Singularity structure of the pi N scattering amplitude in a meson-exchange model up to energies W < 2.0 GeV

Within the previously developed Dubna-Mainz-Taipei meson-exchange model, the singularity structure of the pi N scattering amplitudes has been investigated. For all partial waves up to F waves and c.m. energies up to W = 2 GeV, the T-matrix poles have been calculated by three different techniques: analytic continuation into the complex energy plane, speed-plot and the regularization method. For all 4-star resonances, we find a perfect agreement between the analytic continuation and the regularization method. We also find resonance poles for resonances that are not so well established, but in these cases the pole positions and residues obtained by analytic continuation can substantially differ from the results predicted by the speed-plot and regularization methods.Comment: 21 pages, 4 figures, 4 table

Poles, the only true resonant-state signals, are extracted from a worldwide collection of partial wave amplitudes using only one, well controlled pole-extraction method

Each and every energy dependent partial-wave analysis is parameterizing the pole positions in a procedure defined by the way how the continuous energy dependence is implemented. These pole positions are, henceforth, inherently model dependent. To reduce this model dependence, we use only one, coupled-channel, unitary, fully analytic method based on the isobar approximation to extract the pole positions from the each available member of the worldwide collection of partial wave amplitudes which are understood as nothing more but a good energy dependent representation of genuine experimental numbers assembled in a form of partial-wave data. In that way, the model dependence related to the different assumptions on the analytic form of the partial-wave amplitudes is avoided, and the true confidence limit for the existence of a particular resonant state, at least in one model, is established. The way how the method works, and first results are demonstrated for the S11 partial wave.Comment: 22 pages, 8 figures, 2 table

Stability of the Zagreb Carnegie-Mellon-Berkeley model

In ref. [1] we have used the Zagreb realization of Carnegie-Melon-Berkeley coupled-channel, unitary model as a tool for extracting pole positions from the world collection of partial wave data, with the aim of eliminating model dependence in pole-search procedures. In order that the method is sensible, we in this paper discuss the stability of the method with respect to the strong variation of different model ingredients. We show that the Zagreb CMB procedure is very stable with strong variation of the model assumptions, and that it can reliably predict the pole positions of the fitted partial wave amplitudes.Comment: 25 pages, 12 figures, 19 table

Soft-core meson-baryon interactions. II. πN\pi N and K+NK^+ N scattering

The $\pi N$ potential includes the t-channel exchanges of the scalar-mesons $\sigma$ and f_0, vector-meson $\rho$, tensor-mesons f_2 and f_2' and the Pomeron as well as the s- and u-channel exchanges of the nucleon N and the resonances $\Delta$, Roper and S_{11}. These resonances are not generated dynamically. We consider them as, at least partially, genuine three-quark states and we treat them in the same way as the nucleon. The latter two resonances were needed to find the proper behavior of the phase shifts at higher energies in the corresponding partial waves. The soft-core $\pi N$-model gives an excellent fit to the empirical $\pi N$ S- and P-wave phase shifts up to T_{lab}=600 MeV. Also the scattering lengths have been reproduced well and the soft-pion theorems for low-energy $\pi N$ scattering are satisfied. The soft-core model for the $K^+ N$ interaction is an SU_f(3)-extension of the soft-core $\pi N$-model. The $K^+ N$ potential includes the t-channel exchanges of the scalar-mesons a_0, $\sigma$ and f_0, vector-mesons $\rho$, $\omega$ and $\phi$, tensor-mesons a_2, f_2 and f_2' and the Pomeron as well as u-channel exchanges of the hyperons $\Lambda$ and $\Sigma$. The fit to the empirical $K^+ N$ S-, P- and D-wave phase shifts up to T_{lab}=600 MeV is reasonable and certainly reflects the present state of the art. Since the various $K^+ N$ phase shift analyses are not very consistent, also scattering observables are compared with the soft-core $K^+ N$-model. A good agreement for the total and differential cross sections as well as the polarizations is found.Comment: 24 pages, 20 PostScript figures, revtex4, submitted to Phys. Rev.

