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[en] In order to calculate cross sections with a large number of particles/jets in the final state at next-to-leading order, one has to reduce the occurring scalar and tensor one-loop integrals to a small set of known integrals. In massless theories, this reduction procedure is complicated by the presence of infrared divergences. Working in n = 4 - 2ε dimensions, it will be outlined how to achieve such a reduction for diagrams with an arbitrary number of external legs. As a result, any integral with more than four propagators and generic 4-dimensional external momenta can be reduced to box integrals
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[en] We evaluate the coefficients of the leading poles of the complete two-loop quark self-energy Σ(p) in the Coulomb gauge. Working in the framework of split dimensional regularization, with complex regulating parameters σ and n/2-σ for the energy and space components of the loop momentum, respectively, we find that split dimensional regularization leads to well-defined two-loop integrals, and that the overall coefficient of the leading pole term for Σ(p) is strictly local. Extensive tables showing the pole parts of one- and two-loop Coulomb integrals are given. We also comment on some general implications of split dimensional regularization, discussing in particular the limit σ→1/2 and the subleading terms in the ε-expansion of noncovariant integrals
Journal
[en] We consider one-loop scalar and tensor integrals with an arbitrary number of external legs relevant for multi-parton processes in massless theories. We present a procedure to reduce N-point scalar functions with generic 4-dimensional external momenta to box integrals in (4-2ε) dimensions. We derive a formula valid for arbitrary N and give an explicit expression for N=6. Further a tensor reduction method for N-point tensor integrals is presented. We prove that generically higher dimensional integrals contribute only to order ε for N≥5. The tensor reduction can be solved iteratively such that any tensor integral is expressible in terms of scalar integrals. Explicit formulas are given up to N=6
Journal
[en] The 137Cs and 90Sr concentrations in plants from a forest (altitude 1000 m) and a pasture (1700 m) in the Styrian Koralpe were found to be still high today, ten years after the Chernobyl accident. Following the reactor accident, the 137Cs activity of lichens rose to over 50 KBq kg-1 d.w. from an initial value of approx. 400 Bq. At the Weinebene (1770 m) the biological half-life of 137Cs was 3.1 years for Pseudevernin furfuracea and 2.5 years for the terricolous lichen Cetraria islandica. The biological half-life of 90Sr in Pseudevernia was shorter than that of 137Cs, and was determined to be between 1.2 and 1.6 years. A positive correlation was found to exist between 90Sr and Ca++ concentrations among the plants tested, whereas 137Cs showed no correlation to K+. (author)
Source
Gerzabek, M. (Oesterreichisches Forschungszentrum Seibersdorf GmbH (Austria)); Desmet, G.; Howard, B.J.; Heinrich, G.; Schimmack, W. (eds.); Oesterreichische Bodenkundliche Gesellschaft (OEBG), Vienna (Austria); Umweltbundesamt, Vienna (Austria); Mitteilungen der Oesterreichischen Bodenkundlichen Gesellschaft; v. 53; 313 p; 1996; p. 243-250; Berger; Horn (Austria); International symposium on radioecology 1996; Vienna (Austria); 22-24 Apr 1996; ISSN 0029-893X; 
; Available from Umweltbundesamt, Spittelauer Laende 5, A-1090 Vienna (AT)
; Available from Umweltbundesamt, Spittelauer Laende 5, A-1090 Vienna (AT)
[en] We have developed the self-consistent mean rate approach that makes it possible to analytically solve the coagulation–fragmentation balance equations subject to the mass conservation constraint. The developed approach is not restricted to a specific form of the coagulation and fragmentation rates, thus being applicable to a variety of different coagulation–fragmentation processes. As an example of the practical applicability of the developed method we have calculated the aggregate size distribution and average aggregate diameter for the case of shear induced coagulation–fragmentation
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