abstract

The three classes of axially symmetric space-times, corresponding to homogeneous cosmological models which are filled with perfect fluid are studied in the framework of the Einstein–Cartan theory of gravitation. A general set of equations is given with the admissible non-vanishing torsion and spin components compatible with the symmetry. This is further specialized to the “generalized classical description” of spin, and the “classical description” with only one surviving spin tensor component. Closed and open models have to be necessarily shearing while Euclidean models admit also a zero value of shear. A general expression for shear in all classes of models is derived; it is helpful in proving that the singularity may be prevented in the Einstein–Cartan theory thanks to the repulsive spin–spin interaction. This is possible even in those semiclosed models which do not permit any simply transitive group of motions; they may constitute authentically pulsating models with shear and torsion.

abstract

Various models of the galactic nuclei are discussed. The dense star cluster model for the galactic center is treated in greater detail. It turns out that such model can explain many of its observed properties, i.e. emission of gravitational waves, number density and energy of cosmic rays in the Galaxy, \(\gamma \) and \(X\)-ray emission, infrared and radio spectrum.

abstract

A Schroedinger type quantization of free fields on arbitrary spacelike hypersurfaces in curved space-time is considered. The gravitational field is assumed to be a classical background. In the field representation the state functional depends on the field configuration on the hypersurface. A generalized Tomonaga–Schwinger equation describes the dynamical evolution of the quantum field. The expectation values of the field operators (e.g., energy-momentum tensor) are defined.

abstract

In the framework of Feynman’s quark–parton model for inclusive electroproduction and quark model of Ezawa, Maharana and Miyazawa for hadronic inclusive processes, relations between invariant cross sections for electroproduction of pions and purely hadronic production of pions in the beam fragmentation regions are derived. They are satisfied by data. The ratio of parton fragmentation functions \(\eta =D^{\pi +}_u(z)/D^{\pi +}_d(z)\) is estimated from purely hadronic processes independently from the parton model.

abstract

The shell model with MSDI residual interaction is used to investigate properties of levels in the \(^{42}\)Ca and \(^{42}\)Sc nuclei. The \(^{40}\)Ca core with two active outer nucleons is assumed. The interaction between two outer nucleons is given. The numerical values of 196 two-particle antisymmetrized matrix elements were calculated. Two different ways were used in the construction of the interaction term: (a) The parameters \(A_0\) and \(A_1\) were considered to be state independent, thus being constant in the configuration space, (b) The parameters \(A_0\) and \(A_1\) were allowed to vary in the dependence of the combination of \(j\) values. In order to simulate this dependence three values for \(A_0\) and \(A_1\) were fitted. The reasons of this assumption are discussed. In the calculations performed in these two versions the parameters \(A_0\) and \(A_1\) were adjusted to produce the best agreement with the experimental level schemes. The energy matrices were diagonalized and the calculated level schemes for both \(^{42}\)Ca and \(^{42}\)Sc nuclei are presented. In the both nuclei the density of the calculated levels is significantly less than of the observed levels. This fact leads to the conclusion that some core excitation models play an important role in the formation of low-lying states in the \(^{42}\)Ca and \(^{42}\)Sc nuclei.

abstract

The \(\beta ^+\)-EC decays of isomeric and ground states in \(^{199,201,203}\)Po isotopes, produced in heavy ion reactions have been investigated. On the basis of the single \(\gamma \)-spectra, \(\gamma \)–\(\gamma \) coincidence and conversion electron measurements, the levels in \(^{199,201,203}\)Bi isotopes are presented. The experimental data and the results of theoretical calculations are compared.