges due to the limited availability of actinide target materials and the low neutron-to-proton ratio in the stable projectiles. Consequently, alternative approaches, including multinucleon transfer and radioactivity-induced fusion reactions, have been proposed. Nowadays, modern radioactive beam accelerators, such as the radioactive isotope Beam Factory (RIBF), Heavy Ion Research Facility in Lanzhou (HIRFL), Facility for Rare Isotope Beams (FRIB) and Second-generation System On-line Production of Radioactive Ions (SPIRAL2) [34-37], have been developed, offering new opportunities to explore the “island of stability" via radioactive-beam induced reactions in future experiments.

To describe the heavy-ion collision mechanisms, several macroscopic [38-45] and microscopic models [46-54] were developed and examined. One of the macroscopic models, the dinuclear system (DNS) model, is proved to be a reliable theoretical tool for describing the fusion-evaporation reactions [8, 55-74]. In this study, the optimal reaction systems and the corresponding incident energies for the synthesis of the predicted double magic nuclei ${}_{184}{}^{298}\text{F}\text{l}$ and ${}_{184}{}^{304}120$ via fusion reactions with radioactive beams were investigated using the DNS model.

The remainder of this article is organized as follows: In Sect. 2, the theoretical details of the DNS model are provided, followed by an evaluation of the reliability of the model using the experimental results of the evaporation residue (ER) cross sections of the fusion reactions ⁴⁸Ca+²⁴²Pu and ⁴⁸Ca+²⁴⁴Pu. In Sect. 3, the synthesis of the predicted double magic nucleus ²⁹⁸Fl employing neutron-rich radioactive projectiles and the ²⁴⁴Pu, ²⁴⁸Cm, and ²⁴⁹Bk targets is explored, and the entrance channel effect is discussed. In addition, radioactive-beam-induced reactions for the synthesis of the predicted double magic nucleus ³⁰⁴120 based on the ²⁴⁸Cm, ²⁴⁹Bk, and ²⁴⁹Cf targets were also investigated. In Sect. 4 presents the conclusions of this study.

Theoretical descriptions

Within the framework of the DNS model, the process of forming the superheavy nucleus is divided into capture, fusion, and survival stages, and the expression of the corresponding ER cross section can be written as $\begin{array}{c}{\sigma }_{\text{ER}}\left(E_{\text{c}\text{.m}\text{.}}\right)=\frac{\pi {\hslash }^2}{2\mu E_{\text{c}\text{.m}\text{.}}}{\displaystyle \sum _J(2J+1)}T\left(E_{\text{c}\text{.m}\text{.}}\mathrm{,}J\right)\\ \times P_{\text{CN}}\left(E_{\text{c}\text{.m}\text{.}}\mathrm{,}J\right)W_{\text{sur}}\left(E_{\text{c}\text{.m}\text{.}}\mathrm{,}J\right),\end{array}$ (1) T(E_c.m., J) is the transmission probability of colliding partners overcoming the Coulomb barrier and forming a DNS. $P_{\text{CN}}\left(E_{\text{c}\text{.m}\text{.}}\mathrm{,}J\right)$ is the fusion probability at which the projectile nucleon is transferred to the target, thereby forming a compound nucleus [75]. $W_{\text{sur}}\left(E_{\text{c}\text{.m}\text{.}}\mathrm{,}J\right)$ denotes the survival probability when the compound nucleus undergoes de-excitation via neutron emission rather than fission [76].

