abstract

The coefficients \(\alpha \), \(\beta \), \(\gamma \) and \(\delta \) appearing in the expansion of the nuclear rotational energy in powers of the square of angular velocity are calculated by a microscopic method. Two simplified nuclear two level models ate used: (i) with use of the BCS approximation, and (ii) based on the exact diagonalization of the nuclear rotational Hamiltonian including the short-range pairing forces acting between the nucleons.

abstract

New equations for the nonrelativistic scattering amplitudes in the general type of reactions and for scattering amplitudes of the two relativistic particles are obtained. These equations are analogous to those of the phase functions method. The obtained equations permit the inverse scattering problem to be solved on the basis of the known data on the total cross-sections.

abstract

Linear relations between the double statistical tensors describing the decay angular distributions of resonances produced in the reactions \(0^-+\frac {1}{2} ^+\to J^P+{ \frac {3}{2}}^+\) are derived using the additive quark model. Some of these relations enable one to test spin-parity assignment of the produced meson resonance \(J^P\). Others may be used to study the contributions of natural and unnatural exchange in the \(t\)-channel. Reaction \(K^+ +p \to K^{*0} (1420) +{\mit \Delta }^{++}\) at 5 GeV/\(c\) is studied and it is found that unnatural parity exchange dominates in this case.

abstract

The nuclear inertial mass parameter \(B\) is investigated by means of two slightly different approaches, both making use of the adiabatic approximation for the collective motion. The numerical results are given for two regions: the superheavy nuclei \(108 \leq Z \geq 124\), \(172 Z \leq N \leq 188\) and the neutron-rich nuclei \(88 \leq Z \leq 104\), \(172 \leq N \leq 194\). The influence of the choice of the Nilsson model parameters \(\varkappa \) and \(\mu \) is investigated together with the dependence on the deformation parameters \(\varepsilon \) and \(\varepsilon _4\).

abstract

Calculations concerning some of the resonances in the excitation curve \(^{45}\)Sc\((p,p)\) in the energy range of incident protons \(E_p= 1.6\)–1.8 MeV are presented. Four resonances are considered as analog ones in the compound nucleus \(^{46}\)Ti.

abstract

The gamma-neutrino directional angular distribution is calculated for the muon capture in \(^{10}\)B and in \(^{15}\)N. The dependence on nuclear structure and induced pseudoscalar coupling is investigated. A detailed analysis of the independent multipole amplitudes which describe the transition in \(^{15}\)N to the first excited level of \(^{15}\)C is also given.

abstract

We applied the method of Lie series for the construction of local solutions of classical nonlinear relativistic wave equations. Next we gave the explicit form of solutions for the classical massive Thirring equation, nonlinear Heisenberg equation and the nonlinear equation in \(\lambda {\mit \Phi }^4\) theory.

abstract

It is shown how to determine statistical tensors from the angular distributions in the decays where one of the decay products decays in turn. All tensor components may be estimated by this method, even the components of tensors \(T^L_M\) with odd \(L\) (e.g. Im \(\varrho _{10}\) for spin 1 particles) which cannot be measured by the usual method of moments. In addition, the decay amplitudes can be found if there are more than one coupling constants, like for spin 2 particles. Examples of decays of particles with the following spins are discussed: \(1^+ \to 0^++(1^-\to 0+0)\), \(2^-\to 0^-+(1^- \to 0 - 0)\), \({ \frac {3}{2}}^-\to 0^-+ ({ \frac {3}{2}}^+ \to \frac {1}{2} +0)\), \(2^- \to 0^-+(2\to 0+0)\) and \(1^+ \to 0^-+(2^+ \to 0+0)\).

abstract

The general properties of models where the absorption of systems coherently produced in nuclei is small, because the absorption parameters are replaced by a non-diagonal absorption matrix are investigated. A new class of such models in which the absorption from large diagonal terms of the absorption matrix is partly cancelled by the off-diagonal terms is discussed. The dependence of the mass distribution of the coherently produced system on nuclear radius in this class of models is different from that predicted by Van Hove model. For certain values of parameters the model discussed here gives the mass distribution and absorption parameter independent of the nuclear radius, in apparent agreement with the data.

abstract

The existing data on multiplicity distribution of charged and neutral pions produced in high-energy interactions are analysed in terms of correlation integrals. The two-component picture of particle production is used to explain the data. The model is shown to describe correctly the two- and three-particle correlations between charged pions as well as the two-particle correlations between charged and neutral pions. The possible detailed versions of the model differing at highest energies are discussed.

abstract

We study the experimental characteristics of the \(\pi ^0\) production in high energy \(\pi ^-p\) and \(pp\) collisions. The observed features of charged multiplicity distribution and neutral pion production are described by a phenomenological model which assumes a Czyżewski–Rybicki formula for the total multiplicity distribution and the hypothesis of isospin independence.

abstract

We present here a new method which allows to connect the Bel–Robinson tensor with the gravitational radiation. The method is based on the Einstein canonical pseudotensor.