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[en] Two new methods for determining the coupling constant g are proposed: dispersion relations and integral equalities with a damping function, due to the introduction of which they are practically finite-energy; that enables one to determine the constant g more accurately and reliably. It is shown that the amplitude of forward π⁺ p scattering has only two zeroes in the complex E-plane outside cuts. Two theorems are proved, which establish new conventional exiomatic boundaries: the lower one for [dsigma₁(E)/dΩ][dsigma₂(E)/dΩ] and the upper one for [sigma₁(E)sigma₂(E)]/[sigma₃(E)dΩ]. The second boundary is a specific generalization of the Pomeranchuk theorem

[en] The study of the π^-p → ρ⁰n and π^-p → ωn amplitudes close and below the vector meson production threshold (1.2<√(s)<1.8 GeV) reveals a rich dynamics arising from the presence of specific baryon resonances in this energy range. The interference pattern of the e⁺e^- decays of the ρ⁰- and ω-mesons produced in π^-p reactions reflects directly this dynamics. We discuss this interference pattern in the π^-p → e⁺e^-n reaction as function of the total center of mass energy √(s). We emphasize the importance of an experimental study of this reaction, which could be made with the HADES detector and the available pion beam at GSI. (orig.)

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[en] The uncertainty principle provides the optimal lower bound on the mean square orbital angular momentum for any two-body system in terms of its angular distribution. Lower bound on the mean square total angular momentum is also given

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[en] The question of the existence of the soft-photon expansion and its connection with the derivation of the soft-photon theorem is studied. We find that the soft-phonon expansion does not necessarily exist for all possible bremsstrahlung cross sections, and if such an expansion does not exist for some types of cross section, then the soft-photon theorem cannot be derived for them. We define two different classes of bremsstrahlung cross section for our study, which we call the H-type cross section and the R-type cross section. We find that the R-type cross section can be expanded in powers of k (photon momentum) with all coefficients of the expansion which are independent of k, while the H-type cross section can only have an expansion whose coefficients are all functions of k. Moreover, we have shown that those coefficients which are functions of k must necessarily contain off-shell parameters. Therefore, we conclude that the soft-photon expansion exists and hence the soft-photon theorem can be derived only for the R-type cross section. This strongly implies that the R-type cross section is to be preferred for the study of bremsstrahlung processes

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[en] A simple model of resonance formation and decay in hadronic collisions is studied and compared to the data of the EHS/NA22 Collaboration on π^-p interactions. The data indicate a rather short formation time of resonances, about 0.2-0.4 fm/c. (author)