The expression for the capture cross-section σ_cap is as follows [58]: ${\sigma }_{\text{cap}}\left(E_{\text{c}\text{.m}\text{.}}\right)=\frac{\pi {\hslash }^2}{2\mu E_{\text{c}\text{.m}\text{.}}}{\displaystyle \sum _J\left(2J+1\right)}T\left(E_{\text{c}\text{.m}\text{.}}\mathrm{,}J\right)\mathrm{.}$ (2) where transmission probability is defined as follows: $T\left(E_{\text{c}\text{.m}\text{.}}\mathrm{,}J\right)={\displaystyle \int }f\left(B\right)T\left(E_{\text{c}\text{.m}\text{.}}\mathrm{,}B\mathrm{,}J\right)\text{d}B\mathrm{.}$ (3) Here, $T\left(E_{\text{c}\text{.m}\text{.}}\mathrm{,}B\mathrm{,}J\right)$ follows Ahmed’s formula [77-79]: The parameters of the asymmetric barrier distribution f(B) are adopted from Ref. [80]. The interaction potential of the colliding nuclei is defined as [58] $\begin{array}{c}V\left(R\mathrm{,}{\beta }_1\mathrm{,}{\beta }_2\mathrm{,}{\theta }_1\mathrm{,}{\theta }_2\right)=\frac{1}{2}{C}_1{\left({\beta }_1-{\beta }_1^0\right)}^2+\frac{1}{2}{C}_2{\left({\beta }_2-{\beta }_2^0\right)}^2\\ +V_{\text{C}}\left(R\mathrm{,}{\beta }_1\mathrm{,}{\beta }_2\mathrm{,}{\theta }_1\mathrm{,}{\theta }_2\right)\\ +V_{\text{N}}\left(R\mathrm{,}{\beta }_1\mathrm{,}{\beta }_2\mathrm{,}{\theta }_1\mathrm{,}{\theta }_2\right),\end{array}$ (4) where C_1,2 denotes the nuclear surface stiffness [81]. β_1,2 and ${\beta }_{\mathrm{1,2}}^0$ represent the dynamic quadrupole deformation and static deformation of the projectile and target nucleus, respectively. The Coulomb potential V_C is given by the Wong formula [82] and the nuclear potential V_N is described using the double-folding potential [83].

When the DNS evolves into a compound nucleus, the nucleon transfer process is driven by the driving potential along the degree of mass asymmetry $\eta =\left(A_{\text{1}}-A_{\text{2}}\right)/\left(A_{\text{1}}+A_{\text{2}}\right)$ [58]. The distribution probability of fragments $P\left(Z_{\text{1}}\mathrm{,}{N}_{\text{1}}\mathrm{,}{E}_{\text{1}}\mathrm{,}t\right)$ can be obtained by solving the following set of master equations: $\begin{array}{c}\frac{\text{d}P\left(Z_1\mathrm{,}{N}_1\mathrm{,}{E}_1\mathrm{,}t\right)}{\text{d}t}\\ ={\displaystyle \sum _{Z_1^{\text{'}}}{W}_{Z_1\mathrm{,}{N}_1;Z_1^{\text{'}}\mathrm{,}{N}_1}}\left(t\right)\\ \times \left[d_{Z_1\mathrm{,}{N}_1}P\left(Z_1^{\text{'}}\mathrm{,}{N}_1\mathrm{,}{E}_1\mathrm{,}t\right)-d_{Z_1^{\text{'}}\mathrm{,}{N}_1}P\left(Z_1\mathrm{,}{N}_1\mathrm{,}{E}_1\mathrm{,}t\right)\right]\\ +{\displaystyle \sum _{N_1^{\text{'}}}{W}_{Z_1\mathrm{,}{N}_1;Z_1\mathrm{,}{N}_1^{\text{'}}}}\left(t\right)\\ \times \left[d_{Z_1\mathrm{,}{N}_1}P\left(Z_1\mathrm{,}{N}_1^{\text{'}}\mathrm{,}{E}_1\mathrm{,}t\right)-d_{Z_1\mathrm{,}{N}_1^{\text{'}}}P\left(Z_1\mathrm{,}{N}_1\mathrm{,}{E}_1\mathrm{,}t\right)\right]\\ -\left[{\Lambda }_{\text{qf}}\left(\Theta \left(t\right)\right)+{\Lambda }_{\text{fis}}\left(\Theta \left(t\right)\right)\right]P\left(Z_1\mathrm{,}{N}_1\mathrm{,}{E}_1\mathrm{,}t\right)\mathrm{.}\end{array}$ (5) Here $W_{Z_1\mathrm{,}{N}_1;Z_1^{\text{'}}\mathrm{,}{N}_1}$ denotes the mean transition probability between state (Z₁, N₁) and $\left(Z_1^{\text{'}}\mathrm{,}{N}_1\right)$ [84], with $d_{Z_1\mathrm{,}{N}_1}$ representing the microscopic dimension. The likelihood of the DNS decaying via quasi-fission and the probability of heavy fragment fission are denoted by the quasi-fission probability Λ_qf and the fission probability Λ_fis, which are determined using the one-dimensional Kramers formula [85].

