Regular Series

Vol. 17 (1986), No. 4, pp. 317 – 387

Possible Observation of the Scalar Meson at \(\sim 1280\) MeV in the Reaction \(\pi ^-{\rm p}_{\uparrow } \to \pi ^+\pi ^-{\rm n}\) at 17.2 GeV/\(c\)

Acta Phys. Pol. B 17, 317 (1986)

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Recent analysis of the reaction \(\pi ^-{\rm p}_{\uparrow } \to \pi ^+\pi ^-{\rm n}\) at 17.2 GeV/\(c\) for \(|t| \gt 0.2\) GeV\(^2\) yields relatively narrow scalar resonance, with parameters resembling those of g\(_{\rm s}\)(1240). Its unusual production properties are tentatively explained in terms of a hybrid meson trajectory. Importance of the polarized target information is also discussed.

On the Dyon–Fermion System

Acta Phys. Pol. B 17, 325 (1986)

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A dyon–fermion system is considered. We prove that there is no finite energy, spherically symmetric, time-independent solution of the Yang–Mills–Higgs–Dirac equations with non-vanishing fermionic currents.

\(\theta (1690)\) — Isn’t It a Glueball?

Acta Phys. Pol. B 17, 333 (1986)

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An alternative mixing pattern of \(2^{++}\) mesons \({\rm f}, {\rm f}', \theta \) leads to the conclusion that \(\theta \)(1690) can be understood as a particle containing about 90% of glueball state.

Method of Separating the Angular Coordinates in Two-Body Wave Equations with Spin

Acta Phys. Pol. B 17, 337 (1986)

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An explicit form of total angular momentum eigenfunctions is found for the physical systems described by one three-dimensional space coordinate and arbitrary spin degrees of freedom. The resulting formula is usefully parametrized by the multicomponent radial wave function. The dependence on the angular coordinates is given by action of generalized spherical harmonics. The formula gives a convenient method of separation of the angular coordinates in an arbitrary one- or two-body wave equation with spin. As an example, the method was applied to the relativistic wave equation for one Dirac and one Duffin–Kemmer particle, proposed recently by Królikowski. A corresponding set of radial equations is derived in the case of spherically symmetrical interaction potentials.

Nonperturbative Effects in Electron Positron Annihilation into Mesons

Acta Phys. Pol. B 17, 347 (1986)

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A cross section for electron positron annihilation into three pions is calculated which includes contributions made by exact solutions of nonlinear equations.

Some \(\sigma \)-Like Models in Even-Dimensional Spaces

Acta Phys. Pol. B 17, 351 (1986)

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We propose a class of grassmanian models in \(2k\) dimensions which for \(k = 1\) reduce to CP\(^N\) models and for \(k = 2\) to composite SU(2) Yang–Mills models. We define and discuss the conditions of selfduality for these models and present corresponding one instanton field configurations. Next we consider a universally coupled Dirac field. We exploit the similarity of the matrices used in the construction of one-instanton field configuration to the convenient choice of Dirac gamma matrices to find zero modes of the associated Dirac background problem.

Relativistic Coulomb Scattering

Acta Phys. Pol. B 17, 365 (1986)

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Despite the extensive literature about Coulomb scattering a few problems remain to be solved. Especially the divergence of the phase of the Coulomb wave function is a source of difficulties. Although they have been overcome, not only in the Schrödinger equation, but also in the Dirac equation, a correct treatment in the framework of a relativistic two-body theory was still lacking. Recoil effects in particular were never taken into account, although for high values of the nuclear charge they might be important. \(Z\)-values close to one hundred are beginning to play a role in high-energy scattering of heavy ions, so that, a relativistic two-body theory is called for. Of the many existing quasi-potential theories which could be used for this purpose, we decided to choose the one proposed by us ten years ago. Since the theory can be cast into a form which is almost identical to the nonrelativistic theory, it is possible to take advantage of the known exact solution for this case. In the last section we present our results and compare them with those of the Dirac equation. Also the difference in cross sections for positively and negatively charged projectiles is mentioned there.

Inflation in a Closed Universe

Acta Phys. Pol. B 17, 385 (1986)

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We investigate a class of homogeneous and isotropic cosmological models filled with radiation and constant vacuum energy. We show that in closed models inflation is possible only if the entropy is larger than \(1.7 \cdot 10^{13}\).


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