Radiative capture reaction for ${}^{17}$Ne formation within a full three-body model

Abstract

Background: The breakout from the hot Carbon-Nitrogen-Oxigen (CNO) cycles can trigger the rp-process in type I x-ray bursts. In this environment, a competition between ${}^{15}\text{O}(\alpha ,\gamma ){}^{19}\text{Ne}$ and the two-proton capture reaction ${}^{15}\text{O}(2p,\gamma ){}^{17}\text{Ne}$ is expected. Purpose: Determine the three-body radiative capture reaction rate for ${}^{17}\text{Ne}$ formation including sequential and direct, resonant and non-resonant contributions on an equal footing. Method: Two different discretization methods have been applied to generate ${}^{17}$Ne states in a full three-body model: the analytical transformed harmonic oscillator method and the hyperspherical adiabatic expansion method. The binary $p$--${}^{15}$O interaction has been adjusted to reproduce the known spectrum of the unbound ${}^{16}$F nucleus. The dominant $E1$ contributions to the ${}^{15}\text{O}(2p,\gamma ){}^{17}\text{Ne}$ reaction rate have been calculated from the inverse photodissociation process. Results: Three-body calculations provide a reliable description of ${}^{17}$Ne states. The agreement with the available experimental data on ${}^{17}$Ne is discussed. It is shown that the ${}^{15}\text{O}(2p,\gamma ){}^{17}\text{Ne}$ reaction rates computed within the two methods agree in a broad range of temperatures. The present calculations are compared with a previous theoretical estimation of the reaction rate. Conclusions: It is found that the full three-body model provides a reaction rate several orders of magnitude larger than the only previous estimation. The implications for the rp-process in type I x-ray bursts should be investigated.

Comments: 10 pages, 10 figures. Corrected version