The complete fusion process within the DNS requires overcoming the inner fusion barrier B_fus, which originates from the potential energy difference between the incident point and the B.G. point [86]. Thus, the fusion probability can be obtained by adding the distribution probabilities that overcome the inner fusion barrier. $P_{\text{CN}}\left(E_{\text{c}\text{.m}\text{.}}\mathrm{,}J\right)={\displaystyle \sum _{Z_1=1}^{Z_{\text{B}\text{.G}\text{.}}}{\displaystyle \sum _{N_1=1}^{N_{\text{B}\text{.G}\text{.}}}P\left(Z_1\mathrm{,}{N}_1\mathrm{,}{E}_1\mathrm{,}{\tau }_{\text{int}}\left(J\right)\right)}},$ (6) where the interaction time ${\tau }_{\text{int}}\left(J\right)$ is estimated using the deflection function method [87].

During the survival stage, the excited compound nucleus is unstable and undergoes light particle emission or fission to reach the ground stage. The survival probability for neutron emission competing with fission at excitation energy $E_{\text{CN}}^{*}$ is calculated as $\begin{array}{l}{W}_{\text{sur}}\left(E_{\text{CN}}^{*}\mathrm{,}x\mathrm{,}J\right)\\ =P\left(E_{\text{CN}}^{*}\mathrm{,}x\mathrm{,}J\right){\displaystyle \prod _{i=1}^x}\left[\frac{{\Gamma }_{\text{n}}\left(E_i^{*}\mathrm{,}J\right)}{{\Gamma }_{\text{n}}\left(E_i^{*}\mathrm{,}J\right)+{\Gamma }_{\text{f}}\left(E_i^{*}\mathrm{,}J\right)}\right].\end{array}$ (7) $P\left(E_{\text{CN}}^{*}\mathrm{,}x\mathrm{,}J\right)$ denotes the realization probability that the compound nucleus evaporates x neutrons [88]. The partial decay width for neutron evaporation ${\Gamma }_{\text{n}}$ and the fission decay width ${\Gamma }_{\text{f}}$ were determined using the Weisskopf-Ewing theory [89] and the Bohr-Wheeler transition-state method [90], with the level density given by the standard Fermi gas model [91]. The fission barrier is defined as: $\begin{array}{c}{B}_{\text{f}}\left(E_i^{*}\mathrm{,}J\right)=B_{\text{f}}^{\text{LD}}\left(1-x_{\text{LD}}{T}_i^2\right)\\ +B_{\text{f}}^{\text{M}}\left(E_i^{*}=0\right)\exp \left(-\frac{E_i^{*}}{E_{\text{D}}}\right)\\ -\left(\frac{{\hslash }^2}{2J_{\text{g}\text{.s}\text{.}}}-\frac{{\hslash }^2}{2J_{\text{s}\text{.d}\text{.}}}\right)J\left(J+1\right)\mathrm{,}\end{array}$ (8) Here, $E_i^{*}$ represents the excitation energy prior to the emission of the ith neutron. $B_{\text{f}}{}^{\text{LD}}$ is the macroscopic part determined by the liquid-drop model and $B_{\text{f}}{}^{\text{M}}$ represents the microscopic shell correction [1]. x_LD is a temperature dependent parameter [91]. The range of shell damping energy E_D introduces theoretical uncertainties [64, 92, 93], indicating an excitation-energy-dependent shell effect. $J_{\text{g}\text{.s}\text{.}}$ and $J_{\text{s}\text{.d}\text{.}}$ denote the moments of inertia of the compound nucleus in its ground state and saddle point, respectively, [94, 95].

Based on the ample experimental results obtained from the reactions ⁴⁸Ca+²⁴²Pu→^290-xnFl+xn and ⁴⁸Ca+²⁴⁴Pu→^292-xnFl+xn, the reliability of the DNS model has been evaluated, as illustrated in Fig. 1. For the majority of the experimental data, the calculated ER cross sections are in good agreement within the error margin. This consistency supports the reliability of the DNS model for identifying the optimal reaction systems and the corresponding incident energies for producing new superheavy nuclei through fusion reactions.

