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Scattering observables can be computed in lattice field theory by measuringthe volume dependence of energy levels of two particle states. The dominantvolume dependence, proportional to inverse powers of the volume, is determinedby the phase shifts. This universal relation (\Lu's formula) between energylevels and phase shifts is distorted by corrections which, in the large volumelimit, are exponentially suppressed. They may be sizable, however, for thevolumes used in practice and they set a limit on how small the lattice can bein these studies. We estimate these corrections, mostly in the case of twonucleons. Qualitatively, we find that the exponentially suppressed correctionsare proportional to the {\it square} of the potential (or to terms suppressedin the chiral expansion) and the effect due to pions going ``around the world''vanishes. Quantitatively, the size of the lattice should be greater than$\approx(5 {fm})^3$ in order to keep finite volume corrections to the phaseless than $1^\circ$ for realistic pion mass.Comment: 18 pages, 5 figures, 6 figure

Fitting two nucleons inside a box: Exponentially suppressed corrections to Lüscher’s formula