Master equation theory applied to the redistribution of polarized radiation in the weak radiation field limit. V. The two-term atom

Abstract

In previous papers of this series, we presented a formalism able to account for both statistical equilibrium of a multilevel atom and coherent and incoherent scatterings (partial redistribution). aims: This paper provides theoretical expressions of the redistribution function for the two-term atom. This redistribution function includes both coherent (R_II) and incoherent (R_III) scattering contributions with their branching ratios. methods: The expressions were derived by applying the formalism outlined above. The statistical equilibrium equation for the atomic density matrix is first formally solved in the case of the two-term atom with unpolarized and infinitely sharp lower levels. Then the redistribution function is derived by substituting this solution for the expression of the emissivity. results: Expressions are provided for both magnetic and non-magnetic cases. Atomic fine structure is taken into account. Expressions are also separately provided under zero and non-zero hyperfine structure. conclusions: Redistribution functions are widely used in radiative transfer codes. In our formulation, collisional transitions between Zeeman sublevels within an atomic level (depolarizing collisions effect) are taken into account when possible (i.e., in the non-magnetic case). However, the need for a formal solution of the statistical equilibrium as a preliminary step prevents us from taking into account collisional transfers between the levels of the upper term. Accounting for these collisional transfers could be done via a numerical solution of the statistical equilibrium equation system.

15 pages, no figure, in press in Astronomy & Astrophysics

References in corpus (7)

• Magnetic Diagnostics of the Solar Chromosphere with the Mg II h-k Lines
• The magnetic sensitivity of the Mg ii k line to the joint action of Hanle, Zeeman and magneto-optical effects
• Frequency Redistribution Function for the Polarized Two-Term Atom
• The transfer of resonance line polarization with partial frequency redistribution and J-state interference
• A Note on the Radiative and Collisional Branching Ratios in Polarized Radiation Transport with Coherent Scattering
• Polarized light scattering with Paschen-Back effect, level-crossing of fine structure states and partial frequency redistribution
• The quantum interference effects in the Sc II 4247 A line of the Second Solar Spectrum

Cited by in corpus (5)

• Solving the paradox of the solar sodium D1 line polarization
• Polarized Line Formation in Arbitrary Strength Magnetic Fields: the case of a two-level atom with hyperfine structure splitting
• Importance of Angle-dependent Partial Frequency Redistribution in Hyperfine Structure Transitions Under Incomplete Paschen-Back Effect Regime
• The potential of the wavelength-integrated scattering polarization of the hydrogen Ly-alpha line for probing the solar chromosphere
• Collisional effects in modeling solar polarized lines