Fig. 1Full-screen View

(Color online) Comparison of the calculated results with the available experimental data from the reactions ⁴⁸Ca+^242,244Pu [98-103]. The calculation uncertainties are given by the shaded areas

Results and discussion

3.1

The synthesis of the predicted double-magic nucleus ²⁹⁸Fl with the ²⁴⁴Pu target

Many Fl isotopes have been synthesized via hot fusion reactions using Pu targets [96-103]. Among the available Pu targets, the neutron-rich ²⁴⁴Pu target has emerged as a promising candidate for achieving the next shell closure, N = 184. Through hot fusion reactions with the ²⁴⁴Pu target and radioactive projectiles ^56,57,58Ca, the synthesis of the double-magic nucleus ²⁹⁸Fl predicted by the macroscopic-microscopic model is investigated.

For the reaction ⁵⁶Ca+²⁴⁴Pu→²⁹⁸Fl+2n, the predicted maximal ER cross section of 0.0005 pb which calculated by DNS model, is significantly below the detection limitation. In contrast, the ER cross sections for the reactions ⁵⁷Ca+²⁴⁴Pu→²⁹⁸Fl+3n and ⁵⁸Ca+²⁴⁴Pu→²⁹⁸Fl+4n are presented in Fig. 2. The maximal ER cross section for the latter reaction reaches 0.301 pb, which is approximately an order of magnitude higher than that 0.044 pb for the reaction ⁵⁷Ca+²⁴⁴Pu→²⁹⁸Fl+3n. It is observed that the predicted maximal ER cross sections for the reactions induced by radioactive Ca beams are suppressed when compared to those induced by ⁴⁸Ca. To further investigate this phenomenon, the capture, fusion and survival stages of the reactions ⁴⁸Ca+²⁴⁴Pu→²⁸⁸Fl+4n and ⁵⁸Ca+²⁴⁴Pu→²⁹⁸Fl+4n are investigated in Fig. 3.

Fig. 2Full-screen View

(Color online) The calculated ER cross sections for the reactions ⁵⁷Ca+²⁴⁴Pu→²⁹⁸Fl+3n and ⁵⁸Ca+²⁴⁴Pu→²⁹⁸Fl+4n. The calculation uncertainties are given by the shaded areas

Fig. 3Full-screen View

(Color online) (a) The calculated capture cross sections, (b) fusion probabilities and (c) survival probabilities of the reactions ⁴⁸Ca+²⁴⁴Pu→²⁸⁸Fl+4n (black solid lines) and ⁵⁸Ca+²⁴⁴Pu→²⁹⁸Fl+4n (red dash-dot lines). The experimental values for the reaction ⁴⁸Ca+²⁴⁴Pu are denoted by the black circles [104]

Figure 3(a) shows the calculated capture cross sections for the reactions ^48,58Ca+²⁴⁴Pu alongside the experimental data of the reaction ⁴⁸Ca+²⁴⁴Pu. It reveals an increasing trend for the capture cross sections with increasing $E_{\text{CN}}^{*}$, which can be attributed to the enhanced probability of the colliding nuclei overcoming the Coulomb barrier at elevated $E_{\text{CN}}^{*}$. The alignment between the calculated and experimental results for the reaction ⁴⁸Ca+²⁴⁴Pu supports the predictive ability of the empirical coupled channel model. For the reaction ⁵⁸Ca+²⁴⁴Pu, the excitation energy of the Coulomb barrier V_B+Q is 42.4 MeV. This value is approximately 8.3 MeV higher than that of the reaction ⁴⁸Ca+²⁴⁴Pu, which is 34.1 MeV. Consequently, such a significant increase in the V_B+Q value for the ⁵⁸Ca-induced reaction leads to a suppressed capture cross-section at low $E_{\text{CN}}^{*}$.

