  We combine the hyper-netted chain approximation of liquid state theory with
the mode-coupling theory of the glass transition to analyze the structure and
dynamics of soft spheres interacting via harmonic repulsion. We determine the
locus of the fluid-glass dynamic transition in a temperature -- volume fraction
phase diagram. The zero-temperature (hard sphere) glass transition influences
the dynamics at finite temperatures in its vicinity. This directly implies a
form of dynamic scaling for both the average relaxation time and dynamic
susceptibilities quantifying dynamic heterogeneity. We discuss several
qualitative disagreements between theory and existing simulations at
equilibrium. Our theoretical results are, however, very similar to numerical
results for the driven athermal dynamics of repulsive spheres, suggesting that
`mean-field' mode-coupling approaches might be good starting points to describe
these nonequilibrium dynamics.
