  We demonstrate and test the adiabatic projection method, a general new
framework for calculating scattering and reactions on the lattice. The method
is based upon calculating a low-energy effective theory for clusters which
becomes exact in the limit of large Euclidean projection time. As a detailed
example we calculate the adiabatic two-body Hamiltonian for elastic
fermion-dimer scattering in lattice effective field theory. Our calculation
corresponds to neutron-deuteron scattering in the spin-quartet channel at
leading order in pionless effective field theory. We show that the spectrum of
the adiabatic Hamiltonian reproduces the spectrum of the original Hamiltonian
below the inelastic threshold to arbitrary accuracy. We also show that the
calculated s-wave phase shift reproduces the known exact result in the
continuum and infinite-volume limits. When extended to more than one scattering
channel, the adiabatic projection method can be used to calculate inelastic
reactions on the lattice in future work.
