A special version of the Newton-Kantorovich method is applied to the three-dimensional potential inverse scattering problem in the time domain. The related hyperbolic Cauchy problem with data on the side of the time cylinder is solved by the quasi-reversibility method, and a new stability theorem is established by Carleman-type estimates. The geometrical convergence of the Newton-Kantorovich method, used here, is also established.

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The synthesis and characterization of the Eu-encrypted heteropolyanion [ E U P~W~O O I 1 0 1 '~-are presented. X-ray absorption near-edge structure experiments were used to determine that Eu is trivalent in the anion. Optical spectra confirm this finding. The unusual cyclic voltammogram obtained for the Eu heteropolyanion is discussed in terms of the stability of Eu" under reducing conditions. Time delayed optical fluorescence data are only consistent with two structurally inequivalent Eu ions, both inside the heteropoly cavity. Lifetime measurements of the 5Do state indicate that the two structurally different Eu sites are not occupied in the same anion. In addition, from complementary measurements on samples made in D20, it is determined that there are three waters coordinated to Eu in one site and only two waters coordinated to Eu in the second site. 31P NMR and cyclic voltammetry data, obtained from samples with either one or two sites occupied, are indistinguishable. Possible models to explain the presence of two sites are discussed.

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