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

Dialogue, Praxis and the State: A Response to Richard Jackson

The article argues in favour of an engagement with state actors for critical terrorism scholars, challenging Richard Jackson's assertion that such engagement necessarily involves co-optation

3N Scattering in a Three-Dimensional Operator Formulation

A recently developed formulation for a direct treatment of the equations for two- and three-nucleon bound states as set of coupled equations of scalar functions depending only on vector momenta is extended to three-nucleon scattering. Starting from the spin-momentum dependence occurring as scalar products in two- and three-nucleon forces together with other scalar functions, we present the Faddeev multiple scattering series in which order by order the spin-degrees can be treated analytically leading to 3D integrations over scalar functions depending on momentum vectors only. Such formulation is especially important in view of awaiting extension of 3N Faddeev calculations to projectile energies above the pion production threshold and applications of chiral perturbation theory 3N forces, which are to be most efficiently treated directly in such three-dimensional formulation without having to expand these forces into a partial wave basis.Comment: 25 pages, 0 figure

A new way to perform partial wave decompositions of few-nucleon forces

We formulate a general and exact method of partial wave decomposition (PWD) of any nucleon-nucleon (NN) potential and any three-nucleon (3N) force. The approach allows one to efficiently use symbolic algebra software to generate the interaction dependent part of the program code calculating the interaction. We demonstrate the feasibility of this approach for the one-boson exchange BonnB potential, a recent nucleon-nucleon chiral force and the chiral two-pion-exchange three-nucleon force. In all cases very good agreement between the new and the traditional PWD is found. The automated PWD offered by the new approach is of the utmost importance in view of future applications of numerous chiral N3LO contributions to the 3N force in three nucleon calculations.Comment: 10 pages, 6 figures (24 eps files

A New Treatment of 2N and 3N Bound States in Three Dimensions

The direct treatment of the Faddeev equation for the three-boson system in 3 dimensions is generalized to nucleons. The one Faddeev equation for identical bosons is replaced by a strictly finite set of coupled equations for scalar functions which depend only on 3 variables. The spin-momentum dependence occurring as scalar products in 2N and 3N forces accompanied by scalar functions is supplemented by a corresponding expansion of the Faddeev amplitudes. After removing the spin degrees of freedom by suitable operations only scalar expressions depending on momenta remain. The corresponding steps are performed for the deuteron leading to two coupled equations.Comment: 19 page

The exact three-dimensional half-shell t-matrix for a sharply cut-off Coulomb potential in the screening limit

The three-dimensional half-shell t-matrix for a sharply cut-off Coulomb potential is analytically derived together with its asymptotic form without reference to partial wave expansion. The numerical solutions of the three-dimensional Lippmann-Schwinger equation for increasing cut-off radii provide half-shell t-matrices which are in quite a good agreement with the asymptotic values.Comment: 15 pages, 4 eps figure