Diagnosing the magnetic field is very important in solar physics. The way to diagnose the magnetic field vector is usually through Zeeman effect for the strong magnetic field, but in the weak magnetic field region where Zeeman is less efficient and Hanle effect can provide a useful tool. Using Hanle effect to diagnose the weak magnetic field is popular in the literature these years which need a complete understanding of the polarization mechanisms. A series of International Solar Polarization Workshops which focus on exploring the magnetic field through the polarized radiation have been taken place every three years since the first one in St.Petersberg, Russia, in 1995. As the high polarimetric precision technology were applied through the ZIMPOL (Zurich Imaging Polarimeter), the so-called Second Solar Spectrum shows a great amount of rich and complicated structure of the linear polarization profile. That the linear polarization profile provide a playground for studying of Hanle effect. Through the effort of a lot of scientists, the theories to compute the Hanle effect were developed like the statistical equilibrium equations and radiative transfer equation in the density matrix form. These theories have make great success and solve many problems in the polarization profile formation and still face to some difficult. Here we review the basic theory in scattering polarization to deal with Second Solar Spectrum and Hanle. And we also focus on investigating the scattering induced fractional linear polarization Q/I and U/I of Mg I b triplet in presence of a magnetic field. It is found that the triplet is suitable to study the lower level Hanle effect and very sensitive to the sub-gauss magnetic field. We use the quantum theory under the flat-spectrum approximation developed by Landi Degl’Innocenti, E to the investigate the Hanle effect in the triplet, and adopt a seven-levels atomic model of magnesium, and the radiative transfer does not be considered and the partial frequency effect (PRD) is not taken into account. The fractional linear polarization profile Q/I and U/I at the triplet are presented. The triplet is sensitive to the magnetic field strength between 0.001 and 0.1 gauss corresponding to lower level Hanle effect and between 1 and 10 gauss corresponding to upper level Hanle effect. In the lower level Hanle effect region, as the magnetic strength is increased, the Q/I amplitude of b4 line is increased due to the coupling of atomic alignment in the statistical equations. And in the upper level Hanle effect region, the magnetic sensitivity is proportional to the the parameter ω(2) JuJ? introduced by Landi Degl’Innocenti. It is found that the most sensitive line is b4 and then followed by b2 line. First, the anisotropy factors obtained through the limb darkening of continuum is not suitable to treat the strong lines. Second, the dichroism contribution needs to be considered to fit the observational profile of triplet. Finally, when the weak magnetic is present, the atomic alignment can be increased due to the coupling in the statistical equilibrium equations. On the other hand, due to the dichroism contribution, the Hanle effect can influence the line wings but can not produce any observable signal because of the contribution of the continuum.
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