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Screening of a macroion by multivalent counterions is considered. It is shown that ions form strongly correlated liquid at the macroion surface. Cohesive energy of this liquid leads to strong additional attraction of counterions to the surface. Away from the surface this attraction is taken into account by a new boundary condition for the Poisson-Boltzmann equation. This equation is solved with the new boundary condition for a charged flat surface and a long cylinder. For a cylinder Onsager-Manning theory looses its universality so that apparent charge of the cylinder is smaller than their theory predicts and depends on its bare charge. It can also vanish or change sign.

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The problem of electron tunnelling through a symmetric semiconductor barrier based on zincblende-structure material is studied. The k 3 Dresselhaus terms in the effective Hamiltonian of bulk semiconductor of the barrier are shown to result in a dependence of the tunnelling transmission on the spin orientation. The difference of the transmission probabilities for opposite spin orientations can achieve several percents for the reasonable width of the barriers. Lately spin polarized electron transport in semiconductors attracts a great attention.1 One of the major problems of general interest is a possibility and methods of spin injection into semiconductors. A natural way to achieve spin orientation in experiment is the injection of spin polarized carriers from magnetic materials. Although significant progress has been made recently, 2,3,4,5 reliable spin-injection into low-dimensional electrons systems is still a challenge. Schmidt et al. pointed out that a fundamental obstacle for electrical injection from ferromagnetic into semiconductor was the conductivity mismatch of the metal and the semiconductor structure.6 However, Rashba showed that this problem could be resolved by using tunnelling contact at the metal-semiconductor interface.7 On the other hand Voskoboynikov et al.8 proposed that asymmetric nonmagnetic semiconductor barrier itself could serve as a spin filter. It was demonstrated that spin-dependent electron reflection by inequivalent interfaces resulted in the dependence of the tunnelling transmission probability on the orientation of electron spin. This effect is caused by interface-induced Rashba spin-orbit coupling 9 and can be substantial for resonant tunnelling through asymmetric double-barrier 10,11 or triple-barrier 12 heterostructures. However, in the case of symmetric potential barriers, the interface spin-orbit coupling does not lead to a dependence of tunnelling on the spin orientation.In this communication we will show that the process of tunnelling is spin dependent itself. We demonstrate that a considerable spin polarization can be expected at tunnelling of electrons even through a single symmetric barrier if only the barrier material lacks a center of inversion like zinc-blende structure semiconductors. The microscopic origin of the effect is the Dresselhaus k 3 terms 13 in the effective Hamiltonian of the bulk semiconductor of the barrier.We consider the transmission of electrons with the initial wave vector k = (k , k z ) through a flat potential barrier of height V grown along z [001] direction (see

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