In Fig. 3(b), the fusion probabilities for the reactions ^48,58Ca+²⁴⁴Pu are depicted. The fusion probability exhibited an upward trend with increasing $E_{\text{CN}}^{*}$, which is ascribed to the increased likelihood of overcoming the inner fusion barrier at a high $E_{\text{CN}}^{*}$. Notably, the fusion probability of the reaction ⁵⁸Ca+²⁴⁴Pu was lower than that for the reaction ⁴⁸Ca+²⁴⁴Pu. This difference is primarily due to variations in the inner fusion barrier, which are influenced by the mass asymmetry of the reaction system. A further analysis is shown in Fig. 4 elaborates on the influence of the driving potential in the fusion process. This reveals that the lower mass asymmetry of reaction ⁵⁸Ca+²⁴⁴Pu results in an incident point substantially distant from the B.G. point. Consequently, the inner fusion barrier for the reaction ⁵⁸Ca+²⁴⁴Pu is 13.1 MeV, which is significantly higher than that for the reaction ⁴⁸Ca+²⁴⁴Pu (9.4 MeV). This marked difference in the inner fusion barriers accounts for the observed suppression of the fusion probability for the reaction ⁵⁸Ca+²⁴⁴Pu in Fig. 3(b), revealing the crucial role of mass asymmetry in influencing the formation of the compound nucleus in the fusion process.

Fig. 4Full-screen View

(Color online) The driving potential as a function of mass asymmetry for the reactions ^48,58Ca+²⁴⁴Pu. The entrance channel of the reactions ⁴⁸Ca+²⁴⁴Pu and ⁵⁸Ca+²⁴⁴Pu are represented by the black solid line arrow and the red dashed line arrow

Figure 3(c) illustrates the survival probabilities for the formation of nuclei ²⁸⁸Fl and ²⁹⁸Fl via the 4n-emission channel. The survival probability of the nucleus ²⁹⁸Fl was observed to be slightly higher than that of ²⁸⁸Fl. However, fission became the dominant de-excitation mode at high $E_{\text{CN}}^{*}$, which leads to a downward trend in the survival probabilities. Consequently, the disparity in survival probabilities diminishes in the high $E_{\text{CN}}^{*}$ region. This decline in the survival probability at elevated $E_{\text{CN}}^{*}$, coupled with the suppression of the capture and fusion probabilities, results in a reduced maximal ER cross section for the synthesis of ²⁹⁸Fl using radioactive Ca projectiles in comparison to the Fl isotopes produced with the ⁴⁸Ca beam.

3.2

The synthesis of the predicted double-magic nucleus ²⁹⁸Fl with the ²⁴⁸Cm and ²⁴⁹Bk targets

Among the experimentally accessible actinide targets, ²⁴⁸Cm and ²⁴⁹Bk, which have a neutron number of 152, are the most neutron-rich target materials currently available for fusion reactions aimed at exploring the neutron-rich superheavy nuclei region. Table 1 presents the maximal ER cross sections for the synthesis of the double-magic nucleus ²⁹⁸Fl through fusion reactions using ²⁴⁸Cm and ²⁴⁹Bk targets and radioactive projectiles ^52-54Ar and ^51,52Cl, in comparison to reactions involving the ²⁴⁴Pu target. The maximal ER cross section for a ²⁴⁸Cm-based reaction is 0.129 pb for the reaction ⁵⁴Ar+²⁴⁸Cm→²⁹⁸Fl+4n. In contrast, for the ²⁴⁹Bk-based reactions, the maximal ER cross section achieved with the heaviest known ⁵²Cl projectile was approximately 0.004 pb.

Tab. 1Full-screen View

The predicted maximal ER cross sections, the corresponding optimal incident energy $E_{\text{c}\text{.m}\text{.}}$ and the $E_{\text{CN}}^{*}$ of the radioactive-beam induced reactions for producing the predicted double-magic nucleus ²⁹⁸Fl

