速度-空间密度矩阵理论框架下散射极化中多普勒重分布的理论公式
Theoretical formulation of Doppler redistribution in scattering polarization within the framework of the velocity-space density matrix formalism
摘要：
在极化辐射产生和传输的密度矩阵理论框架内，速度密度矩阵关联是一个重要的物理问题，但在实际应用中，由于采用了速度完全再分布的简化近似，而常常被忽略。在本文中，我们提出了一个应用程序的非LTE问题的极化辐射考虑到这种相关性，通过速度空间密度矩阵形式主义。考虑上下能级无限尖锐的二能级原子，在忽略变速碰撞贡献的情况下，导出了相应的统计平衡方程。将此方程与偏振辐射的辐射转移方程耦合，导出了一组与速度有关的源函数的耦合方程。然后将这组方程具体化为平面平行大气的情况。本文提出的方程提供了一个完整的和坚实的描述的物理纯多普勒再分配，一般描述的再分配矩阵形式主义的框架内的现象。从速度-空间密度矩阵的统计平衡方程和偏振辐射的辐射转移方程出发，导出了相应的再分布矩阵（一般称为R_I），从而说明了这两种方法的等价性。
英文摘要：
Within the framework of the density matrix theory for the generation and transfer of polarized radiation, velocity density matrix correlations represent an important physical aspect that, however, is often neglected in practical applications by adopting the simplifying approximation of complete redistribution on velocity. In this paper, we present an application of the Non-LTE problem for polarized radiation taking such correlations into account through the velocity-space density matrix formalism. We consider a two-level atom with infinitely sharp upper and lower levels, and we derive the corresponding statistical equilibrium equations neglecting the contribution of velocity-changing collisions. Coupling such equations with the radiative transfer equations for polarized radiation, we derive a set of coupled equations for the velocity-dependent source function. This set of equations is then particularized to the case of a plane-parallel atmosphere. The equations presented in this paper provide a complete and solid description of the physics of pure Doppler redistribution, a phenomenon generally described within the framework of the redistribution matrix formalism. The redistribution matrix corresponding to this problem (generally referred to as R_I) is derived starting from the statistical equilibrium equations for the velocity-space density matrix and from the radiative transfer equations for polarized radiation, thus showing the equivalence of the two approaches.
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