abstract

Lie-Bäcklund transformation relating the equation for one-sided type-\(D\) vacuum gravitational instanton with the one for self-dual vacuum gravitational instanton admitting the “rotational” Killing vector field is presented. As the examples, Euclidean Cahen–Defrise solution and Eguchi–Hanson-like metrics are examined.

abstract

The paper discusses action principles simultaneously leading to the general relativistic Lorentz equations of motion in a given background field and to the electromagnetic deviation equations of the first and second order of the Lorentzian world lines. Some consequences of the simultaneous action principles connected with their reparametrization covariance and invariance under gauges of deviations, as well as the corresponding Hamilton–Jacobi equations are also considered.

abstract

A method for numerical calculation of large-\(n\) probabilities from an analytically given form of a generating function is proposed. The method, which uses the Cauchy integral formula, is found to be relatively quickly convergent and gives good control of errors of calculations.

abstract

The microscopic collective hamiltonian for the axial quadrupole vibrations was derived from the QQ + PP model. The generator coordinate method and the generalized gaussian overlap approximation was used. The results were compared with the cranking estimates. The zero-point correction to the potential energy was found important. The mass parameters for the full two-body hamiltonian are nearly the same as for the mean-field approximation to that hamiltonian.

abstract

Within a field theoretical model it is shown that a series of numerical experiments with random initial conditions corresponding to hot nuclear systems leads to final stable fragments in a quite natural way. Besides it is expected that this time-dependent break-up description could give a stimulation on future calculations for mass spectra and at least some hints concerning the questions of a quasi-critical behaviour of a finite system.

abstract

Analysis of the gamma radiation was performed for 65 radioactive particles from the Chernobyl fallout. Isotopic ratios for Ce and Ru isotopes, as well as ratios of radioisotopes of various elements have been systematized and provided information concerning general features of processes leading to the hot particle formation.

abstract

Energies and widths of the substitutional (p3/2, p3/2\(^{-1})_{\rm EN}\) states in \(_{{\mit \Sigma }-}^{12}\)Be and \(^{12}_{{\mit \Sigma }}\)C are determined by solving single particle equations with a complex \({\mit \Sigma }\) potential, containing the Lane potential \(v_{\rm t}\) and a charge independence breaking part \(v_{\rm CB}\). Magnitude of \(v_{\rm t}\) and \(v_{\rm CB}\) compatible with experimental data on \(^{12}_{{\mit \Sigma }-}\)Be and \(^{12}_{{\mit \Sigma }}\)C are discussed. Radial oscillations of the isospin distribution in \(^{12}_{{\mit \Sigma }}\)C are demonstrated.