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

We study the zero channel radius limit of Wigner's R-matrix theory for two cases and show that it corresponds to nonrelativistic effective quantum field theory. We begin with the simple problem of single-channel np elastic scattering in the S-1(0) channel. The dependence of the R-matrix width g(2) and level energy E-lambda on the channel radius a for fixed scattering length a(0) and effective range r(0) is determined. It is shown that these quantities have a simple pole for a critical value of the channel radius, a(p) = a(p) (a(0), r(0)). The H-3(d,n)He-4 reaction cross section, analyzed with a two-channel effective field theory in the previous paper [Phys. Rev. C 89, 014622 (2014)], 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 g(c) and mass m(*)) and the R-matrix parameters (reduced width amplitudes gamma(c) and level energy E-lambda). An excellent three-parameter fit to the observed astrophysical factor S is found for "unphysical" values of the reduced widths, gamma(2)(c) < 0.