abstract

By considering the Riemann space of the general relativity theory as a space imbedded in a pseudo-Euclidean space E\(_{10}\)(1,9), new formalism may be constructed which allows to solve satisfactorily the energy-momentum complex problem of the general relativity theory and other interesting problems.

abstract

A dynamical quark model of mesons based on the principle of a temperate interaction enabling the application of the Tamm–Dancoff method combined with a suitable cut-off is presented. The main result is that it is not at all necessary to assume an unreasonably high value of the coupling constant in order to obtain a very large mass defect of the bound quark–antiquark system.

abstract

The equilibrium deformations of the ground and excited states in nuclei in the Rare-Earth region are calculated using the Nilsson model. The residual interactions are taken into account in the form of the pairing forces. Comparison is made with previous calculations of similar type together with a suggestion of applying the idea of different deformations in ground and excited states of the nucleus in analogue state physics.

abstract

Final state interactions in the three and four body \(\pi ^-\) mesic decays of hypernuclei are considered and a general formalism is developed which enables calculation of the angular and energy distribution. The distorted wave impulse approximation is applied to account for final state interactions. Spin effects, many channels, Coulomb interaction are discussed in detail. the paper contains only the derivation of the basic formulae, a comparison with experiment will be given in the second past of this work.

abstract

The accuracy of the phase-shift approximation in calculating the well-depth of a \({\mit \Lambda }\)-particle in nuclear matter, \(D_{\mit \Lambda }\), is investigated. A model case of a simple \({\mit \Lambda }\)–\(N\) potential is considered. The value of \(D_{\mit \Lambda }\) calculated in the phase-shift approximation is about 10 MeV higher than the value obtained by the complete \(K\)-matrix method. This indicates that the phase-shift approximation is too rough for application in the \(D_{\mit \Lambda }\) problem.

abstract

The static, cylindrically symmetric solutions of Einstein’s unified field equations are derived, in the case when only an electric field is present. It is shown that, in general, the strong field equations lead to untenable physical conclusions.

abstract

A solution of Einstein’s unified field equations corresponding to a static, uniform line charge is derived. It is shown that in the particular case considered the strong and the weak field equations coincide. A possible empirical test of the theory is discussed.

abstract

The binding energy of a \({\mit \Lambda }\) particle in nuclear matter, \(B_{\mit \Lambda }(\infty )\), is calculated with the help of the modified Moszkowski–Scott separation method. This procedure permits one to systematically expand the effective \({\mit \Lambda }\)-nucleon interaction in terms of \(G_s\), the reaction operator for free particles caused by the short range part of the potential alone. The form of the series is discussed. The contribution of all first and second-order terms to the binding energy has been calculated numerically with two central \({\mit \Lambda }N\) potentials. The rearrangement energy is taken into account. The calculated \(B_{\mit \Lambda }(\infty )\) are compared with the empirical value of \(B_{\mit \Lambda }(\infty )\). Possible ways of reducing the calculated value of \(B_{\mit \Lambda }(\infty )\) are discussed.

abstract

Assumptions underlying the search for new exact solutions of Einstein’s field equations for space filled with matter are examined. Three assumptions are retained: spherical symmetry, macroscopic neutrality of matter, and the energy-momentum tensor of a perfect fluid. Schwarzschild canonical coordinates have been used in the previous investigations of this series, now other coordinate systems are introduced, and differential equations relating the metric tensor components and their derivatives are given. These equations which result from the conditions of pressure isotropy provide the basis of a systematic search for exact solutions along similar lines as in preceding papers. Such equations are given both for static and non-static matter distributions. Two other possibilities of deriving new exact solutions of the gravitational field equations are based on proposals presented by Buchdahl and by Heintzmarin. The possibility of deriving matter distributions with pressure anisotropy is mentioned.

abstract

The role of absorption corrections in the experimentally observed line-reversal symmetry breaking is discussed. The absorption parameters are estimated from experimental data and the quark model. It is shown that the absorption corrections cannot explain the experimentally observed effect.

abstract

The absorption correction to the Stodolsky–Sakurai model is decomposed into two parts. The first part differs from the pole term only by a spin independent factor. Consequently, it does not affect the spin density matrix. The corrections which change the density matrix are small.

abstract

The diffraction dissociation of pions and kaons into three particles is discussed under the following assumptions:

• (a) dominance of the natural parity exchange,
• (b) Gribov–Morrison parity rule.

The measurable consequences of these assumptions are derived.

abstract

Two known methods of deducing from quantum electrodynamics the approximately relativistic quantum-mechanical equations for n charged fermions in an external electromagnetic field have been discussed in connection with the problem (not completely solved, as yet) of a consistent quantum-mechanical interpretation of such systems in terms of relativistic particle. observables (in the sense of the “mean” observables of Foldy and Wouthuysen). The important role of a “quasirelativistic” wave equation describing positive as well as negative energy states has been stressed. A new form of such an equation has been proposed and the idea of a new effective method of its reduction to the subspace of positive energy states shortly outlined.

abstract

The influence of the nuclear deformation on the \(K^-\) meson nuclear absorption is discussed for the states \(7i\), \(8k\), \(9l\) in dysprosium. It is found that the absorption rate, \({\mit \Gamma }^{\rm capt}\), increases by a factor of 1.5 to 1.7 due to the nuclear deformation. The value of \({\mit \Gamma }^{\rm capt}\) has also been calculated for the same nucleus on the assumption that a tail of 3 fm has been added to the Fermi distribution of nuclear matter. It is found that \({\mit \Gamma }^{\rm capt}\) increases by a factor of 2 as compared with the Fermi distribution without a tail.

abstract

The paper deals with the problem of motion of two dyons (particles with electric and magnetic charges) in relativistic classical mechanics. It is shown that the Bohr–Sommerfeld quantization rules lead to an exact formula for energy levels.