  We study a low-energy effective field theory (EFT) describing the NN system
in which all exchanged particles are integrated out. We show that fitting the
residue of the 3S1 amplitude at the deuteron pole, rather than the 3S1
effective range, dramatically improves the convergence of deuteron observables
in this theory. Reproducing the residue ensures that the tail of the deuteron
wave function, which is directly related to NN scattering data via analytic
continuation, is correctly reproduced in the EFT at next-to-leading order. The
role of multi-nucleon-electroweak operators which produce deviations from
effective-range theory can then be explicitly separated from the physics of the
wave function tail. Such an operator contributes to the deuteron quadrupole
moment, mu_Q, at low order, indicating a sensitivity to short-distance physics.
This is consistent with the failure of impulse approximation calculations in NN
potential models to reproduce mu_Q. The convergence of NN phase shifts in the
EFT is unimpaired by the use of this new expansion.

Nuclear Theory