Fig. 1. Radioactive secondary beam line in HI-13 tandem accelerator

Fig. 2. Typical inverse kinematics experiment setup for radioactive beam^[4]

Fig. 3. Angular distribution of ⁷Be(d, n)⁸B transfer reaction and DWBA fitting results^[2]

Fig. 4. Comparison between astrophysical S-factor of ¹³N(p, γ)¹⁴O obtained by Nuclear Astrophysics Research Group and other results^[3]

Fig. 5. Angular distribution of ⁸Li(d, p)⁹Li reaction and four DWBA results (a) and the astrophysics reaction rate of ⁸Li(n, γ)⁹Li (b)^[4]

Fig. 6. Comparison between the angular distribution of ¹H(⁶He, ⁶Li)n reaction and different DWBA results^[21]

Fig. 7. Exciting function of ¹³N+p elastic resonance scattering and results analyzed by R-matrix^[23]

Fig. 8. Exciting function of ¹⁷F+p elastic resonance scattering and results analyzed by R-matrix^[25]

Fig. 9. Q3D magnetic spectrometer

Fig. 10. Two-dimensional position-sensitive X4 silicon detector array

Fig. 11. Angular distribution of ¹³C(⁷Li, ⁶He)¹⁴N reaction producing ¹⁴N ground state and the first excited state — the DWBA results reproduced the experimental data well^[29]

Fig. 12. Angular distribution of ¹³C(⁹Be, ⁸Li)¹⁴N reaction and four sets of theoretical calculation results^[30]

Fig. 13. Effect spectrum and background spectrum of ²⁵Mg(⁷Li, ⁶He)²⁶Al reaction^[32]

Fig. 14. Angular distribution and calculation results of ¹⁵N(⁷Li, ⁶Li)¹⁶N reaction^[33]

Fig. 15. Comparison of results of astrophysical reaction rates of ¹³C(α, n)¹⁶O^[42]

Fig. 16. Astrophysical SE2 factor of ¹²C(α, γ)¹⁶O^[52]The data points represent the results of direct measurement (the uncertainty is 56%), the solid line represents the result of considering the data of ¹⁶O ground state ANC (the uncertainty is reduced to 10%), and, compared with the latest value recommended by RMP (dashed line)^[53], the new results increase by 55%.

Fig. 17. Relationship between the black hole mass and the initial mass of the He core of a star, which finally forms the black hole (a), and data of black hole mass measured by LIGO and Virgo (b)^[54]. In the Fig.(a), the point and dashed line below are, respectively, the upper and lower limits based on the present work, and the point and dashed line above are, respectively, the upper and lower limits based on the latest review of reaction rates. There is an obvious difference between the two results.

Table 1. Radioactive nuclear beams produced by GIRAFFE