Reformulation of the pionless effective field theory for practical few- and many-body applications

The effective field theory (EFT) of contact forces which describes few-nucleon systems at distance scales larger than the pion Compton wavelength $\mathrm{E}\mathrm{F}\mathrm{T}(\pi \mathrm{/})$ can be defined in terms of momentum-dependent potentials that contain a fixed number of simple poles and generate the effective-range expansion to a given fixed order. These potentials provide a practical generalization of the standard $\mathrm{E}\mathrm{F}\mathrm{T}(\pi \mathrm{/})$ power-counting scheme which, for instance, naturally accounts for the large effective ranges in the s-wave channels. Nucleon-nucleon phase shifts computed in this formulation of $\mathrm{E}\mathrm{F}\mathrm{T}(\pi \mathrm{/})$ are compared to modern phase-shift analyses, and effective-range parameters are tabulated. The $\mathrm{E}\mathrm{F}\mathrm{T}(\pi \mathrm{/})$ potentials, which provide a rational approximation of the S-matrix, are easily extended into the regime of pion physics through the inclusion of additional S-matrix poles and zeros, and provide an accurate description of data up to pion-production threshold. The potentials in this scheme are in an important sense weak over all relevant distance scales, and are therefore of utility for systematic calculations of many-nucleon observables.