Many-Body Pseudopotential for Hard-Sphere Interaction

A many-body pseudopotential for a hard-sphere system which is mathematically equivalent to the boundary conditions imposed on the wave functions is obtained as a generalization of Huang and Yang's binary pseudopotential, and the lowest order term of the ground state energy resulting from the triple collision is calculated for the Bose system. Instead of the direct perturbational treatment of the pseudopotential, the use of the Ilk-representation for the Bose system is proposed and the ground state energy is calculated in this representation. It is shown that the energy thus calculated is of the formof an expansion in powers of (pa3)li2, where p is the average density and a the hard-sphere diameter, which is in agreement with Lee and Yang's conclusion drawn from the binary collision expansion method. Some discussions associated with the roton spectrum of liquid He4 are given.