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Fusion reactions not only provide key information for studying the dynamic evolution and dissipation mechanisms in quantum many-body systems, but also open up an important avenue for exploring the reaction dynamics and structural characteristics of atomic nuclei. In recent years, with the continuous development of the technology for synthesizing new elements and their isotopes via fusion reactions, a series of new elements and their isotopes have been successfully synthesized. This paper systematically summarizes the synthesis pathways of elements in different mass regions, ranging from hydrogen to mendelevium, as well as the experimental progress of various heavy-ion fusion reactions from light systems to heavy systems. It reviews the advantages and limitations of current theoretical models in describing the capture process, and focuses on analyzing the strengths and shortcomings of phenomenological models and microscopic dynamic models in explaining the fusion behavior of different reaction systems. For the capture cross sections in light nuclei-light nuclei reaction systems, the EBD method, the CCFULL model, the universal Wong formula, and the ImQMD model all demonstrate good agreement with the experimental data. For the systems involving light nuclei-medium mass nuclei and light nuclei-heavy nuclei, the mentioned above models provide satisfactory descriptions. In particular, for the 16O+144Sm reaction system, the results obtained from the CCFULL model show good agreement with experimental data across both the sub-barrier and above-barrier energy regions. For the heavy nuclei-heavy nuclei systems, however, the EBD method holds a distinct advantage. Therefore, in subsequent predictions of the evaporation residue cross sections for superheavy elements, the results calculated by the EBD method can serve as the input for the capture cross section. On this basis, several key scientific issues in fusion reaction research are proposed, including heavy-ion fusion hindrance, the phenomenon of fusion suppression at extreme sub-barrier energies, fusion probability $P_{\text{CN}}$, and the fission barrier of compound nuclei, etc. Furthermore, an outlook and suggestions for future research directions in fusion reactions are provided.
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Keywords:
- fusion reaction /
- nuclear reaction model /
- capture cross section /
- evaporation residue cross section
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图 4 (a) 基于FBD模型计算的48Ca+244Pu的俘获截面$ \sigma_{\text{cap}} $和熔合截面$ \sigma_{\text{fus}} $; (b) 基于FBD模型计算的48Ca+248Cm的俘获截面$ \sigma_{\text{cap}} $和熔合截面$ \sigma_{\text{fus}} $[83]
Figure 4. (a) The capture cross sections $ \sigma_{\text{cap}} $ and fusion cross sections $ \sigma_{\text{fus}} $ for the 48Ca+244Pu system calculated by the FBD model; (b) The capture cross sections $ \sigma_{\text{cap}} $ and fusion cross sections $ \sigma_{\text{fus}} $ for the 48Ca+248Cm system calculated by the FBD model[83].
图 8 (a) 58Ni+58Ni反应不同弥散参数下的熔合激发函数; (b) 58Ni+58Ni反应不同弥散参数下的指数斜率[121]
Figure 8. (a) The fusion excitation functions for the $ ^{58}{\rm{Ni}}+^{58}{\rm{Ni}} $ reaction for different surface diffuseness parameters; (b) The logarithmic slopes for the $ {}^{58}{\rm{Ni}}+{}^{58}{\rm{Ni}} $ reaction for different surface diffuseness parameters[121].
表 1 在轻核-轻核反应体系中, 实验观测到的熔合截面与该入射能量下理论模型的比较
Table 1. Comparison between experimental cross sections and theoretical models for light nuclei-light nuclei fusion reaction systems at the incident energy.
