POLARIZED LINE FORMATION BY RESONANCE SCATTERING .1. BASIC FORMALISM

The model two-level problem of non-LTE line formation in homogeneous p lane atmospheres is reconsidered with the complete account of polariza tion arising in resonance scattering. We use the approximation of comp lete frequency redistribution (CFR) and restrict our discussion to the most important case of axially symmetric radiation fields in semi-inf inite atmospheres. The primary sources are assumed to be partially pol arized. The problem is reduced to the 2 x 2 matrix Wiener-Hopf integra l equation for the matrix source function S(tau). The matrix kernel K- 1(tau) of the Lambda-operator appearing in this equation is represente d as a continuous superposition of exponentials. As we show in Paper I I of the series, this enables one to develop a matrix version of the a nalytical theory which, on the one hand, is a generalization of the sc alar CFR theory and, on the other, is the CFR version of the theory of multiple monochromatic Rayleigh scattering. As a preparatory step for this, we discuss in detail the properties of the kernel matrix K-1(ta u) and the dispersion matrix T(z). The latter is essentially the two-s ided Laplace transform of K-1(tau). We consider the asymptotic behavio r of K-1(tau) and T(z) for large tau and z, respectively. For the part icular case of the Doppler profile the complete asymptotic expansions of these matrices are presented. These results are at the base of the theory presented in Paper II of the series.