We present a new approach to determining the equilibrium structure of a closed (canonical) inhomogeneous fluid which combines grand canonical density functional theory and a series expansion of the distribution functions in powers of $\left(1/\overline{N}\right)$, where $\overline{N}$ is the average number of particles. For hard spheres in a hard spherical cavity, comparison with canonical Monte Carlo results shows that the method is rather accurate, even for small values of $\overline{N}$. In certain (high packing) situations the density profile develops a pronounced peak in the center of the cavity. Accounting properly for such peaks provides a severe test of any density functional approximation.

• Received 14 July 1997

DOI:https://doi.org/10.1103/PhysRevLett.79.2466