Effective field theory as a limit of R-matrix theory for light nuclear reactions

TL;DR

This paper demonstrates that the zero channel radius limit of R-matrix theory is equivalent to non-relativistic effective quantum field theory, establishing a connection between the two frameworks for light nuclear reactions.

Contribution

It shows the equivalence between R-matrix theory at zero channel radius and effective field theory, providing explicit relationships between their parameters.

Findings

R-matrix quantities have a simple pole at a critical channel radius.

The S matrix from R-matrix and effective field theory are identical in the zero-radius limit.

A good fit to experimental data is achieved with unphysical reduced widths.

Abstract

We study the zero channel radius limit of Wigner's R-matrix theory for two cases, and show that it corresponds to non-relativistic effective quantum field theory. We begin with the simple problem of single-channel n-p elastic scattering in the 1S0 channel. The dependence of the R matrix width and level energy on the channel radius, "a" for fixed scattering length a0 and effective range r0 is determined. It is shown that these quantities have a simple pole for a critical value of the channel radius. The 3H(d,n)4He reaction cross section, analyzed with a two-channel effective field theory in the previous paper, is then examined using a two-channel, single-level R-matrix parametrization. The resulting S matrix is shown to be identical in these two representations in the limit that R-matrix channel radii are taken to zero. This equivalence is established by giving the relationship between the low-energy constants of the effective field theory (couplings and mass) and the R-matrix parameters (reduced width amplitudes and level energy). An excellent three-parameter fit to the observed astrophysical factor S is found for "unphysical" values of the reduced widths.