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A nonlinear response theory is developed and applied to electrostaticinteractions between spherical macroions, screened by surrounding microions, incharge-stabilized colloidal suspensions. The theory describes leading-ordernonlinear response of the microions (counterions, salt ions) to theelectrostatic potential of the macroions and predicts microion-inducedeffective many-body interactions between macroions. A linear responseapproximation [Phys. Rev. E 62, 3855 (2000)] yields an effective pair potentialof screened-Coulomb (Yukawa) form, as well as a one-body volume energy, whichcontributes to the free energy. Nonlinear response generates effectivemany-body interactions and essential corrections to both the effective pairpotential and the volume energy. By adopting a random-phase approximation (RPA)for the response functions, and thus neglecting microion correlations,practical expressions are derived for the effective pair and triplet potentialsand for the volume energy. Nonlinear screening is found to weaken repulsivepair interactions, induce attractive triplet interactions, and modify thevolume energy. Numerical results for monovalent microions are in good agreementwith available ab initio simulation data and demonstrate that nonlinear effectsgrow with increasing macroion charge and concentration and with decreasing saltconcentration. In the dilute limit of zero macroion concentration,leading-order nonlinear corrections vanish. Finally, it is shown that nonlinearresponse theory, when combined with the RPA, is formally equivalent to themean-field Poisson-Boltzmann theory and that the linear response approximationcorresponds, within integral-equation theory, to a linearized hypernetted-chainclosure.Comment: 30 pages, 8 figures, Phys. Rev. E (in press

Nonlinear screening and effective electrostatic interactions in charge-stabilized colloidal suspensions