  Proton-proton fusion is considered in the effective field theory of Kaplan,
Savage and Wise. Coulomb effects are included systematically in a
non-perturbative way. Including the dimension-eight derivative coupling which
determines the effective ranges of the scattering amplitudes, next-to-leading
order corrections to the fusion rate are calculated. When the renormalization
mass is well above the characteristic energies of the system, this contribution
gives a rate which is eight percent below the standard value. The difference
can be due to an unknown counterterm which comes in at this order.
