The energy spectra of two nucleons in a cubic volume provide access to the two phase shifts and one mixing angle that define the S matrix in the ${}^{3}S_1\mathrm{\text{−}}{}^{3}D_1$ coupled channels containing the deuteron. With the aid of recently derived energy quantization conditions for such systems, and the known scattering parameters, these spectra are predicted for a range of volumes. It is found that extractions of the infinite-volume deuteron binding energy and leading scattering parameters, including the $S$-$D$ mixing angle at the deuteron pole, are possible from lattice QCD calculations of two-nucleon systems with boosts of $|\mathbf{P}|\le \frac{2\pi }{\mathrm{L}}\sqrt{3}$ in volumes with $10\mathrm{fm}\lesssim \mathrm{L}\lesssim 14\mathrm{fm}$. The viability of extracting the asymptotic $D/S$ ratio of the deuteron wave function from lattice QCD calculations is discussed.

• Received 1 October 2013

DOI:https://doi.org/10.1103/PhysRevD.88.114507