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In this paper, we develop an exhaustive analysis on standing waves with prescribed mass for the coupled Hartree-Fock system, which is introduced by Hartree in the 1920's and developed by Fock for describing large systems of identical fermions. By transforming this problem into different types of constrained variational problems based on the width of the Hartree kernel, we establish several existence, multiplicity and asymptotic properties under suitable conditions on the corresponding physical parameters.
