GENERALIZED RAYLEIGH-SCATTERING .2. MATRIX SOURCE FUNCTIONS

Numerical and analytical data are presented on the matrix source funct ions S(tau) of the standard problem of multiple generalized Rayleigh s cattering (GRS) in homogeneous semi-infinite atmospheres with uniforml y distributed embedded primary sources of partially polarized radiatio n. The source matrices S(tau) are found by the discrete-ordinate solut ion of the relevant 2 x 2 matrix transfer equation and by albedo shift ing technique, which is a version of the accelerated Lambda-iteration approach. The dependence of the solution of the matrix transfer equati on on the parameters of the problem of multiple molecular scattering, albedo of single scattering lambda(I) and depolarization factor W, is carefully considered. (The value W = 1 corresponds to Rayleigh scatter ing, while for scalar isotropic scattering W = 0). From the pair of th e parameters (lambda(I), W) we switch to (lambda(I), lambda(Q)), with lambda(Q) = 0.7 W lambda(I), and instead of the physically natural dom ain of the parameter values, lambda(I) is an element of [0, 1], lambda (Q) is an element of [0, 0.7 lambda(I)], in GRS we consider a wider on e, lambda(I), lambda(Q) is an element of [0, 1]. On the plane with the axes (lambda(I), lambda Q), or the lambda-plane, there is a one-param eter family of curves, the isopols, along which S(O) remains constant. The lambda-plane and the isopols are the basic instruments in our ana lysis. Along with presenting the numerical data we discuss the asympto tic behavior of S(tau) for tau --> infinity. It is shown that the matr ix counterpart of the usual scalar conservative isotropic scattering i s not the ordinary conservative Rayleigh scattering (lambda(I) = 1, la mbda(Q) = 0.7), but the biconsentative scattering, i.e., scattering wi th lambda(I) = lambda(Q) = 1. The analysis of the remarkable propertie s of biconservative scattering naturally leads to matrix generalizatio ns of the Hopf-Bronstein relation, the Hopf constant etc.