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

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