The three-cluster generator coordinate method is applied to different properties of T=1/2 21-nucleon systems. The ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$ and ${}_{}{}^{21}{}_{}{}^{}\mathrm{Na}$ nuclei are described by mixing of different ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+α+n or ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+α+p configurations. A fair agreement with experiment is found for energy spectra and for electromagnetic transition probabilities. We present ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$+α and ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$+n elastic phase shifts, as well as ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$(α,γ${)}^{21}$Ne and ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$(α,n${)}^{20}$Ne low-energy cross sections. The ratio between the corresponding reaction rates is predicted 5 orders of magnitude lower than values currently used in astrophysics. We also compare ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$(p,p’${)}^{20}$Ne($2^{+}$), ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$(p,α${)}^{17}$F, and ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ (p,γ${)}^{21}$Na theoretical cross sections with experimental data. For the proton capture reaction, important in stellar evolution, we do not suggest significant differences with the existing reaction rate.

• Received 1 July 1993

DOI:https://doi.org/10.1103/PhysRevC.48.2746