Extraction of P11 resonances from pi N data

We show that two P11 nucleon resonance poles near the pi Delta threshold, obtained in several analyses, are stable against large variations of parameters within a dynamical coupled-channels analysis based on meson-exchange mechanisms. By also performing an analysis based on a model with a bare nucleon state, we find that this two-pole structure is insensitive to the analytic structure of the amplitude in the region below pi N threshold. Our results are M_pole = (1363^{+9}_{-6} -i79^{+3}_{-5}) MeV and (1373^{+12}_{-10} -i114^{+14}_{-9}) MeV. We also demonstrate that the number of poles in the 1.5 GeV < W < 2 GeV region could be more than one, depending on how the structure of the single-energy solution of SAID is fitted. For three-pole solutions, our best estimated result of a pole near N(1710) listed by Particle Data Group is (1829^{+131}_{-65} -i192^{+88}_{-110}) MeV which is close to the results of several previous analyses. Our results indicate the need of more accurate pi N reaction data in the W > 1.6 GeV region for high precision resonance extractions.Comment: 15 pages, 4 figure

Relativistic O(q4)O(q^4) two-pion exchange nucleon-nucleon potential: configuration space

We have recently performed a relativistic $O(q^4)$ chiral expansion of the two-pion exchange $NN$ potential, and here we explore its configuration space content. Interactions are determined by three families of diagrams, two of which involve just $g_A$ and $f_{\pi}$, whereas the third one depends on empirical coefficients fixed by subthreshold $\pi N$ data. In this sense, the calculation has no adjusted parameters and gives rise to predictions, which are tested against phenomenological potentials. The dynamical structure of the eight leading non-relativistic components of the interaction is investigated and, in most cases, found to be clearly dominated by a well defined class of diagrams. In particular, the central isovector and spin-orbit, spin-spin, and tensor isoscalar terms are almost completely fixed by just $g_A$ and $f_{\pi}$. The convergence of the chiral series in powers of the ratio (pion mass/nucleon mass) is studied as a function of the internucleon distance and, for $r>$ 1 fm, found to be adequate for most components of the potential. An important exception is the dominant central isoscalar term, where the convergence is evident only for $r>$ 2.5 fm. Finally, we compare the spatial behavior of the functions that enter the relativistic and heavy baryon formulations of the interaction and find that, in the region of physical interest, they differ by about 5%.Comment: 27 pages, 33 figure

Slow viscoelastic relaxation and aging in aqueous foam

Like emulsions, pastes and many other forms of soft condensed matter, aqueous foams present slow mechanical relaxations when subjected to a stress too small to induce any plastic flow. To identify the physical origin of this viscoelastic behaviour, we have simulated how dry disordered coarsening 2D foams respond to a small applied stress. We show that the mechanism of long time relaxation is driven by coarsening induced rearrangements of small bubble clusters. These findings are in full agreement with a scaling law previously derived from experimental creep data for 3D foams. Moreover, we find that the temporal statistics of coarsening induced bubble rearrangements are described by a Poisson process.Comment: 7 pages, 3 figure

Exact results on the Kondo-lattice magnetic polaron

In this work we revise the theory of one electron in a ferromagnetically saturated local moment system interacting via a Kondo-like exchange interaction. The complete eigenstates for the finite lattice are derived. It is then shown, that parts of these states lose their norm in the limit of an infinite lattice. The correct (scattering) eigenstates are calculated in this limit. The time-dependent Schr\"odinger equation is solved for arbitrary initial conditions and the connection to the down-electron Green's function and the scattering states is worked out. A detailed analysis of the down-electron decay dynamics is given.Comment: 13 pages, 9 figures, accepted for publication in PR

Cd-vacancy and Cd-interstitial complexes in Si and Ge

The electrical field gradient (EFG), measured e.g. in perturbed angular correlation (PAC) experiments, gives particularly useful information about the interaction of probe atoms like 111In / 111Cd with other defects. The interpretation of the EFG is, however, a difficult task. This paper aims at understanding the interaction of Cd impurities with vacancies and interstitials in Si and Ge, which represents a controversial issue. We apply two complementary ab initio methods in the framework of density functional theory (DFT), (i) the all electron Korringa-Kohn-Rostoker (KKR) Greenfunction method and (ii) the Pseudopotential-Plane-Wave (PPW) method, to search for the correct local geometry. Surprisingly we find that both in Si and Ge the substitutional Cd-vacancy complex is unstable and relaxes to a split-vacancy complex with the Cd on the bond-center site. This complex has a very small EFG, allowing a unique assignment of the small measured EFGs of 54MHz in Ge and 28MHz in Si. Also, for the Cd-selfinterstitial complex we obtain a highly symmetrical split configuration with large EFGs, being in reasonable agreement with experiments

Model Dependence of the Properties of S11 Baryon Resonances

The properties of baryon resonances are extracted from a complicated process of fitting sophisticated, empirical models to data. The reliability of this process comes from the quality of data and the robustness of the models employed. With the large of amount of data coming from recent experiments, this is an excellent time for a study of the model dependence of this extraction process. A test case is chosen where many theoretical details of the model are required, the S11 partial wave. The properties of the two lowest N* resonances in this partial wave are determined using various models of the resonant and non-resonant amplitudes.Comment: 24 pages, 10 figures; revised fits with error estimates, expanded comparison between CMB and K-matrix model