Nuclear and Coulomb mean fields seen by a fragment, in the assembly of interacting nuclear species, are calculated following a statistical method, and used in a grand canonical model to describe the multifragmentation process. The nuclear mean field enhances the yield of neutrons and other light mass fragments dramatically, without significantly affecting the yields of relatively heavier fragments. It greatly enhances the multiplicities of these particles and hence provides an additional mechanism, other than dynamical and deformation effects, usually assumed to explain the data. The nuclear interaction is found to lower the temperature to a physically accepted value. The role of the Coulomb interaction in producing a minimum in the mass yield distribution, which has been questioned recently, is reaffirmed by extensive calculations.