Reaction	Ec.m. (MeV)	$E_{\text{CN}}^{*}$(MeV)	${\sigma }_{\text{ER}}^{\text{max}}$(pb)
244Pu(58Ca,4n)298Fl	189.8	43.0	${0.301}_{-0.130}^{+0.204}$
248Cm(54Ar,4n)298Fl	178.5	53.0	${0.129}_{-0.046}^{+0.070}$
244Pu(57Ca,3n)298Fl	191.2	43.0	${0.044}_{-0.015}^{+0.021}$
248Cm(53Ar,3n)298Fl	178.8	51.0	${0.020}_{-0.006}^{+0.008}$
249Bk(52Cl,3n)298Fl	170.3	60.0	${0.004}_{-0.001}^{+0.001}$
244Pu(56Ca,2n)298Fl	194.3	44.0	${0.0005}_{-0.0001}^{+0.0002}$
248Cm(52Ar,2n)298Fl	180.0	49.0	${0.0003}_{-0.00006}^{+0.00008}$
249Bk(51Cl,2n)298Fl	170.3	57.0	${0.0001}_{-0.00002}^{+0.00002}$

Show more

Despite the higher number of neutrons in the ²⁴⁸Cm and ²⁴⁹Bk targets, Table 1 suggests that the maximal ER cross sections achieved by these targets do not present a clear advantage over those achieved by the ²⁴⁴Pu-based reactions. Further examination of the entrance channel effects is shown in Fig. 5, which includes the capture cross sections, fusion probabilities and ER cross sections for the reactions ⁵³Ar+²⁴⁸Cm→²⁹⁸Fl+3n and ⁵²Cl+²⁴⁹Bk→²⁹⁸Fl+3n. High V_B+Q values for the reactions ⁵³Ar+²⁴⁸Cm (46.9 MeV) and ⁵²Cl+²⁴⁹Bk (56.2 MeV) significantly suppress the capture cross sections for these reactions as depicted in Fig. 5(a), in comparison to the reaction ⁵⁸Ca+²⁴⁴Pu in Fig. 3(a).

Fig. 5Full-screen View

(Color online) (a) The calculated capture cross sections, (b) fusion probabilities and (c) ER cross sections of the reactions ⁵³Ar+²⁴⁸Cm→²⁹⁸Fl+3n and ⁵²Cl+²⁴⁹Bk→²⁹⁸Fl+3n. The calculation uncertainties are given by the shaded areas

During the fusion process, as illustrated in Fig. 5(b), the fusion probability for the reaction ⁵²Cl+²⁴⁹Bk is slightly higher than that for the reaction ⁵³Ar+²⁴⁸Cm, owing to the relatively higher mass asymmetry of the ⁵²Cl+²⁴⁹Bk reaction. It can be observed that the high mass asymmetry values contribute to the fusion probabilities for these reactions, surpassing that of the reaction ⁵⁸Ca+²⁴⁴Pu in Fig. 3(b). Despite the enhancement in the fusion stage, the maximal ER cross sections for synthesizing ²⁹⁸Fl remain suppressed in reactions based on ²⁴⁸Cm and ²⁴⁹Bk targets in Fig. 5(c), primarily due to the reduced capture cross sections. Note that ⁵⁸Ca is a weakly bound nucleus. The complex structure and low binding energy of ⁵⁸Ca may lead to neutron evaporation or projectile breakup, potentially suppressing the ER cross section.

3.3

Investigations on the synthesis of the predicted double-magic nucleus ³⁰⁴120

For the synthesis of the double-magic nucleus ³⁰⁴120 predicted by the relativistic mean-field model, the reaction systems employing the radioactive projectiles and the experimentally accessible heavy actinide targets ²⁴⁹Cf, ²⁴⁹Bk and ²⁴⁸Cm are investigated. The calculated maximal ER cross sections and corresponding incident energies for these reactions to synthesize ³⁰⁴120 are presented in Table 2. This reveals that among the investigated reaction systems, the highest maximal ER cross section of 0.046 fb emerges in the reaction ⁵⁸V+²⁴⁹Bk→³⁰⁴120+3n.

