We derive general results for the mass shift of bound states with angular momentum $\ell \ge 1$ in a finite periodic volume. Our results have direct applications to lattice simulations of hadronic molecules as well as atomic nuclei. While the binding of $S$-wave bound states increases at finite volume, we show that the binding of $P$-wave bound states decreases. The mass shift for $D$-wave bound states as well as higher partial waves depends on the representation of the cubic rotation group. Nevertheless, the multiplet-averaged mass shift for any angular momentum $\ell$ can be expressed in a simple form, and the sign of the shift alternates for even and odd $\ell$. We verify our analytical results with explicit numerical calculations. We also show numerically that similar volume corrections appear in three-body bound states.

• Received 28 March 2011

DOI:https://doi.org/10.1103/PhysRevLett.107.112001