Hard-sphere gases as ideal gases with multi-core boundaries: An approach to two- and three-dimensional interacting gases

By regarding a hard-sphere gas as an ideal gas confined in a container with a multi-core ( excluded sphere) boundary, we treat the hard-sphere interaction in an interacting gas as the boundary effect on an ideal quantum gas; this enables us to treat an interacting gas as an ideal one. We calculate the equation of state for a three-dimensional hard-sphere gas with spin j, and compare it with the results obtained by other methods. The equation of state for a two-dimensional hard-sphere gas is difficult to calculate by usual methods; by this approach one can calculate it directly.