Rayleigh scattering: Volterra equation for the matrix source function

Multiple Rayleigh scattering is examined in a semi-infinite atmosphere with uniformly distributed primary sources of partially polarized radiation. The resulting linear polarization is described by a 2×2 matrix transfer equation. A matrix generalization of Rybicki's two point Q-integral is obtained for this case. It is shown that the Volterra equation for the matrix source function for this problem is a particular case of our Q integral. Applying the Laplace transform to it yields the matrix form of the Ambartsumyan-Chandrasekhar H-equation. The Volterra equation for Sobolev's matrix resolvent function is another simple consequence of this equation. Translated from Astrofizika, Vol. 52, No. 2, pp. 301–310 (May 2009).