Tab. 2Full-screen View

The same as in Table 1, but for producing the predicted double-magic nucleus ³⁰⁴120

Reaction	Ec.m. (MeV)	$E_{\text{CN}}^{*}$(MeV)	${\sigma }_{\text{ER}}^{\text{max}}$ (fb)
249Bk(58V,3n)304120	237.1	38.0	${0.046}_{-0.016}^{+0.022}$
248Cm(59Cr,3n)304120	246.3	37.0	${0.042}_{-0.015}^{+0.021}$
249Cf(58Ti,3n)304120	229.8	39.0	${0.036}_{-0.012}^{+0.017}$
249Cf(59Ti,4n)304120	230.0	47.0	${0.025}_{-0.008}^{+0.014}$
248Cm(60Cr,4n)304120	255.2	46.0	${0.019}_{-0.006}^{+0.011}$
249Bk(59V,4n)304120	245.4	48.0	${0.017}_{-0.005}^{+0.009}$
248Cm(58Cr,2n)304120	246.2	36.0	${0.008}_{-0.002}^{+0.003}$
249Bk(57V,2n)304120	237.0	37.0	${0.008}_{-0.002}^{+0.002}$
249Cf(57Ti,2n)304120	227.5	38.0	${0.006}_{-0.001}^{+0.002}$

Show more

Figure 6 further illustrates the ER cross sections for the reactions ⁵⁸Ti+²⁴⁹Cf→³⁰⁴120+3n, ⁵⁹Ti+²⁴⁹Cf→³⁰⁴120+4n, ⁵⁸V+²⁴⁹Bk→³⁰⁴120+3n, ⁵⁹V+²⁴⁹Bk→³⁰⁴120+4n, ⁵⁹Cr+²⁴⁸Cm→³⁰⁴120+3n, ⁶⁰Cr+²⁴⁸Cm→³⁰⁴120+4n. It can be found that the 3n-emission channel is promising for the synthesis of ³⁰⁴120. Nevertheless, the maximal ER cross sections are approximately 10^-2 femtobarns, which is significantly lower than the current detection capabilities. Therefore, the advancement of experimental methodologies is required, including the development of more experimentally feasible neutron-rich radioactive projectiles, enhancement of radioactive beam intensities, improvement of detection techniques, and exploration of alternative reaction mechanisms such as multi-nucleon transfer reactions. These approaches are critical for reaching the center of the predicted island of stability.

Fig. 6Full-screen View

(Color online) The predicted ER cross sections for the reactions (a) ⁵⁸Ti+²⁴⁹Cf→³⁰⁴120+3n, ⁵⁹Ti+²⁴⁹Cf→³⁰⁴120+4n, (b) ⁶⁰Cr+²⁴⁹Bk→³⁰⁴120+3n, ⁵⁹V+²⁴⁹Bk→³⁰⁴120+4n and (c) ⁵⁹Cr+²⁴⁸Cm→³⁰⁴120+3n, ⁶⁰Cr+²⁴⁸Cm→³⁰⁴120+4n. The calculation uncertainties are given by the shaded areas

Summary

In this study, a comprehensive investigation of radioactive-beam-induced fusion reactions was conducted to approach the center of the predicted “island of stability.” By employing radioactive projectiles ^56-58Ca, ^52-54Ar and ^51,52Cl combining with the ²⁴⁴Pu, ²⁴⁸Cm and ²⁴⁹Bk targets, the synthesis of the predicted double-magic nucleus ²⁹⁸Fl is investigated. The maximum ER cross section of 0.301 pb appears in the reaction ⁵⁸Ca+²⁴⁴Pu→²⁹⁸Fl+4n. The capture, fusion and survival stages are discussed for the reactions ⁴⁸Ca+²⁴⁴Pu→²⁸⁸Fl+4n and ⁵⁸Ca+²⁴⁴Pu→²⁹⁸Fl+4n, revealing that the critical influence of the Coulomb barrier and mass asymmetry results in the reduced maximal ER cross section for the reaction ⁵⁸Ca+²⁴⁴Pu→²⁹⁸Fl+4n. The effects of the entrance channel were also investigated, indicating that the ²⁴⁴Pu target is more promising than the neutron-rich ²⁴⁸Cm and ²⁴⁹Bk targets for synthesizing the nucleus ²⁹⁸Fl, primarily owing to the influence of the Coulomb barrier. Additionally, for the synthesis of the predicted double-magic nucleus ³⁰⁴120, the maximal ER cross section is predicted to be 0.046 fb for the reaction ⁵⁸V+²⁴⁹Bk→³⁰⁴120+3n, necessitating further development in both experimental techniques and reaction mechanisms.