On the population dynamics of Eudiaptomus gracilis Sars and Heterocope borealis Fischer in the Bodensee-Obersee. Part B. Eudiaptomus gracilis Sars. [Translation from: Trudy Instituta Biologii Vnutrennykh Vodnany 12(15) 170-174, 1966.]

Experimental research was conducted to study the development of eggs of Eudiaptomus gracilis Sars. The egg production was studied as well as the population dynamics. Factors like losses in the lake and through the effluent Rhine at Konstanz were considered

Two-Body T-Matrices without Angular Momentum Decomposition: Energy and Momentum Dependencies

The two-body t-matrix is calculated directly as function of two vector momenta for different Malfliet-Tjon type potentials. At a few hundred MeV projectile energy the total amplitude is quite a smooth function showing only a strong peak in forward direction. In contrast the corresponding partial wave contributions, whose number increases with increasing energy, become more and more oscillatory with increasing energy. The angular and momentum dependence of the full amplitude is studied and displayed on as well as off the energy shell as function of positive and negative energies. The behavior of the t-matrix in the vicinity of bound state poles and resonance poles in the second energy sheet is studied. It is found that the angular dependence of T exhibits a very characteristic behavior in the vicinity of those poles, which is given by the Legendre function corresponding to the quantum number either of the bound state or the resonance (or virtual) state. This behavior is illustrated with numerical examples.Comment: 19 pages (revtex), 15 figure

Recent investigations on zooplankton in the Limnological Institute of the University of Freiburg, in Falkau (Germany). [Translation from: Acta cient.Venezolana 18, 94-97, 1967. ]

Histochemical experiments are conducted in order to study the interrenal cells of European brook lamprey (Lampetra planeri)

Treatment of Two Nucleons in Three Dimensions

We extend a new treatment proposed for two-nucleon (2N) and three-nucleon (3N) bound states to 2N scattering. This technique takes momentum vectors as variables, thus, avoiding partial wave decomposition, and handles spin operators analytically. We apply the general operator structure of a nucleon-nucleon (NN) potential to the NN T-matrix, which becomes a sum of six terms, each term being scalar products of spin operators and momentum vectors multiplied with scalar functions of vector momenta. Inserting this expansions of the NN force and T-matrix into the Lippmann-Schwinger equation allows to remove the spin dependence by taking traces and yields a set of six coupled equations for the scalar functions found in the expansion of the T-matrix.Comment: 4 pages, Contribution to The 19th International IUPAP Conference on Few-Body Problems in Physics, 31.08 - 05.09.2009, Bonn, German

Nucleon-Nucleon Scattering in a Three Dimensional Approach

The nucleon-nucleon (NN) t-matrix is calculated directly as function of two vector momenta for different realistic NN potentials. To facilitate this a formalism is developed for solving the two-nucleon Lippmann-Schwinger equation in momentum space without employing a partial wave decomposition. The total spin is treated in a helicity representation. Two different realistic NN interactions, one defined in momentum space and one in coordinate space, are presented in a form suited for this formulation. The angular and momentum dependence of the full amplitude is studied and displayed. A partial wave decomposition of the full amplitude it carried out to compare the presented results with the well known phase shifts provided by those interactions.Comment: 26 pages plus 10 jpg figure

Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves

We extend our subtractive-renormalization method in order to evaluate the 1S0 and 3S1-3D1 NN scattering phase shifts up to next-to-next-to-leading order (NNLO) in chiral effective theory. We show that, if energy-dependent contact terms are employed in the NN potential, the 1S0 phase shift can be obtained by carrying out two subtractions on the Lippmann-Schwinger equation. These subtractions use knowledge of the the scattering length and the 1S0 phase shift at a specific energy to eliminate the low-energy constants in the contact interaction from the scattering equation. For the J=1 coupled channel, a similar renormalization can be achieved by three subtractions that employ knowledge of the 3S1 scattering length, the 3S1 phase shift at a specific energy and the 3S1-3D1 generalized scattering length. In both channels a similar method can be applied to a potential with momentum-dependent contact terms, except that in that case one of the subtractions must be replaced by a fit to one piece of experimental data. This method allows the use of arbitrarily high cutoffs in the Lippmann-Schwinger equation. We examine the NNLO S-wave phase shifts for cutoffs as large as 5 GeV and show that the presence of linear energy dependence in the NN potential creates spurious poles in the scattering amplitude. In consequence the results are in conflict with empirical data over appreciable portions of the considered cutoff range. We also identify problems with the use of cutoffs greater than 1 GeV when momentum-dependent contact interactions are employed. These problems are ameliorated, but not eliminated, by the use of spectral-function regularization for the two-pion exchange part of the NN potentialComment: 40 pages, 21 figure