Radioactive-isotope (RI) beams are essential for studies on relevant astrophysical reactions involving RIs. RIs play important roles in high-temperature stellar environments, but the experimental study of RI-involving astrophysical reactions is still challenging for many cases, mainly due to the limited intensity of the RI beam. Researchers have devised several methods to overcome this difficulty. Here we discuss the development of the RI beams at the low-energy RI beam separator CRIB, operated by Center for Nuclear Study, the University of Tokyo. We also introduce recent successful cases of astrophysical reaction study at CRIB. One is a study on the 22Mg(α, p), which is a relevant reaction in high-temperature stellar environment such as X-ray bursts. Another is an experiment on the 7Be(n, p) and 7Be(n, α) reactions in the Big-Bang nucleosynthesis with the “Trojan-horse” method, performed for investigating the 7Li abundance problem in the primordial universe
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