M. Sander

Analysis of NN amplitudes up to 2.5 GeV: An optical model and geometric interpretation

We analyse the SM97 partial wave amplitudes for nucleon--nucleon (NN) scattering to 2.5 GeV, in which resonance and meson production effects are evident for energies above pion production threshold. Our analyses are based upon boson exchange or quantum inversion potentials with which the sub-threshold data are fit perfectly. Above 300 MeV they are extrapolations, to which complex short ranged Gaussian potentials are added in the spirit of the optical models of nuclear physics and of diffraction models of high energy physics. The data to 2.5 GeV are all well fit. The energy dependences of these Gaussians are very smooth save for precise effects caused by the known

{pi}{pi}, K{pi}, and {pi}N potential scattering and a prediction of a narrow {sigma} meson resonance

\Delta

Meson-meson potentials from lattice QCD and inverse scattering

and N

Inversion potentials for meson-nucleon and meson-meson interactions

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Modeling of nucleon-nucleon potentials, quantum inversion versus meson exchange pictures

resonances. With this approach, we confirm that the geometrical implications of the profile function found from diffraction scattering are pertinent in the regime 300 MeV to 2.5 GeV and that the overwhelming part of meson production comes from the QCD sector of the nucleons when they have a separation of their centres of 1 to 1.2 fm. This analysis shows that the elastic NN scattering data above 300 MeV can be understood with a local potential operator as well as has the data below 300 MeV.

Nucleon‐nucleon potentials from quantum inversion and Arndt’s phase shifts SP82, SM86, FA91, SM93, SP94

Low energy scattering and bound state properties of the {pi}N , {pi}{pi}, and K{pi} systems are studied as coupled channel problems using inversion potentials of phase shift data. In a first step we apply the potential model to explain recent measurements of pionic hydrogen shift and width. Second, predictions of the model for the pionium lifetime and shift confirm a well-known and widely used effective range expression. Third, as an extension of this confirmation, we predict an unexpected medium effect of the pionium lifetime which shortens by several orders of magnitude. The {sigma} meson shows a narrow resonance structure as a function of the medium-modified mass with the implication of being essentially energy independent. Similarly, we see this medium resonance effect realized for the K{pi} system. To support our findings we present also results for the {rho} meson and the {Delta}(1232) resonance. {copyright} {ital 1997} {ital The American Physical Society}

Theoretical Predictions for Pionium Searches

Potentials between light-light and heavy-light mesons are computed from meson-meson Green’s functions in the framework of quenched lattice QCD with Kogut-Susskind fermions. Comparisons with a full QCD simulation and a simulation using an O(a2) tree-level and tadpole improved gauge action show that dynamic quarks and lattice discretization errors have no drastic influence. Calculations from inverse scattering theory propose a similar shape for \(K\bar K\) potentials, whereas a good qualitative agreement with ππ potentials could not be obtained.

Sensitivity of nucleon-nucleus scattering to the off-shell behavior of on-shell equivalent NN potentials.

Two-body interactions of elementary particles are useful in particle and nuclear physics to describe qualitatively and quantitatively few- and many-body systems. We are extending for this purpose the quantum inversion approach for systems consisting of nucleons and mesons. From the wide range of experimentally studied two-body systems we concentrate here on πN, ππ, nor, K + N, Kπ and . As input we require results of phase shift analyses. Quantum inversion Gelfand-Levitan and Marchenko single and coupled channel algorithms are used for Schrodinger type wave equations in partial wave decomposition. The motivation of this study comes from our two approaches: to generate and investigate potentials directly from data by means of inversion and alternatively use linear and nonlinear boson exchange models. The interesting results of inversion are coordinate space informations about radial ranges, strengths, long distance behaviors, resonance characteristics, threshold effects, scattering lengths and bound state properties.

Faddeev calculations for omega-meson and d' 0^-, pi NN resonance

The notion of interacting elementary particles for low and medium energy nuclear physics is associated with definitions of potential operators which, inserted into a Lippmann-Schwinger equation, yield the scattering phase shifts and observables. In principle, this potential carries the rich substructure consisting of quarks and gluons and thus may be deduced from some microscopic model. In this spirit we propose a boson exchange potential from a nonlinear quantum field theory. Essentially, the meson propagators and form factors of conventional models are replaced by amplitudes derived from the dynamics of self-interacting mesons in terms of solitary fields. Contrary to deduction, we position the inversion approach. Using Gel’fand-Levitan and Marchenko inversion we compute local, energy-independent potentials from experimental phase shifts for various partial waves. Both potential models give excellent results for on-shell NN scattering data. In the off-shell domain we study both potential models in (p, pγ) bremsstrahlung, elastic nucleon-nucleus scattering and triton binding energy calculations. It remains surprising that for all observables the inversion and microscopic meson exchange potentials are equivalent in their reproduction of data. Finally, we look for another realm of elementary interactions where inversion and meson exchange models can be applied with the hope to find more sensitivity to discern substructure dynamics.

P--matrix analyses of NN, pi N, pipi and Kpi potentials.

SAID phase shifts from 1982–1994 are used to calculate the pp and np quantum inversion nuclear potentials with the Gelfand–Levitan and Marchenko fundamental equations. With inversion we transform this historical development of data analyses into a development of NN potentials.