Calculations of $p(n,\gamma )d$ reaction in chiral effective field theory

TL;DR

This paper calculates the low-energy proton-neutron radiative capture cross section using chiral effective field theory, demonstrating convergence and consistency with experimental data through systematic inclusion of higher-order interactions.

Contribution

The study provides a chirally consistent calculation of the $p(n,) d$ reaction cross section up to N2LO, showing improved convergence and reduced regulator dependence compared to previous models.

Findings

Results agree well with experimental data.

Cross sections show convergence with chiral order.

Regulator dependence is weak at higher orders.

Abstract

We present a calculation of the radiative capture cross section $p(n,\gamma )d$ in the low-energy range, where the $M1$ reaction channel dominates. Employing the LENPIC nucleon-nucleon interaction up to the fifth order (N4LO) that is regularized by the semi-local coordinate space regulators, we obtain the initial and final state wave functions, and evaluate the phase shifts of the scattering state and deuteron properties. We derive the transition operator from the chiral effective field theory up to the next-to-next-to leading order (N2LO), where we also regularize the transition operator using regulators consistent with those of the interactions. We compute the capture cross sections and the results show a converging pattern with the chiral-order expansion of the nucleon-nucleon interaction, where the regulator dependence of the results is weak when higher-order nucleon-nucleon interactions are employed. We quantify the uncertainties of the cross-section results due to the chiral-order truncation. The chirally complete and consistent cross-section results are performed up to N2LO and they compare well with the experiments and other theoretical predictions.