Regular Series


Vol. 16 (1985), No. 9, pp. 791 – 898


Stochastic Properties of the Friedman Dynamical System

abstract

Some mathematical aspects of the stochastic cosmology are discussed in its relationship to the corresponding ordinary Friedman world models. In particular, it is shown that if the strong and Lorentz energy conditions are known, or the potential function is given, or a stochastic measure is suitably defined then the structure of the phase plane of the Friedman dynamical system is determined.


On the Equivalence of Different Regularization Methods

abstract

The \(\hat R\)-operation preceded by the regularization procedure is discussed. Some arguments are given, according to which the results may depend on the method of regularization, introduced in order to avoid divergences in perturbation calculations.


Fermion Masses from Gravity Induced Superpotential

abstract

The Nanopoulos–Srednicki superpotential has been generalized to include Planck slot non-renormalizable terms, including one proportional to Tr(\(A^4\)), \(A^a_b\), being the 24-adjoint representation. The symmetry breaking mechanism is shown to stay intact. We postulate a new generation of particles and estimate their masses from mass-generation number graphs. New mass ratios in terms of parameters is proposed. Those parameters can be adjusted to yield any mass ratio at the grand unification mass scale. The parameters are also compared under some very restrictive conditions, by equating the mass ratios to the experimental values.


Cumulative Pion Production in Collisions of Relativistic Nuclei

abstract

The model of the cumulative-type processes in nucleus–nucleus collisions is formulated. It is based on the “gathering” scheme applied earlier for describing the cumulative particle production in hadron–nucleus interactions. Invariant cross sections for pion production are calculated and compared with the experimental data obtained at initial kinetic energy of 2.1 GeV/nucleon. The predictions of the model are given for primaries available at Dubna accelerator.


Extended Superkinematics

abstract

The supersymmetric extensions of the kinematical groups with \(N\) bispinor generators are considered. The case of anti-de Sitter group is treated in detail. It is proved that the maximal internal symmetry group is then SO(\(N\)).


Solvable Quantum-Mechanical Model with Exponential Spectrum and Gauge Structure

abstract

An exactly solvable, one-dimensional quantum-mechanical model of a new kind is constructed. It gives an exponentially rising discrete energy spectrum bounded from below and displays an explicit gauge invariance. To our knowledge, such a type of spectrum is novel for mechanical systems.


Prospects for Measuring the Mass of Galactic Neutrinos with Coherent Detectors

abstract

Detection of a cosmic neutrino background may become possible in the future by observation of the second order coherent weak interaction with suitably isolated and tuned physical systems. By considering the example of reflection forces on a material slab it is shown that, by variations in detector geometry and orientation, it would be possible in principle to separately determine the number density, mean velocity, and rest mass of the interacting particles, and to establish their identity as neutrinos through consistency with both the expected interaction potential and astrophysical bounds on the measured parameters. The possibility of separate estimation of neutrino and antineutrino fluxes, by using material lens arrays to produce changes in particle density dependent on the sign of the interaction potential, is also discussed.


Rotational Bands in Some Odd Mass \(1f_{7/2}\) Nuclei

abstract

The properties of \(^{45}\)Sc, \(^{45}\)Ti, \(^{51}\)Cr and \(^{55}\)Fe were probed with proton beam of energies ranging from 3.5 MeV to 5.0 MeV using Chandigarh Variable Energy Cyclotron. Doppler Shift Attenuation (DSA) technique was adopted to deduce the lifetime of excited states. The spin of levels and mixing ratio of \(\gamma \)-transitions were deduced from the analysis of \(\gamma \)-ray angular distribution data. Most of the states in these nuclei were found to follow \(J(J+ 1)\) rule and the transition probability \(B\)(E2) of \(\gamma \)-rays, from these levels, were found to be enhanced over single particle estimates. The existence of several rotational bands is therefore suggested in these odd mass \(1f_{1/2}\) nuclei. Apart from this, some new information regarding lifetimes and mixing ratios has been obtained for these nuclei.


Heavy Ion Reactions with Alpha Particle Transfer

abstract

Nuclear reactions between heavy ions with alpha particle transfer are considered. Theoretical studies for these heavy ion reactions are introduced. Theoretical expressions for the differential cross section are developed using pure Coulomb interaction between the interacting particles in the initial and final channels. Numerical calculations are carried out for the reaction \(^{12}\)C(\(^{13}\)C, \(^9\)Be)\(^{16}\)O using the Coulomb Wave Born approximation and also by the DWBA. The agreement between the theoretical calculations and the experimental data is good. The extracted spectroscopic factors are reasonable.


Nuclear Giant Resonances in a Relativistic Mean-Field Theory

abstract

Isoscalar and isovector giant resonances in doubly magic nuclei are studied in a relativistic meson–baryon field theory. Time-dependent oscillations about static ground-state configurations are described by linearized equations of motion. Coulomb effects are included. Variational estimates of the solutions to these equations are obtained using relativistic Hartree results to define the equilibrium densities. Energies and transition densities are found for the lowest-lying collective modes, and the systematic dependence of the energies on baryon number is examined.


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