A direct determination of the density matrix in a nuclear system

We introduce an iterative steepest descent approach to determine directly the best one-body density matrix which minimizes the total energy of a nuclear system in the Hartree-Fock approximation, without solving the HF equations. An application is shown to the ²⁰Ne deformed nucleus with a Skyrme interaction. The possibility to introduce external shape constraints to describe general form of deformations is discussed.