Dispersion Relation Analyses of Pion Form Factor, Chiral Perturbation Theory and Unitarized Calculations

The Vector Pion form factor below 1 GeV is analyzed using experimental data on its modulus, the P-wave pion pion phase shifts and dispersion relation. It is found that causality is satisfied. Using dispersion relation, terms proportional to s squared and s cubed are calculated using the experimental data, where s is the momentum transfer. They are much larger than the one-loop and two-loop Chiral Perturbation Theory calculations. Unitarized model calculations agree very well with dispersion relation results.Comment: 10 pages, 4 PostScript figures some minor changes and added reference

When is it possible to use perturbation technique in field theory ?

The vector pion form factor is used as an example to analyze this question. Given the experimental radius of the pion, the crucial question is whether perturbative methods could be used for the effective chiral lagrangian to calculate the pion form factor. Our analysis shows that the pion rms radius is far too large (or the related rho resonance mass is too low) for the perturbation theory to be valid.Comment: 11 pages, Latex, 4 eps figs. Contribution to the proceedings of the workshop "QCD2000" Villefranche-sur-Mer, France, January 200

On the Sutherland's Integrability Condition for Two-Dimensional N-Particle Systems

Following Sutherland's work on one-dimensional integrable systems we formulate and study its two-dimensional version. Physically it expresses the absence of true 3-body forces among an assembly of N particles leaving exclusively effective 2-body interactions. This criterion may be a suitable candidate for an integrability condition.Comment: 13 pages,uses LATeX2e and epsf. File prepared using the uufiles packag

Phyto-evaluation of Cd-Pb Using Tropical Plants in Soil-Leachate Conditions

Sources of soil contamination can exist in various types of conditions including in the form of semifluids. In this study, 3 different types of tropical plants, Acacia (Acacia mangium Willd), Mucuna (Mucuna bracteata DC. ex Kurz) and Vetiver (Vetiveria zizanioides L. Nash), were tested under different levels of soil-leachate conditions. The relative growth rate, metal tolerance, and phytoassessment of cadmium (Cd) and lead (Pb) accumulation in the roots and shoots were determined using flame atomic absorption spectrometry. Tolerance index, translocation factor, metal accumulation ratio, and percentage metal efficacy were applied to assess the metal translocation ability among all the 3 types of plants. Significantly higher (P \u3c .05) accumulation of Cd and Pb was exhibited in the roots and shoots of all 3 plants growing under the soil-leachate conditions. However, negative growth performance and plant withering were observed in both Acacia and Mucuna with increased application of higher soil-leachate levels. Vetiver accumulated remarkably higher total concentration of Cd (116.16-141.51 mg/kg) and Pb (156.37-365.27 mg/kg) compared with both Acacia and Mucuna. The overall accumulation trend of Cd and Pb in the 3 plants growing under the soil-leachate conditions was in the order of Vetiver \u3e Acacia \u3e Mucuna. The findings of the study suggest that Vetiver has great potential as Cd and Pb phytoremediator in soil-leachate conditions