  We outline a general method for computing nuclear capture reactions on the
lattice. The method consists of two major parts. In this study we detail the
second part which consists of calculating an effective two-body capture
reaction on the lattice at finite volume. We solve this problem by calculating
the two-point Green's function using an infrared regulator and the capture
amplitude to a two-body bound state. We demonstrate the details of this method
by calculating on the lattice the leading M1 contribution to the radiative
neutron capture on proton at low energies using pionless effective field
theory. We find good agreement with exact continuum results.
