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178 45'K. " However, this interpretation now appears to be invalid not only because of the existence of the rise effect, but also because long-range interstitial motion in tungsten does not seem to occur until about 45'K.Finally, although the exact nature of the rise-eGect mechanism is not clear, comparison of Figs. 6 and 8 indicates that the irradiation-induced background decrement anneals during close-pair recovery substages, suggesting that close-pair configurations are essential to the mechanism. The background reductions between 35 and 45'K might then be interpreted as the disappearance of defect-dislocation interactions through mutual annihilation of the close-pair constituents. On the other hand, the decrement increases near 26'K might suggest the conversion of one close-pair configuration into another more stable configuration which in its interaction with dislocations produces a larger decrement. V. CONCLUSIONSFor an applied stress frequency of about 600 Hz, the results of the present research on Stage I in tungsten have revealed the existence of a prominent irradiationinduced internal-friction peak near 30'K. Peak properties such as its temperature half-width, dependence on stress direction, apparent independence of dislocation background, and radiation doping, and disappearance during close-pair resistivity recovery imply that it was '6 J. A. DiCarlo, C. L. Snead, Jr. , and A. N. Goland, Bull. Am.Phys. Soc. 13, 381 (1968). produced by the stress-induced ordering of close-pair interstitials. Directional-dependence results suggest that the 30'K interstitials are not trigonal defects, that is, crowdions, but probably are orthorhombic defects in general and (110) split interstitials in particular. The split configuration for this interstitial is also supported by activation energy determinations which show its reorientation energy to be lover than its migration energy. In fact, were it not for a combination of this latter result and the low-observation temperature, internal-friction measurements in the employed frequency range would probably not have detected the interstitial at all. This conclusion is especially true in the case of electron irradiation since at these low irradiation temperatures it becomes impractical to use electrons to produce total defect concentrations greater than those attained here ( 10 '). Nevertheless, the present results do suggest that, given a high enough defect concentration and a low enough stress frequency, self-interstitials in the bcc metals, like impurity interstitials, can be detected and studied by internal-friction techniques. ACKNOWLEDGMENTSThe authors wish to acknowledge the experimental assistance of the Dynamitron technicians and J. Palmer of the Instrumentation Department. One of the authors (J. A.D. ) would like to express his thanks to the National Aeronautics and Space Administration for its 6nancial support during the latter stages of this work.X-ray emission and absorption spectra in metals may display singularities near the Fermi-level threshold. These sing...

The many-body approach of the preceding paper is generalized to include self-energy and vertex renormalization is self-consistent fashion. The algebra of parquet diagrams is developed in terms of an unknown divergent parameter (related to the deep-hole Green's function 9), and of an unknown irreducible interaction R. The resulting interaction operator y is used to calculate 9 and R; the corresponding coupled equations are solved self-consistently in the weak coupling limit. The spectral densities of the deep-hole Green's function and of the x-ray response function are calculated explicitly; in the weak coupling limit, the Mahan singularity found in the preceding paper is unaffected by renormalization. The self-consistent formalism presented here describes the reaction of divergent fluctuations on themselves, and should, therefore, be useful in other more complicated problems, such as the Kondo effect.

Résumé. 2014 L'absorption optique dans les semiconducteurs dopés à gap direct, dans lesquels la bande de

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