[en] We propose a modified scheme for calculating the single-particle excitation spectrum of the impurity Anderson model. It is based on the second order perturbation theory, but modifies the self-energy so as to reproduce the correct atomic limit and to fulfill the Friedel sum rule. Therefore, it offers a simple scheme valid over wide range of excitation energy and parameters, and would be useful also for potential application to the lattice problems. (author)

[en] In order to obtain the optimum conditions for micro-hardness measurements of sintered UO₂, two kinds of hardness tests (Vickers and Knoop) were examined with non-irradiated UO₂ of 2.5 and 5 μm in grain size. The hardness values were obtained as a function of the applied load in the load range of 25 -- 1,000 g. In the Vickers test, cracks were generated around the periphery of an indentation even at lower load of 50 g, which means the Vickers hardness is not suitable for UO₂ specimens. In the Knoop test, three stages of load dependence were observed for sintered pellet as well as for a single crystal by Bates. Load dependence of Knoop hardness and crack formation were discussed. In the range of applied load around 70 -- 100 g there were plateau region where hardness values were nearly unchanged and did not contain any cracks in the indentation. The plateau region represents a hardness of a specimen. From a comparison between the hardness values of 2.5 μm and those of 5 μm UO₂, it was approved that the degree of sintering controls the hardness in the plateau region. (author)