abstract

The equations of isentropic rotational motion of a perfect fluid are investigated with use of the Darboux theorem. It is shown that, together with the equation of continuity, they ensure the existence of four scalar functions which constitute a dynamically distinguished set of coordinates. If in this system of coordinates the metric tensor is constant along the lines tangent to velocity and vorticity fields, then the field equations with \(T_{ij}=(\in \pm p)\mu _i\mu _j-pg_{ij}\) can be completely integrated. The resulting metrics divide into 3 families, first of which contains 6 types of new solutions with non-zero pressure. All of them are given explicitly in terms of hypergeometric or confluent hypergeometric functions, type IV being the only one containing entirely elementary functions. The second family contains only the solution of Gödel, and the third one — only the solution of Lanczos.

abstract

After some remarks dealing with the generators of unitary transformations we consider the canonical quantization of free fields in a static space-time: expansion of the field operators, complete and orthonormal systems of classical solutions, definition of creation and annihilation operators, occupation number representation of the Hamiltonian.

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A new modified quasirelativistic equation (different from that of Breit) for \(N\) charged Dirac particles in the external stationary electromagnetic field is proposed. This equation is an amplified quantum-mechanical Bethe–Salpeter equation obtained by adding (in a semi-phenomenological manner) terms which take into account radiative corrections. The application of this approximate equations is limited to third order terms in the fine structure constant \(\alpha \).

abstract

The photon propagator in the compensating current dependent quantum electrodynamics, formulated previously, is investigated. In particular, it is shown that the vacuum polarization tensor can be defined in the same way as in conventional quantum electrodynamics. Since the theory is fully gauge-invariant, this tensor is a transverse quantity before renormalization and therefore there is no trouble with the quadratically divergent term in \({\mit \Pi }^{\mu \nu }\). The problem of a proper definition of the current operator is also considered. It is shown that the definitions proposed by Heisenberg and Euler, Schwinger and Brandt can be generalized to the case of an arbitrary compensating current, described previously. The definition of the current gives a certain prescription of the regularization, which ensures transversity of the vacuum polarization tensor at every step of calculations. We also discuss the difference between this method of regularization and other methods. A perturbation expansion of the current operator is calculated up to the third order and it is shown that it is independent of the compensating current.

abstract

Multiplicity distribution of secondary particles in inelastic hadron collision at high energy is studied in the semiclassical impact parameter representation. The scaling function is shown to consist of two factors: one geometrical and the other dynamical. We propose a specific choice of these factors, which describe satisfactorily the elastic scattering, the ratio of elastic to total cross-section and the simple scaling behaviour of multiplicity distribution in p–p collisions. Two versions of diffractive-excitation like models (global and local excitation) are presented as interpretation of our choice of dynamical factor.

abstract

An analysis of the diffraction dissociation processes in \(K^+\)p interactions at 5 and 8.2 GeV/\(c\) \(K^+\) incoming momentum is presented. An isospin analysis was performed for the single dissociation processes: \[K^+ \to K^*(890)\pi \ \ {\rm and}\ \ p\to {\mit \Delta }(1236),\] observed in the reactions: \[K^+{\rm p}\to K^*(890)\pi {\rm N}\ \ {\rm and}\ \ K^+{\rm p} \to K\pi {\mit \Delta }(1236).\] It confirmed the dominance of the \(I = 1/2\) component in the \(Q\) bump and in the low mass \({\mit \Delta }\pi \) enhancement. It is found that the interference term between the isospin 1/2 and isospin 3/2 amplitudes is small for \(Q\) region and is quite sizable for the low \({\mit \Delta }\pi \) mass enhancement.

abstract

A generalization of the Heisenberg quantum theoretical multiplication law is proposed. What kind of modification this introduces to the usual results of quantum mechanics is shown. The large domain of applicability of the generalized product is indicated.

abstract

A model of multiparticle production in high energy hadron collisions developed by Heisenberg more than 20 years ago is reexamined and compared to recent data on multiplicities, dispersion of multiplicities and partial cross-sections. It is found that, contrary to popular belief, the behaviour of the multiplicity predicted by his strong coupling model is still consistent with the data. Predictions about the intimate connection between the so-called KNO-scaling, and the constancy of the inelastic cross-section are discussed in the light of the present experimental results.

abstract

Diffractive production on nuclei is calculated using as an input a specific model for diffractive production on nucleons. In this model diffractive production is described as a shadow of non-diffractive multiple production of particles. The mechanism for non-diffractive production is taken to be hadronic bremsstrahlung of independently produced clusters. It is shown that such a model naturally explains the strikingly simple pattern of absorption observed in coherent production on nuclei. Possible generalizations of these results are indicated.

abstract

The results of several recent experiments suggest the existence of composite structure of the nucleon. Consequently some analogies in the properties of nucleons and nuclei are arising. For example, the diffraction pattern of elastic proton–proton collision, emerging at high energies, is similar to that of the proton–nucleus collision.

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The properties of the generalization of a Regge-behaved dual amplitude with Mandelstain analyticity (DAMA) to production processes are studied. A procedure of analytic continuation of \(A_5\) into the physical domain is suggested. The amplitude has necessary dual, asymptotic and resonance properties.

abstract

Short-living isomeric states in neutron-deficient Rh isotopes were investigated with Ge(Li) detectors and a toroidal iron-free electron spectrometer. Decay schemes were proposed for \(^{97m}\)Rh (44 \(m\)), \(^{98m}\)Rh (3.5 \(m\)), and \(^{110m}\)Rh (4.7 \(m\)). The properties of the isomeric transitions observed in Rh isotopes support the shell model interpretation of the low-lying excited states.

abstract

The level structure of \(^{130}\)Ba was studied from the \(\beta ^+\)-decay of \(^{130}\)La. The gamma rays emitted in the decay were measured using a Ge(Li) detector. The \(^{130}\)La isotope was produced in the \(^{130}\)Ba(p,n) \(^{130}\)La reaction at a proton energy of \(E \simeq 9.5\) MeV. A \(^{130}\)La \(\to \) \(^{130}\)Ba decay scheme is proposed.

abstract

The excited quark model and the additive quark model constraints on the angular decay distributions of \(B^*\) produced by virtual photons in the process \(\gamma _{\rm virt} \to PB^*\) are obtained. Some of the quark model relations are compared with the experimental data to check the quark model, others are used to obtain for \(\Delta ^{++}\) the ratio of the cross-sections for production by longitudinal and transverse photons on protons \(R = \sigma _{\rm L}/\sigma _{\rm T}\). The agreement of the quark model predictions with experiment is found to be good.