abstract

It is proposed that the electromagnetic field in the nonsymmetric unified field theory should be related to the skewsymmetric part of the fundamental tensor by a second grade differential operation. The form of this relation suggested leads to a correction factor in the Coulomb law.

abstract

A cylindrically symmetric solution of Einstein’s unified field equations is derived for the case when neither of the fields tentatively interpreted as electro- and magnetostatic vanishes. The form of the solution suggests a new interpretation of the geometry which will be proposed in a separate article.

abstract

In the paper formulae for the angular distribution and its asymmetry are presented. The expansion of the angular distribution and its asymmetry into Legendre polynomials provides information about the contribution of the selected partial amplitudes to the asymmetry of the angular distribution. The restriction on the asymmetry coefficient \(A(\theta )\) which follows from isospin conservation in the reaction \(A(a,b)B\) is also presented.

abstract

In a closed Einstein universe Green’s functions of electrostatics and magnetostatics are given. An integral representation of the retarded potentials is constructed which is valid for a large class of timedependent sources; the exceptional cases are discussed. The results are generalized for closed universes with Robertson–Walker-metric.

abstract

Covariant and Hamiltonian forms of the Dirac equation (for a charged particle in an external electromagnetic field) amplified by the Pauli terms, have been investigated in connection with the problem of reduction to the subspace of positive energy states.

abstract

An amplified Dirac equation has been approximately reduced to the subspace of positive energy states following the “elimination” and “transformation” methods generalized to this case, successively. Their mutual equivalence has been verified by explicit calculations accomplished to the third order of approximation.

abstract

A general class of wave equations is considered which as a special case contains the new wave equations proposed by Dirac. it is shown that it is possible to introduce the interaction with an external electromagnetic field if we choose different members of the considered class. A particular case of such wave equations is treated in some detail.

abstract

Several concrete examples of quantum Markovian processes are considered in detail. The diffusional character of the transition amplitudes found with the use of the Feynman path integral is demonstrated. Two cases of processes with boundaries (absorbing or reflecting) are discussed. Finally, the quantum analogue of the Poisson as well as the Ornstein–Uhlenbeck processes are described.

abstract

The problem of the effective radius value for strong interaction of two nuclei, which is obtained in analysing the differential cross-section of an elastic scattering, is studied.

abstract

Interpretation of the ternary fission is suggested in this paper. The proposed model makes it possible to explain the cross-section value, its dependence on energy and preferableness of fission into the fragments of comparable mass.

abstract

The question of which experiments provide the simplest way of obtaining information on the fission barrier for arbitrary nuclei (not only fissioning) is studied. With this aim in view it is suggested to use the form of the mass distribution of the fission fragments and the model developed by the authors, which is based on the inelastic shock mechanism.

abstract

The model is formulated for the process of nucleus fission in heavy ion reactions. This model includes the fission channel of a compound nucleus, in accordance with the statistical theory, as well as a new channel of direct fission occurring without the stage of the compound nucleus production.

abstract

Using a suitable normalized coordinate system the Hamiltonian for \(N\)-free relativistic spinless particles may be written in the following form \(H=\sqrt {(\sum ^N_{\alpha =1}m_{\alpha })^2+\sum ^{N}_{\alpha =1}\pi _{\alpha }^2}\). A generalized Poincaré group is identified as a group of symmetry of the system. The relativistic grand orbital momentum tensor \({\mit \Gamma }_{ij}(i,j=1,2, \dots , 3N-3)\) is defined and its connection with the many-body impact parameter — \(b\) has the following simple form \({\mit \Gamma }^2 = b^2[M^2-(\sum ^{N}_{\alpha =1}m_{\alpha })^2]\), where \(M\) is the total invariant mass of the system, and \({\mit \Gamma }^2=\frac {1}{2} \sum ({\mit \Gamma }_{ij})^2\) is Poincaré invariant. The whole scheme is presented for a three particle system, but can be easily generalized to \(N \gt 3\).

abstract

The measurements of differential cross-section of the elastically scattered alpha particles with energies 23.5 and 27.7 MeV on Nb, Pd, Ag, In, Sn, Ta, Pt, Au, Pb and Bi targets, made of natural elements, were performed in a wide range of angles. The experimental procedure and the results are presented. It was observed that the oscillatory structure of \(\frac {\sigma (\theta )}{\sigma _R}\) disappears continuously when energy is lowered from higher to lower values and approaches the Coulomb barrier. The slope of \(\frac {\sigma (\theta )}{\sigma _R}\) and the cross-section values, obtained at backward angles, varies more rapidly with energy in the vicinity of the Coulomb barrier.