where formula_5 is the coordinate of the formula_6-th boson. If the average spacing between the particles in a gas is greater than the scattering length (that is, in the so-called dilute limit), then one can approximate the true interaction potential that features in this equation by a pseudopotential. At sufficiently low temperature where the de Broglie wavelength is much longer than the range of boson-boson interaction, the scattering process can be well approximated by the s-wave scattering (i.e. formula_7 in the partial wave analysis, a.k.a. the hard-sphere potential) term alone. In that case, the pseudopotential model Hamiltonian of the system can be written as: