Asymptotic normalization coefficient method for two-proton radiative capture

TL;DR

This paper extends the asymptotic normalization coefficient method to three-body two-proton radiative capture processes, highlighting the importance of correlations and Coulomb interactions, with an application to the $^{15}$O + $p$ + $p$ to $^{17}$Ne process.

Contribution

The paper generalizes the asymptotic normalization coefficient method to three-body radiative captures, addressing the complex Coulomb correlations involved.

Findings

The method can be applied to three-body radiative captures.

Highly correlated nature of the three-body process is essential.

Application to $^{15}$O + $p$ + $p$ demonstrates the approach.

Abstract

The method of asymptotic normalization coefficients is a standard approach for studies of two-body non-resonant radiative capture processes in nuclear astrophysics. This method suggests a fully analytical description of the radiative capture cross section in the low-energy region of the astrophysical interest. We demonstrate how this method can be generalized to the case of three-body $2p$ radiative captures. It was found that an essential feature of this process is the highly correlated nature of the capture. This reflects the complexity of three-body Coulomb continuum problem. Radiative capture $^{15}$O+$p$+$p \rightarrow ^{\,17}$Ne+$\gamma$ is considered as an illustration.