反应体系 $ E_{\text{c.m.}} $(MeV) $ \sigma_{\text{fus}}^{\text{exp}} $(mb) $ \sigma_{\text{fus}}^{\text{ECC}} $(mb) $ \sigma_{\text{fus}}^{\text{EBD2}} $[62](mb) $ \sigma_{\text{fus}}^{\text{CCFULL}} $[65](mb) $ \sigma_{\text{fus}}^{\text{Wong}} $(mb) $ \sigma_{\text{fus}}^{\text{ImQMD}} $(mb) 12C+14C→26Mg 8.000 393.355[30] 936.203 513.288 606.788 505.773 477.836 14N+16O→30P 11.988 429.722[27] 777.552 445.524 — 448.672 476.894 16O+16O→32S 12.514 433.638[29] 659.073 337.543 413.014 334.054 342.434 12C+20Ne→32S 14.965 467.280[28] 873.843 639.505 762.936 696.192 698.062 
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表 2 在轻核-中重核、轻核-重核反应体系中, 实验观测到的俘获截面与该入射能量下理论模型的比较
Table 2. Comparison between experimental cross sections and theoretical models for light nuclei-medium mass nuclei and light nuclei-heavy nuclei fusion reaction systems at the incident energy.
反应体系 $ E_{\text{c.m.}} $(MeV) $ \sigma_{\text{cap}}^{\text{exp}} $[71](mb) $ \sigma_{\text{cap}}^{\text{ECC}} $(mb) $ \sigma_{\text{cap}}^{\text{EBD2}} $[62](mb) $ \sigma_{\text{cap}}^{\text{CCFULL}} $[65](mb) $ \sigma_{\text{cap}}^{\text{Wong}} $(mb) $ \sigma_{\text{cap}}^{\text{ImQMD}} $(mb) 12C+206Pb→218Ra 80.150 872.246 1113.600 986.338 852.125 1113.373 1322.925 14N+232Th→246Bk 86.390 823.000 656.404 676.666 — 745.517 912.004 15N+209Bi→224Th 82.297 705.589 785.167 704.484 — 769.015 965.097 16O+209Bi→225Pa 93.185 688.362 732.198 659.206 — 743.462 917.345 16O+144Sm→160Yb 80.89 876.000 870.274 776.450 879.439 857.778 1013.1636 16O+208Pb→226Th 100.72 949.000 974.760 888.832 1173.059 1022.355 1222.394 23Na+48Ti→71As 45.207 687.284 645.242 583.905 — 682.850 757.438 28Si+208Pb→236Cm 156.821 726.666 371.941 656.247 471.170 766.809 1032.956 30Si+238U→268Sg 169.001 780.325 638.769 673.966 447.388 751.604 976.721 34S+89Y→123Cs 91.050 505.000 465.149 434.505 — 464.238 544.124 37Cl+100Mo→137Pr 94.539 250.231 217.034 274.459 — 280.626 346.832
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表 3 在重核-重核反应体系中, 实验观测到的俘获截面与该入射能量下理论模型的比较
Table 3. Comparison between experimental cross sections and theoretical models for heavy nuclei-heavy nuclei fusion reaction systems at the incident energy.
反应体系 $ E_{\text{c.m.}} $(MeV) $ \sigma_{\text{cap}}^{\text{exp}} $[72](mb) $ \sigma_{\text{cap}}^{\text{ECC}} $(mb) $ \sigma_{\text{cap}}^{\text{EBD2}} $[62](mb) $ \sigma_{\text{cap}}^{\text{Wong}} $(mb) $ \sigma_{\text{cap}}^{\text{ImQMD}} $(mb) 48Ca+238U→286Cn 214.7 502 ± 100 375.835 359.819 367.476 562.973 48Ca+244Pu→292Fl 204 126 ± 63 133.976 153.076 160.059 195.093 48Ca+248Cm→296Lv 206 69 ± 35 108.700 120.816 132.157 176.872 48Ti+238U→286Fl 226 250 ± 40 191.874 153.741 197.252 256.668 52Cr+232Th→284Fl 261 410 ± 100 364.361 255.807 344.598 603.500 52Cr+248Cm→300120 251 88 ± 10 145.230 77.347 117.075 146.084 54Cr+248Cm→302120 242 15 ± 3 58.305 36.777 60.473 70.529 64Ni+238U→302120 301 123 ± 37 42.351 139.730 137.971 452.075
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