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 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.