Bibliothek

Notizen: Zusammenfassung The dispersion relation for the 3-3-amplitude given byChew, Goldberger, Low andNambu cannot be tested presently because of the experimental uncertainties of the scattering phase, but it discriminates between several interpolations of the experimental data. The only conclusion which can be drawn from the discrepancy found byTsuchida andKakazawa is that the Breit-Wigner formula is not suitable. We have shown that the experimental values are consistent with the dispersion relation if an effective range formula is used up to 120 MeV. The result for the coupling constantf 2=0.097 is somewhat higher than the value used in the effective range formula, but the difference is probably not larger than the terms which are neglected in the derivation of the dispersion relation.

Notizen: Abstract The cross section forπ 0-production is calculated from the results of the dispersion relation approach ofChew, Goldberger, Low andNambu and compared with the experimental data. The predictions are made using the measured values of all scattering phase shifts. A fit of the theoretical result toσ(90

Notizen: Abstract The perturbation theoretical results for the self-energy and the mass of the polaron are given in 4-th order. Even for a coupling strength usually assumed in NaCl (g2=6) the deviations from the values found inFeynman's variational approach are negligible. A remark concerning the approximation character ofFeynman's method is made from the comparison of the expressions for the self-energy.

Notizen: Abstract The pion-nucleon forward scattering amplitude has been calculated from new data of the total cross sections, using several assumptions on the energy dependence above 20 GeV. The results are presented as complex diagrams of the forward amplitude, which are of interest for the discussion of the nucleonic resonances and the non-resonant background scattering. In addition the predictions for the elastic forward cross sections are given as well as the contributions of the real parts to this quantity. A comparison with the new Saclay data of the charge exchange forward cross section leads to the estimate αρ≈0.6, if a Regge behaviour is assumed above 20 GeV. There are indications in favour of a new $$T = \tfrac{1}{2}$$ resonance at the total c.m. energyW≈2.8 GeV.

Notizen: Abstract The difference between theπ + p andπ − p diffraction peaks is used for an estimate of the imaginary part of the charge exchange scattering amplitude. The imaginary part has a narrow peak in the forward direction and passes over to negative values at a momentum transfert of about −0.15(GeV/c)2. If the charge exchange amplitude is dominated by the contribution of theρ Regge pole, the peak is mainly due to thet-dependence of the residue function and a narrow forward peak is expected in the charge exchange angular distribution.

Notizen: Abstract The total cross sections up to 65 GeV/c and the experimental real parts of the isospin evenπN forward amplitude are compatible with the dispersion relation. However the arguments which led to the introduction of theP′ Regge pole (α p′≈0.5) are not valid. The data are compatible with the existence of the integral in Lehmann's sum rule, which implies a finite real partD +(∞) at infinity. — The isospin odd combinationσ − is still consistent with the reggeizedρ-exchange model and with Pomeranchuk's theorem.

Notizen: Abstract The effective range parameterb − for πN s-wave scattering is calculated from fixed-t dispersion relations, using experimental information for the imaginary parts. The result is compared with that of other calculations, based on Ward identities and phenomenological Lagrangians. It is pointed out that a direct determination ofb − from experimental data is not possible. Since the Δ-propagator is not unique, the Δ-exchange amplitudes are given for a one-parameter class of propagators (Appendix).

Notizen: Abstract The small pion-nucleon scattering phase shifts have been calculated byChew, Goldbeeger, Low andNameu, using relativistic dispersion relations and the data of the first resonance. The authors introduced several approximations without going into the details of their validity. It is the aim of this paper to give a more accurate treatment, because it turned out that the approximations used byChew et al. result in pretty large errors, at least for the s-waves. First we retain the neglect of all contributions to the dispersion integral other than the 33-part and consider the s-wave amplitude Re f s (−) =(sin 2α1−sin 2α3)/6q. For 200 MeV (lab.) pions, the correct evaluation of the recoil effects leads to a value 2.8 times lower than the 1/M-approximation and the projection, carried through without an approximation, deviates by 20% from the first terms of the expansion used by CGLN. At zero kinetic energy a comparison with the dispersion relation for forward scattering shows that the above mentioned neglected contributions to the dispersion integral amount to 35±15%. The combination of the s-phases was recalculated, replacing the first two approximations of CGLN by an exact treatment. In order to take care of the main part of the neglected contributions to the dispersion integral, we added the value found at zero kinetic energy. The energy dependence, not accounted for by this procedure, should result in a one-sided deviation from the experimental data. Comparison with these data, however, shows that the absolute values as well as the energy dependence of the calculated curve agree reasonably with the measurements up to 333 MeV. Cini et al. andHamilton et al. have used an interpolation formula which represents the measured s-wave data by adjusting parameters, whereas in this paper the combination of s-phases is calculated from α33 and σtot. Our result for the s-wave scattering lengths a1−a3=0.255 is compatible with P=1.60 for thePanofsky ratio and with the measured photomeson cross section which near threshold shows no deviations from the perturbation theoretical values for charged pions (f2=0.080). It is doubted that in this energy region the small additional contributions, which follow from the dispersion theory of photoproduction in its present state, are really an improvement of the perturbation theoretical results. The scattering lengths of the p-waves have been calculated, taking into account only the 33-part of the dispersion integral, but without the recoil approximation of CGLN (f2=0.080): a33=0.189, a13=−0.045, a13−a31=0.0007, a11=−0.147. The formulae for these scattering lengths and the corresponding q2-coefficient of the s-wave amplitude fulfilGeffens relation identically, if the total cross sections occuring in the integral are replaced by their 33-parts. This changes the value of the integral by 5 to 10%. The approximations ofChew et al. have been used in the discussion of the influence of the ππ-interaction on the πN-scattering phase shifts. Our result makes it worthwhile to reconsider this question.

Notizen: Abstract The results of a phenomenological analysis are compared with the Regge model.

Notizen: Abstract It is shown that the original version of the sum rule relating the isovector part of the nucleon magnetic moment to aπ N scattering amplitude is not consistent with the experimental data. However there is good agreement for the corrected version ofMaiani andPreparata.