Low-Lying Excitations in a Bose Gas of Hard Spheres

The pseudopotential method is used to calculate that low-lying excitation energies of a Bose gas of hard spheres at $T=0\mathrm{}$ to an order beyond that previously calculated by this technique. The results are in agreement with those obtained by Beliaev using a different approach. The phonon velocity is found to be equal to the velocity of compressional waves to the order of approximation considered.