  This paper determines the excess free energy associated with the formation of
a spherical cavity in a hard sphere fluid. The solvation free energy can be
calculated by integration of the structural changes induced by inserting the
cavity using a number of different exact thermodynamic pathways. We consider
three such pathways, including a new density route derived here. Structural
information about the nonuniform hard sphere fluid in the presence of a general
external field is given by the recently developed hydrostatic linear response
(HLR) integral equation. Use of the HLR results in the different pathways gives
a generally accurate determination of the solvation free energy for cavities
over a wide range of sizes, from zero to infinity. Results for a related
method, the Gaussian Field Model, are also discussed.
