We show that the magnetic moments of LS closed shell nuclei plus or minus one nucleon derived from non-relativistic Hartree-Fock mean-fields are as bad as those obtained in relativistic approaches of nuclear structure. Deviations with respect to more complete results in both cases are ascribed to the mean-field approximation which neglects some degrees of freedom in the nucleus description.PACS: 21.10.Ky.Magnetic moments of LS closed shell nuclei plus or minus one nucleon have generally been revisited each time that new concepts have been introduced in the description of the nucleus. This was the case for instance with mesonic exchange currents, [-1], or high momentum components in the nuclear wave function [2]. Presently, this is the case with possible relativistic effects [-3]. As these effects account for part of the dressing of the nucleon in the nuclear medium, it is expected that the relativistic approaches should a priori provide a better description of the magnetic moments of the above nuclei. In fact, results obtained in the mean-field approximation (see [4] and other references therein) are worse than those obtained in the simplest non-relativistic model which assumes a nucleon moving in the field of an inert core, the interaction being local (Schmidt values). Recently, several corrections which might affect the isoscalar part of these quantities have been proposed [5][6][7] and, at first sight, somewhat improve the situation. However, a better understanding of their origin and relationship seems to be necessary. In [5,7], it is assumed that the magnetic moment is determined by the current at zero momentum transfer, what does not seem to hold quite generally. In ]-6], the appropriate part of the current has been considered, but results are limited to the a-co model.Meanwhile, different attempts to derive mesonic * Laboratoire associ6 au C.N.R.S.exchange currents (MEC) directly from the NN interaction have been done [-8, 9]. Usually, these ones are put into the form of two-body operators, but they may give rise to a single-particle current after summing over all contributions of the core nucleons. The MEC approach is generally supposed to be on a safe ground and has not been seriously questioned in the past. In the same spirit as the above attempts, one may think to start from some single-particle potential (or some Hartree-Fock Hamiltonian in the present work), instead of the two-body interaction, and derive from it a single-particle interaction current to be used in calculating magnetic moments. The apparent advantage of this approach is to rely on quantities such as the effective mass or the single-particle spin-orbit force which are currently used to characterize some potential for the first one, or determined from nuclear spectra for the second one. As we will see, corrections obtained in this way are quite large and lead to discrepancies with experiment which are similar to those obtained in approaches based on relativistic meanfield approximations. This feature tends to show that the problem raise...