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.
Categories: nucl-th