  We develop a microscopic theory to analyze the phase behaviour and compute
correlation functions of dense assemblies of soft repulsive particles both at
finite temperature, as in colloidal materials, and at vanishing temperature, a
situation relevant for granular materials and emulsions. We use a mean-field
statistical mechanical approach which combines elements of liquid state theory
to replica calculations to obtain quantitative predictions for the location of
phase boundaries, macroscopic thermodynamic properties and microstructure of
the system. We focus in particular on the derivation of scaling properties
emerging in the vicinity of the jamming transition occurring at large density
and zero temperature. The new predictions we obtain for pair correlation
functions near contact are tested using computer simulations. Our work also
clarifies the conceptual nature of the jamming transition, and its relation to
the phenomenon of the glass transition observed in atomic liquids.
