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The K-matrix approach is mostly used when analyzing the overlapping resonances. It provides unitarity of the scattering matrix, however, its parameters are not physical quantities; the resonant and background contributions cannot be separated; and the scattering amplitudes have zeros between the positions of resonances. The parameters of the Breit—Wigner (BW) functions are the masses and widths of resonances; however, the sum of such functions violates unitarity. We construct a unitary S-matrix by taking into account the interference of BW functions. In the examples presented in the paper, these two approaches are compared.

The properties of f 0(980), f 0(1370) and f 0(1500) mesons are studied by means of a generalization of the Breit-Wigner approach preserving unitarity in case of several overlapping resonances.

The situation on the ρ-meson excited states is studied. A few of such broad overlapping resonances were found during the recent years, but their properties are not well established as yet and there is a long-standing discussion on the existence of lowest-mass ρ(1250) excitation. The analyses are usually based on Breit-Wigner type formulas which do not satisfy unitarity relation in the case of overlapping resonances. Our analysis takes into account an explicitly unitarized multichannelS-matrix and we give a good description of thep-wave ππ scattering, the e+ e−→2π and e+ e−→4π processes up to about 2 GeV.

The multichannelM-matrix method is applied to a nucleon-antinucleon system by taking into account elastic proton-antiproton scattering, charge exchange reaction and annihilation. Thes, p andd-waves are considered with the effective-range approach to describe the differential and total cross-sections for elastic proton-antiproton scattering and charge-exchange scattering, total cross-sections and real-to-imaginary ratio of the forward amplitude of elastic scattering. Thep-wave bound state which leads to high anisotropy of\(\bar pp\) reactions was found.

MultichannelM-matrix method is applied to an N¯N-system with taking into account elasticp¯ p-scattering, charge-exchangep¯ p → n¯ n reaction andp¯ p annihilation. The isospin breaking in theM-matrix is discussed. We describe the differential and total cross-sections forp¯ p → p¯ p andp¯ p → n¯ n processes, cross-section σtot(p¯ p) and the real-to-imaginary ratio of the forward amplitude of elasticp¯ p scattering. The fitting leads to bound state in thep-wave near thep¯ p-threshold, which elucidates a significant role of this wave at small energies.

We have made a computer investigation of coherent effects in polarized systems of nuclear or electron spins using a microscopic approach. The many-body problem is reduced to simulation of dynamics of spins that interact with each other and with external fields. We show that a spin system in a resonance circuit can emit a coherent superradiative pulse when the system is initially in an essentially unstable state. For a polarized spin system without circuit, we have found a new regime of coherent emission in the case of an external resonance pumping.

Here we present results of our investigation of coherent effects in polarized spin systems on the basis of a microscopic model but not using the phenomenological Bloch equations. A computer simulation is realized for a system of nuclear or electron spins interacting with realistic dipole-dipole forces. Different initial and external conditions are analyzed for a spin system coupled with a resonator or one without the resonator and in the presence of an external oscillating field or without this pumping. Insofar as the phenomenological equations presuppose the uniformity of a system, it requires a microscopic model to show accurately when the coherence does appear. To this end, we introduce the coherence coefficients and consider their time behavior in detail. Some peculiarities due to dipole spin interactions, which are not present in the Bloch equations, are noted.

The properties of f 0(980), f 0(1370) and f 0(1500) mesons are studied by means of a generalization of the Breit-Wigner approach preserving unitarity in case of several overlapping resonances.

Coherent effects in polarized systems of nuclear or electron spins using a microscopic model are studied, but not the Bloch equations. It is shown that the spin system in a resonance circuit can emit a coherent superradiant pulse when the system is initially in an essentially unstable state, at a time much shorter than the spin dephasing time T2 when the coupling of the system with the circuit is sufficiently strong, and at the time longer than T2 when this coupling is weak. The important role if dipole spin-spin interactions is elucidated.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The existing methods of constructing an explicitly resonance, unitary S matrix are reviewed. These methods can be used for describing groups of resonances r i with identical quantum numbers in the case where they overlap, when |E r i −E r j |∼Γ r i +Γ r j . The relation between these methods is studied in detail. The description of excited states by means of the Breit–Wigner formulas is used most often in many problems of resonance physics and nuclear physics, and in this review we focus on the construction of a unitary, T -invariant, multichannel, multiresonance S matrix of the Breit–Wigner type. As a real application of these methods we study the excitation spectrum of vector ρ and ω mesons. The possibility of interpreting these as quark–antiquark excited states is discussed.

The existence of theρ′ (1250)-meson is studied. Determination of the inelastic resonance masses and widths, and the background parameters is considered.M-matrix parametrisation of the ππ, πω partial amplitudes is compared with the parametrisation as a sum of the inelastic resonance term and the background amplitude. It is shown that the small inelastic background concealsρ′ in ππ channel. Taking the background into account provide a good description of the ππ scattering data at\(\Gamma _{\rho '\pi \pi } /\Gamma _{\rho '\pi ^0 \omega } \approx 0.15\).