Two particle states in an asymmetric box and the elastic scattering phases

Abstract

The exact two-particle energy eigenstates in a generic asymmetric rectangular box with periodic boundary conditions in all three directions are studied. Their relations with the elastic scattering phases of the two particles in the continuum are obtained for both ${D}_{4}$ and ${D}_{2}$ symmetries. These results can be viewed as a generalization of the corresponding formulas in a cubic box obtained by L\"uscher before. In particular, the s-wave scattering length is related to the energy shift in the finite box. Possible applications of these formulas are also discussed.