Nuclear reaction study with radioactive ion beams is one of the most exciting research topics in modern nuclear physics. The development of radioactive ion beams has allowed nuclear scientists and engineers to explore many unknown exotic nuclei far from the valley of nuclear stability, and to further our understanding of the evolution of the universe.

The recently developed radioactive ion beam facility at the Lawrence Berkeley National Laboratory's 88-inch cyclotron is denoted as BEARS and provides ¹¹C, ¹⁴O and ¹⁵O radioactive ion beams of high quality. These moderate to high intensity, proton-rich radioactive ion beams have been used to explore the properties of unstable nuclei such as ¹²N and ¹⁵F.

In this work, the proton capture reaction on ¹¹C has been evaluated via the indirect d(¹¹C,¹²N)n transfer reaction using the inverse kinematics method coupled with the Asymptotic Normalization Coefficient (ANC) theoretical approach. The total effective ¹²N→¹¹C +p ANC is found to be [special characters omitted] = 1.83 ± 0.27 fm^-1. With the high ¹¹C beam intensity available, our experiment showed excellent agreement with theoretical predictions and previous experimental studies. This study also indirectly confirmed that the ¹¹C(p,γ) reaction is a key step in producing CNO nuclei in supermassive low-metallicity stars, bypassing the slow triple alpha process.

The newly developed ¹⁵O radioactive ion beam at BEARS was used to study the poorly known level widths of ¹⁶F via the p(¹⁵O,¹⁵O)p reaction. Among the nuclei in the A=16, T=1 isobaric triad, many states in ¹⁶N and ¹⁶O have been well established, but less has been reported on ¹⁶F. Four states of ¹⁶F below 1 MeV have been identified experimentally: 0^-, 1^-, 2-, and 3^- (E_x = 0.0, 0.19, 0.42, and 0.72 MeV, respectively). Our study utilized R-matrix analysis and found that the 0^- state has a level width of 23.1 ± 2.2 keV, and that the broader 1 ^- state has a width of 91.1 ± 9.9 keV. The level width of the 2^- state is found to be 3.3 ± 0.6 keV which is much narrower than the compiled value of 40 ± 30 keV, while a width of 14.1 ± 1.7 keV for the 3^- state is in good agreement with the reported value (< 15 keV). These experimental level widths of all four levels are also in accordance with theoretical predictions using single particle shell model calculation.