Charge state distribution of ¹⁶O from the ⁴He( ¹²C,¹⁶O)γ reaction of astrophysical interest studied both experimentally and theoretically

In astrophysics, ⁴He(¹²C,¹⁶O)γ reaction places an important role. At Kyushu University Tandem accelerator Laboratory (KUTL), the measurement of ⁴He(¹²C, ¹⁶O)γ cross section is in progress in the energy range of astrophysical nuclear reaction. Since the charge state of product ¹⁶O ions after passing through the gas target is spread and only one charge state can be measured at terminal detector, it is necessary to know the charge state distribution of ¹⁶O ions passing through the He gas target precisely. Here, we report the charge state distribution of the ¹⁶O recoils both experimentally and theoretically. Experimentally, we measured the equilibrium charge state distribution of ¹⁶O ions in the windowless helium gas target with the beam energy of primary ¹⁶O ions at 7.2, 4.5, and 3.45 MeV at KUTL. The measured results showed a Gaussian distribution for the charge state fraction. Theoretically, we proposed a framework for the charge state distribution study. Charge state distribution was computed by solving a set of differential equations including a series of charge exchange cross sections. For the ionization cross section, plane-wave Born approximation was applied and modified by taking target atomic screening as a function of momentum transfer into account. For the capture cross section, continuum distorted wave approximation was applied and the influence of the gas target density was taken into account in the process of electron capture. Using above charge exchange cross sections, the charge state evolution was simulated. According to the equilibrium distribution, we compared the theoretical calculation to the experimental data. After taking into account the density effects in the charge exchange process, the theoretical charge state distributions shows a good agreement with the experimental data. Both experimental and theoretical results are useful to understand the charge fraction of recoil oxygen created via ⁴He(¹²C, ¹⁶O)γ reaction, especially in the energy range of astrophysical nuclear reaction.