Study of nonlocality effects in direct capture reactions with Lagrange-mesh $R$-matrix method

TL;DR

This paper uses the Lagrange-mesh R-matrix method to analyze nonlocality effects in direct capture reactions, showing that nonlocal potentials improve the accuracy of astrophysical S-factor calculations and should be used in future models.

Contribution

It introduces the application of the Lagrange-mesh R-matrix method to study nonlocality effects in direct radiative capture reactions, highlighting the importance of nonlocal potentials.

Findings

Nonlocal potentials yield results closer to experimental data.

Differences between local and nonlocal potentials are smaller than other uncertainties.

Small diffuseness narrow potentials fit broad resonance data well.

Abstract

We apply the Lagrange-mesh $R$-matrix method to calculate the $S$-factor for the $^{13}$C$(p,\gamma)^{14}$N and $^{16}$O$(p,\gamma)^{17}$F direct radiative capture reactions. By comparing the astrophysical $S$-factors calculated with nonlocal and local potentials, we investigate the nonlocality effects coming from the nuclear potentials in the direct capture reactions. Our calculations are in good agreement with the experimental data and indicate a nonnegligible difference in the results of local and nonlocal potentials. The use of small diffuseness narrow potentials also provides a remarkably good fit in the case with multiple broad resonances. Our findings suggest that the nonlocal potential improves the calculated results although the difference between the local and nonlocal potentials is smaller than uncertainties from other sources. We propose the nonlocality potential should be used in the potential model calculation of future astrophysics rates evaluation.