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Let the potential of a one-dimensional scalar particle be F(ic) = FoS_ 00 00 5(^-Xj), -<*> , constitute an ergodic stationary Markov process. The stationary density T(z) of the (ZJ) satisfies a first-order linear differentialdifference equation, and the node density is given (with probability 1) by Hm^^ z 2 T (z) (Rice's formula). Numerical results are obtained by integrating the second-order linear differential equation satisfied by the Fourier transform of T(z). ELECTRON LEVELSIN ONE-DIMENSIONAL RANDOM LATTICE 1177

Abstract. Scattering polarization measurements were obtained with THEMIS in July 2000, close to the solar south Pole and to the east Equator and in a period of maximum solar activity. Using the THEMIS multi-lines spectro-polarimetric mode (MTR), we observed simultaneously four spectral domains containing the 460.7 nm Sr i line, several molecular lines around 515.9 nm and the Na i D1 and Na i D2 lines. This allows us to scan different altitudes in the solar atmosphere at the same time and provides us with a large set of constraints to study the behaviour of the magnetic field. This paper is devoted to the Sr i line which exhibits quite a strong linear polarization peak outside active regions. A detailed radiative transfer modeling is performed in order to interpret the observed center-to-limb variations of the line intensity and polarization. It was shown previously (Faurobert-Scholl 1993) that this line, which is sensitive to the Hanle effect, can be used as a diagnostic tool for the presence of weak turbulent magnetic fields in the solar photosphere outside active regions. The line polarization rates that we measured in July 2000 are 25% lower than what has been reported previously, for observations near the minimum, or in the increasing phase, of the activity cycle (Stenflo et al. 1980). They are in agreement with other observations performed with a different observational set-up in August 2000 (Bommier & Molodij 2001). We show that they are consistent with the presence of a weak turbulent magnetic field with an average strength between 20 G and 30 G in the upper solar photosphere. This is about twice the value which was derived from previous observations. This result raises the possiblity of a long-term variation of the turbulent photospheric magnetic field with the activity cycle.

Abstract. The polarized line transfer equation for the Hanle effect is solved in the framework of an exact partial frequency redistribution (PRD) theory developed by Bommier (1997a,b). In that theory the effect of collisions on the Hanle effect is considered self-consistently. We follow that approach in the line transfer computations presented here. The theory formulated by Bommier clearly recognizes two levels of approximations for exact PRD, in order to facilitate the solution of the line transfer equation. The second level employs angle-dependent redistribution functions, and numerically represents a more difficult problem compared to the third level, which involves only the use of angle-averaged frequency redistribution functions. We present a method which can solve the problem in both the levels of approximation. The method is based on a perturbative approach to line polarization. Although computationally expensive, it offers the only practical means of solving the angle-dependent Hanle PRD problem. We discuss the numerical aspects of assembling the so called "frequency domain dependent redistribution matrices", and also an efficient way of computing the scattering integral. Some examples are presented to illustrate the interesting aspects of the Hanle-PRD problem with angle-dependent frequency redistribution. A comparison of the emergent profiles computed under angle-averaged and angle-dependent redistribution is carried out, and the effect of collisions is investigated. We show that it is necessary to incorporate an angle-dependent redistribution mechanism especially in the computation of the Stokes U parameter. We demonstrate that the use of simple frequency domains is good enough in practical applications of the Hanle PRD theory.