Velocity of sound in a dense, hard-sphere Bose liquid

The collective approach is used to calculate the velocity of sound in a dense system of bosons interacting via a two-body hard-sphere potential. The calculation is carried out with a hard-sphere potential that is equivalent to the real potential between ⁴He atoms over the density range of liquid ⁴He. The agreement between the calculated and experimental results is good over the entire range. The idea behind the calculation is that the space spanned by the collective variables is larger than the physical space and when the interaction is strong, it becomes very important to reduce the effect of nonphysical states in the calculation of physical quantities, by imposing certain physical constraints.