Corrections to nucleon capture cross sections computed in truncated Hilbert spaces

TL;DR

This paper develops extrapolation formulas to correct for errors in nucleon capture cross sections caused by Hilbert space truncation, improving the accuracy of theoretical predictions in astrophysics.

Contribution

It introduces a theoretical foundation and formulas for estimating and correcting truncation errors in capture cross sections, applicable to few-body and many-body nuclear calculations.

Findings

Effective extrapolation formulas demonstrated for proton-proton fusion.

Results improve the accuracy of capture cross section calculations.

Applicable to both light and heavy nuclei in astrophysical models.

Abstract

Nucleon capture cross sections enter various astrophysical processes. The measurement of proton capture on nuclei at astrophysically relevant low energies is a challenge, and theoretical computations in this long-wavelength regime are sensitive to the long-distance asymptotics of the wave functions. A theoretical foundation for estimating and correcting errors introduced in capture cross sections due to Hilbert space truncation has so far been lacking. We derive extrapolation formulas that relate the infrared regularized capture amplitudes to the infinite basis limit and demonstrate their efficacy for proton-proton fusion. Our results are thus relevant to current calculations of few-body capture reactions such as proton-proton fusion or proton capture on the deuteron, and they also open the way for the use of {\it ab initio} many-body wave functions represented in finite Hilbert spaces in precision calculations of nucleon capture on heavier nuclei.