Diagnostic of the magnetic field vector using the atomic density matrix formalism.

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The authors present the work which has been done and which is being done using the atomic density matrix formalism, for the interpretation of linear polarization measurements, leading to the magnetic field diagnostic in astrophysical media. This formalism has been used for interpreting polarization data from solar prominences, leading to original results on the prominence magnetic field obtained through the Hanle effect. An attempt is made to solve the coupled problem of polarized radiative transfer and statistical equilibrium in the case of weak, intermediate and strong magnetic fields, using a method of the integral method type; the advantages of this method, with respect to other methods, of the differential method type, are briefly discussed.

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