The results for the classical single-particle motion in the Woods–Saxon potential with octupole deformation including the spin-orbit interaction are reported. The dependence of the nucleonic dynamics on the potential diffuseness and on the spin-orbit coupling is studied. The model is examined by means of qualitative (Poincaré sections) as well as quantitative (Lyapunov exponents, power spectrum) methods. The transition from order to chaos is observed When the spin-orbit coupling increases. The role of the diffuseness of the potential in suppressing chaos is also shown.

The present paper proposes a basis for new gravitational mechanics. The problem of finding the spectrum of mass-energy is reduced to a new kind of eigenvalue problem which intrinsically contains the fundamental length \(l=\sqrt {Gh/c^3}\).

General approach to the problem of the operator ordering for the flat phase space is given. It is shown how the operator ordering is determined by some natural axioms. The Weyl, symmetric and the Born–Jordan orderings are considered. The general form of the momentum operator in curvilinear coordinates is found.

A semiempirical model of neutrinos and charged leptons of three families is presented, predicting nonconventionally \(m_{\nu _e} \simeq 2m_{\nu _\mu } \simeq m_{\nu _\tau }\) and successfully \(m_{\tau } = 1776.80\) MeV, the latter when experimental values of \(m_e\) and \(m_{\mu }\) are used. The model implies for weak-interaction eigenstates the oscillation \(\nu _{\mu } \to \nu _{\tau }\) 56 times more probable than the oscillation \(\nu _e \to \nu _{\mu }\) (if the latter appears).

The supersymmetric extensions of \(\kappa \)-Poincaré algebra are considered. All extensions of algebraic sector are classified. It is shown that, under some assumptions, no regular coproduct can be introduced.

Isotopic variation of rms charge radii of even isotopes of Zr and Mo has been evaluated using an optimized one body potential and using the experimental occupation probabilities of the proton states near the Fermi surface. We have obtained excellent agreement both in the case of single particle(-hole) energies and rms charge radii of the chain of isotopes of Zr and Mo. Calculated values of equivalent radii and model independent Fourier–Bessel coefficients show good agreement with the experiment.

Within the Standard Model, strong isospin invariance, and the nuclear domain of \(u, d\) quarks, the parity violating asymmetry in polarized electron scattering is predicted and the neutrino scattering cross section is directly related to the electron scattering cross section, for inelastic \((0^+0)_{\rm gnd} \to (0^+0)*\) nuclear excitations (assuming pure quantum numbers for both states). With the inclusion of strange quarks, the asymmetry measures a new nuclear matrix element of the strangeness current, if the inelastic charge form factor for that transition is large enough for the experiment. The ground and first excited states of \(^4\)He have \((J^{\pi }=0^+, T=0)\); thus the analysis is applicable to future CEBAF experiments on parity violation and possible neutrino scattering experiments on this nucleus. Existing low momentum transfer \(q^2\) data on the inelastic charge form factor for the \((0^+0)_{\rm gnd} \to (0^+0)*\) transition in \(^4\)He (which show it growing relative to the elastic one) are fit within simple nuclear models, and predictions are made for higher \(q^2\). The more quantitative analysis for \(^4\)He is significantly complicated by the fact that the excited state lies just above the break-up threshold. It is desirable to first have an experimental measurement of this form factor to higher \(q^2\), using the predicted magnitude as a guide.